What force controls probability?

[Pup]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet. :)

[Dave1001]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet. :)

Great question. At the base level, nothing is "forcing" the coin tosses to even out. Each individual coin toss still has a 50% chance of going either way. And technically, with 1000 coin tosses all could be heads. It's just very improbable. Reminds me of the improbability drive in The Hitchhiker's Guide To The Galaxy :D

Since Einstein said "God does not play dice" to ridicule quantum theory, yet quantum theory is accepted today, I think perhaps quantum mechanics may drive randomness and probability in the universe?

Someone who knows much more about this should weigh in.

Also, has the idea of infinite parallel universe been ruled out? Because if it still has a lot of support, then there's a universe with every possible coin toss in it. And the universes where 1000 tosses results in 500 heads and 500 tails is just one set of an infinite amounts of sets of universes, with every other combination also being infinitely represented in other universes. Right? Or am I missing something here?

[Badly Shaved Monkey]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

[patnray]

There is no force that acts on the coin to prevent it coming up heads a billion times in a row. That result is not prohibited, just extremely unlikely. So unlikely that we would question the "fairness" of such a coin or the toss.

Nothing "makes the predicted results happen". The landings do not "organize themselves". If they did then the Gambler's Fallacy would be true...

A coin toss is sufficiently complex that the result is random and either outcome has a probability of 0.5 every time the coin is tossed. The coin doesn't "know" about the previous tosses.

It is the randomness that causes the observed result. The upward force and induced spin rate varies slightly for each toss. The air currents are slightly different each time, etc. It is conceivable that someone could practice a particular flipping technique and acheive enough consistency to skew the results one way, but that wouldn't be a random event...

Another way to see it is that we know it is a random process precicely because the measured outcome, over a large number of trials, is 50/50. Any other result would be a strong indication that something non-random is happening... Then, and only then, does it make sense to seek a force acting on the coin (or other cause).

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

[Badly Shaved Monkey]

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

That's because we Europeans are living 8 hours in your future and I'm not at work now. ;)

But I should be in bed. Nighty night.

[Dave1001]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

I think you may be taking the coin toss aspect of it too literally. My understanding is that "coin toss" was just as stand-in for probability in general. Technically, a coin toss is not random if watches what is probably only a relatively few factors, such as the starting face, the force/direction/torque applied by the hand, and at what point in the arc the coin was caught and in what manner. A good scientist could probably study a coin tosser, and based on initial conditions predict how a given coin toss would go, or how a series of coin tosses would go for them.

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics. What did Einstein mean when he said that God did not play dice in reference to quantum physics? And what does it mean that the scientific community today believes that he was wrong about that? Does that mean that randomness, random chance exist in the universe?

[Dave1001]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

I think you may be taking the coin toss aspect of it too literally. My understanding is that "coin toss" was just as stand-in for probability in general.

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics. What did Einstein mean when he said that God did not play dice in reference to quantum physics? And what does it mean that the scientific community today believes that he was wrong about that? Does that mean that randomness, random chance exist in the universe?

[Badly Shaved Monkey]

Well, the glib answer is that there are 2 or 3 choices: hidden variables, nothing and God.

[Dave1001]

Well, the glib answer is that there are 2 or 3 choices: hidden variables, nothing and God.

My understanding is that where Einstein and the proponents of quantum theory disagreed is that Einstein didn't believe that true randomness existed in the universe (I guess that means he believed there were hidden variables?) and quantum theorists wrote it into quantum theory. That the quantum theorists won out means that today most scientists in the field believe that true randomness DOES exist in the universe?

Please, we are in need of people who know this area of science better, lol.

[Jekyll]

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics.[?]
Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

In the majority of simple examples, be it tossing a coin, rolling a dice, drawing balls from an urn, or the movement of particles in an ideal gas, it is possible to think of the probabilities as expressing the symmetry of a system. Swapping of the labels heads and tails on a coin, or one and six on a dice, shouldn't change our expectation of the outcome if the dice and coin are fair.

This tells us a hell of lot and is enough to guarantee the behaviour of these systems without introducing the need for magic randomness fairies or god playing dice. You can then push this idea and extended it by gently deformation of the probabilities so that it copes with asymmetries in a uniquely consistent way. By the time you've done this, you have a very accurate application of probability theory to the physical world with out needing to claim that randomness exists.
So probability might well just be a mental construct, but it is one that can describe the world extremely well.

However, all bets are off with quantum thingies and there might really be magic randomness fairies at the bottom of it. ;)

[Dave1001]

Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

In the majority of simple examples, be it tossing a coin, rolling a dice, drawing balls from an urn, or the movement of particles in an ideal gas, it is possible to think of the probabilities as expressing the symmetry of a system. Swapping of the labels heads and tails on a coin, or one and six on a dice, shouldn't change our expectation of the outcome if the dice and coin are fair.

This tells us a hell of lot and is enough to guarantee the behaviour of these systems without introducing the need for magic randomness fairies or god playing dice. You can then push this idea and extended it by gently deformation of the probabilities so that it copes with asymmetries in a uniquely consistent way. By the time you've done this, you have a very accurate application of probability theory to the physical world with out needing to claim that randomness exists.
So probability might well just be a mental construct, but it is one that can describe the world extremely well.


Right, I don't think anyone denies that probability is useful for modeling phenomenon in the universe. And our general instincts for probability are probably hardwired into our brains, a product of natural selection that sort-of self-validates (how do we know that probability is a real useful model? Because we follow elements of it instinctually, and we live to reproduce).

I think the question here for me is whether there are hidden variables that determine where an individual coin toss or dice roll falls on the spread, and I think the answer is yes, barring an actual randomness generator element being at play in these phenomenon, be it from quantum physics or something else.

[The Atheist]

Very Nietzsche, or very Monty Python, I thought the OP was very neat - the answers are keeping me laughing, well done, mate!

Anyone for a nice cup of really hot tea?

[Jekyll]

Right, I don't think anyone denies that probability is useful for modeling phenomenon in the universe. And our general instincts for probability are probably hardwired into our brains, a product of natural selection that sort-of self-validates (how do we know that probability is a real useful model? Because we follow elements of it instinctually, and we live to reproduce).

I think the question here for me is whether there are hidden variables that determine where an individual coin toss or dice roll falls on the spread, and I think the answer is yes, barring an actual randomness generator element being at play in these phenomenon, be it from quantum physics or something else.
I'd go with that. One of the nice ways about approaching it through symmetry is that; it doesn't matter whether these phenomena are truly random or not. Which is a huge relief as if there really is a random variable in there somewhere, we would have no way of showing that it isn't deterministic with a hidden parameter.

[Dunstan]

Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

I find it easiest to think of probability (at least at the macro, non-QM level) as being an expression of uncertainty based on limited information.

Suppose I have a normal, complete, well-shuffled deck of cards and three people, Alice, Bob, and Carl. I deal the first five cards face down to Bob. I then ask all three of them "what's the probability that the next card is a spade?"

The "truth" is that the next card either is a spade or it isn't. But Alice and Bob don't know which, so all they can give is a probability number.

Alice knows only that the top card could be any of the 52 cards in a deck, 13 of which are spades, so she says "one in four."

Bob picks up the five cards I dealt him, sees that none of them are spades, and says "13 in 47."

Carl knows that the deck is marked (and how) and therefore can see that the next card is the four of clubs, so he answers "zero."

All three give different answers to the same question about the same card, because each of them possesses different information.

Oh, and re coin tosses: I'm too lazy to Google it at the moment, but I seem to recall seeing a recent study that found that a coin toss is .000001% (or something like that) more likely to be a head than a tail (or vice versa; and I'm sure it depends on which coin they were studying).

[Dave1001]

I find it easiest to think of probability (at least at the macro, non-QM level) as being an expression of uncertainty based on limited information.

Suppose I have a normal, complete, well-shuffled deck of cards and three people, Alice, Bob, and Carl. I deal the first five cards face down to Bob. I then ask all three of them "what's the probability that the next card is a spade?"

The "truth" is that the next card either is a spade or it isn't. But Alice and Bob don't know which, so all they can give is a probability number.

Alice knows only that the top card could be any of the 52 cards in a deck, 13 of which are spades, so she says "one in four."

Bob picks up the five cards I dealt him, sees that none of them are spades, and says "13 in 47."

Carl knows that the deck is marked (and how) and therefore can see that the next card is the four of clubs, so he answers "zero."

All three give different answers to the same question about the same card, because each of them possesses different information.

Oh, and re coin tosses: I'm too lazy to Google it at the moment, but I seem to recall seeing a recent study that found that a coin toss is .000001% (or something like that) more likely to be a head than a tail (or vice versa; and I'm sure it depends on which coin they were studying).

Illuminating. So for these type probability questions, if you know all the "hidden information", the answer is always "zero" or "100%". But true random chance, as I think is posited by quantum theory, would be different.

What's also interesting is how probability can drive rational decision making. I wonder what the first battle in recorded history is where mathematical principles of probability were consciously applied to strategy.

"It's very improbable that this big gift horse has greek warriors inside it"

[Dunstan]

What's also interesting is how probability can drive rational decision making. I wonder what the first battle in recorded history is where mathematical principles of probability were consciously applied to strategy.

Probably depends on what you mean by "consciously." I think military leaders have probably always believed that the outcome of large battles is uncertain, and I'm sure they've always thought in terms of "if we occupy the high ground, we have a better chance of winning."

Cost-benefit analysis probably came pretty early, too. "A raid on their supply wagons is unlikely to succeed, but if it does, we will cripple their army, and if doesn't we only lose a small raiding party."

If you mean specifically using numbers and explicitly doing expected value or expected utility calculations, I suspect that's only happened very recently, as in 20th century.

However, all I know of military strategy is what I learned from playing Axis & Allies and Civilization, so have your salt shaker handy when you read this.

[CriticalThanking]

Also note that the same thing that "prevents it" from landing 1000 heads also "prevents it "from landing the exact sequence HTTTHTHTHHHTT...... etc. Each specific sequence is equally (un)likely assuming no biases. As other threads in the past have discussed, the all X sequence appears special to us while we ignore the amazing odds against getting the exact sequence we obtained.

CT

[fuelair]

Since Einstein said "God does not play dice" to ridicule quantum theory, yet quantum theory is accepted today, I think perhaps quantum mechanics may drive randomness and probability in the universe?

Or am I missing something here?

Actually he/she pitches pennies. (Like pinching pennies but not really.)

[Dave1001]

If you mean specifically using numbers and explicitly doing expected value or expected utility calculations, I suspect that's only happened very recently, as in 20th century.


Yeah, that's what I mean. Given that probability is not very difficult math in easiest easiest practical formulations, I'd be surprised if it wasn't applied to military strategy until the 20th century. I wonder when it was first historically recorded being applied to games such as cards and dice.

[Unnamed]

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

...

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?
I think your problem is that you are interpreting probability backwards: a probability is an observation, not something with an independent existence that exerts a "force".

At least that's the frequentist (http://plato.stanford.edu/entries/probability-interpret/#FreInt) interpretation, which I personally like. Check the link for the other interpretations.

In other words, first you flip the coin many times (either in reality or as a thought experiment), then you see that it lands heads up about 50% of the time, and only then you conclude that the probability was 50%.

Other people in the thread have discussed what makes the probability 50% (rather than 75%, or 100% heads), but I wanted to clarify this first.

[Unnamed]

Yeah, that's what I mean. Given that probability is not very difficult math in easiest easiest practical formulations, I'd be surprised if it wasn't applied to military strategy until the 20th century. I wonder when it was first historically recorded being applied to games such as cards and dice.
Wikipedia attributes the formalization of probability theory to Pascal (http://en.wikipedia.org/wiki/Blaise_Pascal#Contributions_to_mathematics) in 1654, in the context of gambling. I'd like to hear about earlier applications.

[anor277]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

...............

I might be arguing in circles here, but is entropy, the statistical probability for disorder, and which may be precisely measured and quantified, the underlying factor?

[Badly Shaved Monkey]

Very Nietzsche, or very Monty Python, I thought the OP was very neat - the answers are keeping me laughing, well done, mate!

Anyone for a nice cup of really hot tea?

and a piece of fairy cake?

[Mosquito]

Isn't it actually so that if you flip a coin many times and count the number of heads and tails, the absolute difference will tend to grow, while the relative difference will tend to 50-50?

I think I did some experimenting with this as a kid, and found that one of these would seem to grow a little faster than the other, though not so much as to mess up the probability. So while the absolute difference kept growing, it constituted a smaller and smaller part of the whole.

Like this:

10 flips: 6H, 4T, diff 2 (20%)
100 flips 56H, 44T, diff 12 (12%)
1000 flips 524H, 476T, diff 48 (4.8%)
etc.

The diff grows, the relative difference tends towards 50-50.


Mosquito - Heads I win, Tails you loose

[Jekyll]

I find it easiest to think of probability (at least at the macro, non-QM level) as being an expression of uncertainty based on limited information.
So do I normally, but I'm far to lazy to explain over the internet how you can actually use that to derive an acurate discription of what's going on in a model when that uncertanty is hard coded. It all comes down to symmetry anyway. :D
I'm not a physist but I imagine you can deal with quantum physics in exactly the same way, the only difference being that it might, in principle, not be possible to extract the relevent information a priori.
Oh, and re coin tosses: I'm too lazy to Google it at the moment, but I seem to recall seeing a recent study that found that a coin toss is .000001% (or something like that) more likely to be a head than a tail (or vice versa; and I'm sure it depends on which coin they were studying).

Yes, there is a 30 page masters theses on how, if you take a coin lying heads up and gently toss it so that it just turns through at least a full rotation and doesn’t bounce it is more likely to land heads up.

On the other hand there is a three page paper by ET Jaynes describing a lazy afternoon spent with a pickle lid (an idealised unfair coin) and flipping it normally like a coin didn't seem to introduce any bias, although spining it on a table and throwing it like a frisby did.

[Beady]

Uhm, excuse me?

But has anyone, anywhere, at any time, ever established that there is, in fact, a force of any sort that influences a coin toss? Or any other random event? Seems an awful lot like what the homeopaths come up with, such as water "remembering."

[Cuddles]

Yeah, that's what I mean. Given that probability is not very difficult math in easiest easiest practical formulations, I'd be surprised if it wasn't applied to military strategy until the 20th century. I wonder when it was first historically recorded being applied to games such as cards and dice.

The maths behind probability may not be that complex, but it is probably the most misunderstood phenomenon ever. People constantly misinterpret, or plain refuse to believe, what the maths tells them. The game show where you pick a door and then the host removes one and asks if you want to change your choice is an obvious example (sorry, can't remember the name). No matter how much the answer is explained, many people simply cannot grasp that the "obvious" answer is wrong, evern though the simple maths shows this. The same is true for many, if not most, probablistic things.

Going back to the military question, how many last stands and suicidal attacks have there been, succesful and failiures? I would say probability has always been applied to strategy and then ignored.

[Stir]

I've pinpointed what bothers me in this thread, an obvious error in the OP:

I understand the concept of probability

Clearly false!!

One of the fundamental understandings of probability is that the prior coin flips in no way influence future flips ... and this can even be tested:

If there was such an influence or force, then I could conceal the results of the first thousand flips, and the woo being tested would be able to determine whether those hidden flips were skewed toward heads (or not) by studying the sequence of future flips. But (given a fair coin) all future sequences of heads and tails are equally likely.

OK? OK!

[Hellbound]

This seems to have been touched on before, but allow me to give it a try.

I'll use a coin toss as an example, but it would work with any random event (I believe).

A coin toss has two possible outcomes, heads or tails. This means we can have two outcomes: H or T.

Now, let's do two flips. We can have the results HH, HT, TH, or TT. Note that 50% of these cases produce a 50/50 split.

Let's go to four flips. Our results can be:
HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT. Out of the 16 possibilities:
2 are all one side (all H or all T).
4 have three heads and a tail
4 have three tails and a head.
6 are 50/50.

So, there's more possibilities that come out to 50/50 than any other result. Even the non-50/50 results, if "averaged" would cancel each other out to 50/50.

However, this doesn't answer your question, it just explains the aggreagate/collective behavior of multiple events. The same analysis can be used to show that 7 is the most likely result of throwing two dice and adding the results (or 10/11 for three, or 14 for 4, etc). Just amount any aggregate of a random event can be evaluated this way (here comes the catch) assuming each possibility is equally likely.

ANd that's the key. THe aggregate behavior of multiple coin tosses approaches 50/50 because the chances for a single toss are 50/50. So, to the question about forces that affect probability, the answer is "whatever forces apply to a single instance of the event in question."

[Dave1001]

The maths behind probability may not be that complex, but it is probably the most misunderstood phenomenon ever. People constantly misinterpret, or plain refuse to believe, what the maths tells them. The game show where you pick a door and then the host removes one and asks if you want to change your choice is an obvious example (sorry, can't remember the name). No matter how much the answer is explained, many people simply cannot grasp that the "obvious" answer is wrong, evern though the simple maths shows this. The same is true for many, if not most, probablistic things.

Going back to the military question, how many last stands and suicidal attacks have there been, succesful and failiures? I would say probability has always been applied to strategy and then ignored.

That's not what I'm asking. I'm asking for the first time in recorded history where military strategists (or game enthusiasts) are recorded in the historical record as consciously appling basic mathematical principles of probability in the strategy-making process.

I'm aware that most humans are wired to situationally make irrational decisions based on probability. The game show Deal or No Deal is studied by economists because of that. I think there was an article in Slate about it: people will generally irrationally choose to avoid a low probability of great harm even when it means missing a chance for moderate benefit, when a rational analysis of the cost/benefit and probabilities would clearly indicate that they should take the risk.

[Jorghnassen]

I think there was an article in Slate about it: people will generally irrationally choose to avoid a low probability of great harm even when it means missing a chance for moderate benefit, when a rational analysis of the cost/benefit and probabilities would clearly indicate that they should take the risk.

What's irrational about giving more weight to potential harm than potential benefit? Suppose I offer you to play a game where there's a 5% chance you'll lose both eyes and 95% chance you'll win 5 bucks without any bodily harm, would you play? Or would you rather play a game were there's 50% chance you'll owe me a quarter or 50% chance you win $2. Objectively, you're more likely to win and have a bigger payoff in the first game, but the second game is much less dangerous in the case of a lost (though you are more likely to lose at the second game). So what is the rational choice?

[Thomas]

What's irrational about giving more weight to potential harm than potential benefit? Suppose I offer you to play a game where there's a 5% chance you'll lose both eyes and 95% chance you'll win 5 bucks without any bodily harm, would you play? Or would you rather play a game were there's 50% chance you'll owe me a quarter or 50% chance you win $2. Objectively, you're more likely to win and have a bigger payoff in the first game, but the second game is much less dangerous in the case of a lost (though you are more likely to lose at the second game). So what is the rational choice?
I don't think anyone would put their eyes at risk for 5 bucks. But you'll probably (pun intended) get some takers on your second game.
The rational choice would be not to put your eyes at stake for five bucks and rip you off in the second game instead (provided one gets more than one try, you didn't mention that).

[Dunstan]

What's irrational about giving more weight to potential harm than potential benefit? Suppose I offer you to play a game where there's a 5% chance you'll lose both eyes and 95% chance you'll win 5 bucks without any bodily harm, would you play? Or would you rather play a game were there's 50% chance you'll owe me a quarter or 50% chance you win $2. Objectively, you're more likely to win and have a bigger payoff in the first game, but the second game is much less dangerous in the case of a lost (though you are more likely to lose at the second game). So what is the rational choice?

There's nothing irrational about what you're describing. You're comparing apples (losing both eyes) and oranges (money). In standard rational choice models, you'd need to place a dollar value on the loss of both eyes (or convert both "loss of both eyes" and "gain of X dollars" into "utility units"). No person in his right mind would play the first game, since the loss of both eyes presumably vastly outweighs the benefit of winning five dollars.

Nor is it necessarily irrational for someone to decline a game that, like your second game, has a positive expected value. (Assuming that is an option -- I'm changing your hypothetical.) People do not act to maximize their expected wealth, they act to maximize their expected utility. Economists have long understood that the diminishing marginal utility of money makes people risk-averse.

Translating that into plain English: each dollar you gain brings you less benefit than the one before. $100 would mean more to you if you were poor than if you were rich. Most of us would play your second game because gaining $2 means more to us than losing $0.25 does. But if you change the numbers to $200,000 and $25,000, some people might decline, since the harm of losing $25,000 (which for some people would mean losing their house or car or having to drop out of college, etc.) could outweigh the benefit of gaining $200,000. Change the dollar amounts to Win = 4 x your entire net worth, and Lose = your entire net worth, and I suspect most of us would pass.

(Of course, what you'd really want to do in these examples is get some backers to share in your risk.)

It's risk-aversion that explains the existence of insurance: people are willing to pay $y to be insured against an expected loss of $x, even if y>x.

[Thomas]

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet. :)
Well, you sort of have to go there to answer the question, though. Because..
So, to the question about forces that affect probability, the answer is "whatever forces apply to a single instance of the event in question."
Only thing left to discuss now, is what exact forces acts upon a given phenomenon considered random (from flipping a coin to the Heisenberg indeterminacy principle).

[CaptainManacles]

What drives it toward 50% over time? Our conception of things like "50%". The odds of getting HHTT and HHHHH on 4 flips are still the same, nothing is driving a change in probability, but we happen to view (in most cases correctly) HHTT and TTHH as being relatively the same outcome. So in the long run, there's a larger percentage of outcomes that we would classify as "50%", or for other distributions, tendency towards average outcomes. This is called the central limit theorem, and is what drives enthropy.

[LW]

That's not what I'm asking. I'm asking for the first time in recorded history where military strategists (or game enthusiasts) are recorded in the historical record as consciously appling basic mathematical principles of probability in the strategy-making process.

The oldest military manual that I've seen that contains explicit references to probability theory is from 1919, but that book (Ampumaoppi by General Paul von Gerich) is based on older sources (I think that it is an adapted translation from a Russian original but that is not mentioned anywhere in the book). I would guess that that particular application was already in use by late 19th century the latest. The subject of probability analysis in the book was rifle fire: namely, what is the distribution pattern of fired rounds. The book contains formulas that allow a company commander to estimate how effective his rifle fire will be against opponent at different ranges. [And many of the example situations would have been more suited to the mid-19th century battles than post-WWI battlefield: things like lines of men facing each other on open ground.]

Though, that use of the theory is more tactical. The main problem of applying probability theory to the strategy is that it is practically impossible to assign probabilities that are accurate enough to most of the events.

[Asolepius]

I have only skimmed this thread because you are all much too clever for me :) I think it was Hawking who said that quantum theory is actually quite deterministic, and if we could measure what was happening with all the particles at the quantum level, we could predict anything at the macro level. But of course there are too many particles, so what we see appears to be randomness. For practical purposes, we can treat this pseudo-randomness as the real thing.

The question also reminds me of my own field of clinical trials. We assign patients to treatments randomly to minimise the effects of undetected factors. Human bodies are very complex, and we don't know what else is going to change with treatment, so we try to damp out those effects by randomising them. It seems a bit like not knowing what those quanta are doing. Actually the randomisation lists we use are computer generated so they are deterministic and not really random. But again the process that produces the lists is complex and the result is close enough to random to make no practical difference.

Just random thoughts.........

[Jorghnassen]

Thomas, Dunstan: my toy example was just illustrate the idea of "low probability of great harm vs chance of moderate benefit" and how the words irrational and rational shouldn't be used to describe a decision based on these probabilities. But I'll admit that Dunstan's modified version of my game 2 is a nicer example.

CaptainManacles: You seem to be thinking of the laws of large numbers (and misstating/misinterpreting it, which is common).

[Dave1001]

Edit

[Ginarley]

My view on this is as follows:

Probability is a general descriptive model of observed behaviour.

A model is a simplification of reality.

Simplification is achieved through assumptions.

The assumptions are based on an approximation of what we expect based on theoretical gymnastics and observations.

Therefore the only link between probability and the real world is that probability is defined around real world observations. This is no different to any other theory (such as quantum physics or whatever) because we have no idea what is at the absolute root of cause and effect. Therefore all we can do with modelling is match observations and assume it is practically useful even if it is not based at the true roots of cause and effect. In this sense every model faces the same problem, not just probablility.

Cheers

[Dave1001]

Thomas, Dunstan: my toy example was just illustrate the idea of "low probability of great harm vs chance of moderate benefit" and how the words irrational and rational shouldn't be used to describe a decision based on these probabilities. But I'll admit that Dunstan's modified version of my game 2 is a nicer example.

CaptainManacles: You seem to be thinking of the laws of large numbers (and misstating/misinterpreting it, which is common).

I think "irrational" and "rational" could still be used within this context, and in fact, we implicitly make these type decisions all the time. That's why it's interesting to me that we're not adaptively optimized to make these decisions rationally.

I probably don't have a perfect idea of the math, but I do think with the right respective risk percentages, it's irrational not to risk losing both eyes for a gain of $5. Would one submit to a one in a googleplex risk of losing one's eyes for a 50% chance at winning $5? I certainly would, and I'd play that game over and over again for the rest of my life. Even if the marginal utility of extra $5 bills was low for me, but significantly greater than zero. I think it would be irrational not to.

We already play these games all the time. Do you leave your house to go to work or do errands? By leaving your house, your risk of losing both of your eyes probably increases slightly. But the moderate rewards you get for doing whatever day of work or errands makes it more than worth it for you.

But I believe I've read that when risks for great loss are somewhat greater than microscopic (and salient to the assessor, such as death in a plane crash is for many folks) our species shows a marked tendency for irrational decision making.

[Jorghnassen]

Buying the lottery is an irrational decision, especially if you keep doing it.

But, rationally, the best way to survive is to avoid great harm, so it is very reasonable to want to eliminate that risk as much as possible (it cannot of course, be completely eliminated), so picking lower gains while reducing a potential but non negligeable probability of great harm, is in fact, quite rational, if you value survival or your current state of comfort above moderate benefits. Now if you don't run errands and don't work, you will eventually die of starvation.

PS: I guess I won't be making money off organ trafficking. Damn...

[Dave1001]

Buying the lottery is an irrational decision, especially if you keep doing it.


yes. That's taking advantage of the greed element of irrational risk calculation. Hence a lot of people consider the lottery to be a regressive tax on folks who irrationally calculate risk/reward percentages. Of course, it wouldn't be irrational with the right prize size, odds of winning, and price of ticket. I think there are folks who consciously search out lotteries worldwide where those ratios actually work out to the ticket purchaser's benefit.


But, rationally, the best way to survive is to avoid great harm, so it is very reasonable to want to eliminate that risk as much as possible (it cannot of course, be completely eliminated), so picking lower gains while reducing a potential but non negligeable probability of great harm, is in fact, quite rational, if you value survival or your current state of comfort above moderate benefits.

Now if you don't run errands and don't work, you will eventually die of starvation.

PS: I guess I won't be making money off organ trafficking. Damn...

I think the element you're not considering here are the actual relative risk percentages. For example the risk of dying in a plane crash on a commercial airliner is extraordinarily low, but very salient for some people. And so they'll irrationally forsake the moderate gains that they'd have a good chance of picking up as a result of such an airplane flight because of the very low probably chance of a great loss in the form of dying in an airplane crash. They would still probably get on the plane at some point (perhaps if there was a 95% chance of receiving $2 million dollars at the end of the plane flight), but their risk calculation becomes irrationally distorted because of the saliency of the great harm (despite it's very low probability of occuring).

[andyandy]

Buying the lottery is an irrational decision, especially if you keep doing it.




what price hope?

[drkitten]

Buying the lottery is an irrational decision, especially if you keep doing it.

Only under very specialized and unrealistic assumptions. (One of the big problem with game theory is that no one remembers the simplifying assumptions that Johnny VN had to make to get it off the ground.)


JVN assumed that the game player was "risk-neutral"; that the mere act of playing a game did not give him any pleasure or discomfort. Look at how many people go to considerable time and expense merely to get to a casino to play games, and you'll see how unrealistic that assumption is/was.

He also assumed that the "value" placed on the prize by the player was directly proportional to the monetary sum involved. Again, this is ridiculous; people value dollars differently depending upon how many they have. That's why I no longer eat pot noodles; the "value" to me of eating food that doesn't taste like salty styrofoam is now worth more than the financial cost of real food -- quite a difference from my "bright college days."

If the value of a dollar to you is sufficiently small, and the value of possibly winning several million is sufficiently large, buying a lottery ticket is extremely rational.

[Dave1001]

Only under very specialized and unrealistic assumptions. (One of the big problem with game theory is that no one remembers the simplifying assumptions that Johnny VN had to make to get it off the ground.)


JVN assumed that the game player was "risk-neutral"; that the mere act of playing a game did not give him any pleasure or discomfort. Look at how many people go to considerable time and expense merely to get to a casino to play games, and you'll see how unrealistic that assumption is/was.

He also assumed that the "value" placed on the prize by the player was directly proportional to the monetary sum involved. Again, this is ridiculous; people value dollars differently depending upon how many they have. That's why I no longer eat pot noodles; the "value" to me of eating food that doesn't taste like salty styrofoam is now worth more than the financial cost of real food -- quite a difference from my "bright college days."

If the value of a dollar to you is sufficiently small, and the value of possibly winning several million is sufficiently large, buying a lottery ticket is extremely rational.

Sure, this is important in theory. And not hard to test empirically (which I'm sure has been done in great depth). However, in practice, the question is whether most lottery players have a good sense of what their actual odds to winning per dollar invested is. Do they accurately assess the odds add on an "entertainment factor" and then choose to buy the lottery ticket? Or do they have an inflated sense of their chances of winning? If they have an inflated sense of their chance of winning (due to the saliency of the 100 millions dollars or whatever), then I would posit that their decision making-process is irrational, in a way similar to a person who refuses to fly on a plane because of an inflated sense of the chance of death.

[drkitten]

However, in practice, the question is whether most lottery players have a good sense of what their actual odds to winning per dollar invested is.

No, that's an entirely irrelevant question.

They gain more pleasure from the thought that they might win a million dollars than they lose from not having a relatively nominal sum available for other spending.

Ergo, it's rational.

[Filip Sandor]

The idea of behind a "force" causing the 50/50 heads or tails landings is a misconception of a what is really just a mathematical model of the coin toss. In reality the coin simply does what it does - except that it can only land one of two ways - heads or tails... which gives you the "50/50" model used to help interpret the outcome, roughly, before you make a toss; it does not force the outcome however.

Take for example a game of roulette at the casino: you have roughly a 50/50 "chance" that the ball will land on either RED or BLACK (excluding the GREEN zeros). Let's assume your friend joined one of the tables before you came in the casino and has had a chance to already see 3 of the results and lets say all three were BLACK... in his mind, according to the 50/50 "chance model," the next hit is more likely be a RED than a BLACK, but for you, who has just joined the table now the chances are 50/50 even. Does this change the past 3 hits on the board? No, of course not. Does it affect the next hit? The answer is of course, no. Probability is a mathematical concept so it does not 'affect' reality. Quantum mechanical probability is based on certain physical calculations which are made prior to an outcome which is not the same thing because on the roulette wheel and the coin toss there are no real useful calculations made before the toss and therefore: no real accurate prediction can be made on what will come 'out' since you don't know what is going 'in'. Hope that helps.

[Kaarjuus]

I have only skimmed this thread because you are all much too clever for me :) I think it was Hawking who said that quantum theory is actually quite deterministic, and if we could measure what was happening with all the particles at the quantum level, we could predict anything at the macro level. But of course there are too many particles, so what we see appears to be randomness. For practical purposes, we can treat this pseudo-randomness as the real thing.

I doubt that Hawking said this, because it's patently untrue. The Heisenberg principle (http://en.wikipedia.org/wiki/Heisenberg_principle) of quantum mechanics states that one cannot measure values (with arbitrary precision) of certain conjugate quantities, which are pairs of observables of a single elementary particle. One cannot with certainty find out both the position and the momentum of a particle.

[dogjones]

OK, so the outcome of one toss doesn't affect the next one, so therefore it is a 50/50 chance of either outcome at every toss, regardless of the next one. Fine.

In that case, how do you calculate odds of outcomes within a "set" of tosses? Suppose you take a coin with the intent of tossing it 10 times. Before you start the tossing, you calculate the odds of at least 1 toss of this set of 10 turning up heads. What would be the correct calculation?

After that, you begin tossing (oooo! hark at the double entendre!). The first toss comes up tails. The odds for "one of the tosses in this set of 10 coming up heads" now must change, because one of the outcomes is now known - yes? How?

You do this until the last toss. They have all been tails. I am assuming the odds for "one of the tosses in this set coming up heads" are now at 50/50?

Or were they always at 50/50, from the first toss?

[drkitten]

In that case, how do you calculate odds of outcomes within a "set" of tosses?

Er, you take a course in probability or discrete mathematics? Calculations like this can get tiresome rather quickly, and the calculations can be somewhat lengthy.

The basic principle is that if the probability of x is p_x, and the probability of y is p_y, then the probability of both x and y is p_x times p_y if the two events are independent. Similarly, if the probability of x is p_x, then the probability of not-x is 1 minus p_x.

Then you just work it out by cases.



Suppose you take a coin with the intent of tossing it 10 times. Before you start the tossing, you calculate the odds of at least 1 toss of this set of 10 turning up heads. What would be the correct calculation?

Well, the probability of any given coin coming up tails is 1/2. So the probability of two independent tosses coming up tails is 1/2 times 1/2, or 1/4. The probability of *three* independent tosses coming up tails is 1/2 times 1/2 times 1/2, or 1/8. Similarly, the probability of all ten tosses coming up tails is 1/2 times itself ten times, or 1/1024.

If not all tosses came up tails, then at least one must have come up heads. So the probability of at least one heads is 1- (1/1024) or 1023/1024.


After that, you begin tossing (oooo! hark at the double entendre!). The first toss comes up tails. The odds for "one of the tosses in this set of 10 coming up heads" now must change, because one of the outcomes is now known - yes? How?

After the first coin toss has been performed, the odds are no longer 50/50 -- "odds" really only describes events that haven't already happened. Otherwise, I'll give you 2:1 on the Pittsburgh Steelers winning the 2006 Superbowl. Any takers?

[Kaarjuus]

In that case, how do you calculate odds of outcomes within a "set" of tosses? Suppose you take a coin with the intent of tossing it 10 times. Before you start the tossing, you calculate the odds of at least 1 toss of this set of 10 turning up heads. What would be the correct calculation?


You add all the probabilities of all possible outcomes where at least one toss is heads together. The probability of the first toss being heads and all the rest tails, then the probability of the first toss being tails, the second toss being heads and the rest tails, and then... and so on until all the possibilities have been exhausted.


After that, you begin tossing (oooo! hark at the double entendre!). The first toss comes up tails. The odds for "one of the tosses in this set of 10 coming up heads" now must change, because one of the outcomes is now known - yes? How?


There are now not ten, but nine tosses. The sum of probabilities changes, as there are less numbers.


You do this until the last toss. They have all been tails. I am assuming the odds for "one of the tosses in this set coming up heads" are now at 50/50?


Yes, now the odds of getting heads are 50:50, which they have been for every single coin toss til this one.

[Dave1001]

No, that's an entirely irrelevant question.

They gain more pleasure from the thought that they might win a million dollars than they lose from not having a relatively nominal sum available for other spending.

Ergo, it's rational.

I think your own qualifiers make it a relevant question. For example "the thought that they might win" and "relatively nominal sum": that implies the assumption that they are accurately making just the type of calculations I was talking about. If they aren't, by implication of your own post, they're not making a rational choice.

I can understand a theory that the cost of the tickets are based solely on the marginal utility of that amount of money for most people. But if the odds of winning (beside their being greater than zero) didn't matter at all to the rationality of the choice than lottery companies should make the odds 1 in a googleplex. Of course the odds do matter. But are the typical ticket buyers assessing them rationally? In other words, most lottery ticket buyers may rationally be able to say that 1 in a googleplex odds for 1 million dollars in exchange for a $1 ticket is not rational enough odds for them to get pleasure in buying a ticket. But are they rationally analyzing odds that aren't so obviously extreme?



My previous post, for ease of reader comparison:


However, in practice, the question is whether most lottery players have a good sense of what their actual odds to winning per dollar invested is. Do they accurately assess the odds add on an "entertainment factor" and then choose to buy the lottery ticket? Or do they have an inflated sense of their chances of winning? If they have an inflated sense of their chance of winning (due to the saliency of the 100 millions dollars or whatever), then I would posit that their decision making-process is irrational, in a way similar to a person who refuses to fly on a plane because of an inflated sense of the chance of death.

[Molinaro]

Buying the lottery is an irrational decision, especially if you keep doing it.


In Canada, all lotteries are non-profit operations. The money either goes to charity, or to government coffers.

Therefore, buying a ticket is always a rational decision, because I'm 100% ok with where that money goes.

What I see you doing to defend your comment, quoted above, is that you are offering irrational reasons why someone might buy a ticket -- and then calling it irrational in general.

That doesn't come across as the least bit convincing.

[Meffy]

The force that controls probability is magnetism. Specifically, little electromagnets under the roulette wheel.

Y'know, I've got to find a less dishonest casino. =@.o=

[Dave1001]

In Canada, all lotteries are non-profit operations. The money either goes to charity, or to government coffers.

Therefore, buying a ticket is always a rational decision, because I'm 100% ok with where that money goes.

What I see you doing to defend your comment, quoted above, is that you are offering irrational reasons why someone might buy a ticket -- and then calling it irrational in general.

That doesn't come across as the least bit convincing.

I think he was mostly limited just by human language and efficiency, counting on us to see his points without endless wordy footnotes. I suspect loopholes of the type you described were already completely forseeable to him when he made his post, as they probably were to most of us. His general point, that buying lottery tickets is an irrational way to achieve $1 million net worth holds up. If one buy a lottery ticket for a million dollar lottery, one is usually buying something worth quite a bit less than the possibility of getting one million dollars in that time frame.

A good question is what is the most a probability expert who designed or runs the lottery would pay for the ticket . I assume that is likely to be the highest rational price. How would one value the odds of winning $1 million dollars? Is $1 the fair price for 1 in a million odds? Is $0.50 the fair price for 1:2million odds? Let's ignore the marginal utility of money, taxes, and the time value of money to start with. Is it that simple or are there more complicated factors that I'm missing?

[Filip Sandor]

OK, so the outcome of one toss doesn't affect the next one, so therefore it is a 50/50 chance of either outcome at every toss, regardless of the next one. Fine.

In that case, how do you calculate odds of outcomes within a "set" of tosses?

However you calculate it, it will only be a math model of what might happen and not what WILL happen. That's the whole point of probability theories - they depict possibilities not certainties. Trust me, I tried my luck at the casino with this probability crap when I was a bit younger and it doesn't work - the cards don't listen to the numbers in my head.

[Kaarjuus]

Therefore, buying a ticket is always a rational decision, because I'm 100% ok with where that money goes.


So, essentially, you buy lottery tickets to support charities or government coffers. Which is, of course, a good cause.

But why not give the money to the charities directly? So that there's no possibility of you winning the lottery and therefore depriving the charities of the money you and everyone else gave them by buying tickets? If the point is to give money to the charities, why risk them losing the money?

[69dodge]

Take for example a game of roulette at the casino: you have roughly a 50/50 "chance" that the ball will land on either RED or BLACK (excluding the GREEN zeros). Let's assume your friend joined one of the tables before you came in the casino and has had a chance to already see 3 of the results and lets say all three were BLACK... in his mind, according to the 50/50 "chance model," the next hit is more likely be a RED than a BLACK,Why would he think that?

If I were him, I wouldn't think that.

[69dodge]

No, that's an entirely irrelevant question.

They gain more pleasure from the thought that they might win a million dollars than they lose from not having a relatively nominal sum available for other spending.

Ergo, it's rational.I don't think I understand you.

It seems like you'd say that anything anyone does is rational, because, after all, they decided to do it, didn't they? But I guess you don't mean that.

Can you give an example of what you'd consider irrational behavior?

[69dodge]

If the value of a dollar to you is sufficiently small, and the value of possibly winning several million is sufficiently large, buying a lottery ticket is extremely rational.Is there any way to determine the relative values to someone of a definite dollar and of a small chance at winning a million dollars, besides just seeing if they play the lottery? I don't see any. And if there isn't any, you're basically saying that anyone who plays the lottery is rational by definition.

I'm not sure what "rational" means exactly, or what it ought to mean, but defining it as synonymous with "anything that anyone decides to do" seems pretty pointless.

[LawnOven]

Change the dollar amounts to Win = 4 x your entire net worth, and Lose = your entire net worth, and I suspect most of us would pass.


Unless you are like me, and have a negative net worth.

I would definately play that game. :)

[69dodge]

You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way.If you divide the number of heads by the number of tails, that ratio will gradually approach 1 as you keep flipping the coin. But if you subtract the number of tails from the number of heads, that difference will not approach 0. There will be lots of excess heads or tails at the end too, not only along the way. But not so many, compared to the total number of flips, that the ratio will be far from 1.

But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?The separate coin flips don't organize themselves. Nothing prevents the coin from landing heads up every time. Every sequence of heads and tails is just as likely as every other sequence. There are simply so many more sequences that are roughly half heads and half tails than there are sequences of any other ratio, so it makes sense that the sequence you get will probably be one of the many half-and-half ones rather than, say, the single all-heads one.

[ond_magiker]

The idea of behind a "force" causing the 50/50 heads or tails landings is a misconception of a what is really just a mathematical model of the coin toss. In reality the coin simply does what it does - except that it can only land one of two ways - heads or tails... which gives you the "50/50" model used to help interpret the outcome, roughly, before you make a toss; it does not force the outcome however.

Take for example a game of roulette at the casino: you have roughly a 50/50 "chance" that the ball will land on either RED or BLACK (excluding the GREEN zeros). Let's assume your friend joined one of the tables before you came in the casino and has had a chance to already see 3 of the results and lets say all three were BLACK... in his mind, according to the 50/50 "chance model," the next hit is more likely be a RED than a BLACK, but for you, who has just joined the table now the chances are 50/50 even. Does this change the past 3 hits on the board? No, of course not. Does it affect the next hit? The answer is of course, no. Probability is a mathematical concept so it does not 'affect' reality. Quantum mechanical probability is based on certain physical calculations which are made prior to an outcome which is not the same thing because on the roulette wheel and the coin toss there are no real useful calculations made before the toss and therefore: no real accurate prediction can be made on what will come 'out' since you don't know what is going 'in'. Hope that helps.


I don't quite follow. Are you saying it's correct of my friend to believe the next outcome is more probable to be red than black? If so, I can understand him, as many people believe this, but they are of course totally wrong.

[drkitten]

Is there any way to determine the relative values to someone of a definite dollar and of a small chance at winning a million dollars, besides just seeing if they play the lottery?

Ask them?

A person who claims not to want money, but then plays the lottery anyway, would arguably be acting irrationally. (Unless there were some social benefit gained from playing the lottery -- "Oh, I just do it because I like to flirt with the cute ticket-seller.....")

[drkitten]

I think your own qualifiers make it a relevant question. For example "the thought that they might win" and "relatively nominal sum": that implies the assumption that they are accurately making just the type of calculations I was talking about.

It does not. The amount of psychological "lift" you get from the hope may not depend on the accuracy of the calculation -- or even on the existence of a calculation.

[Jorghnassen]

Funny how rational and irrational (also what is "common sense" and what isn't) aren't so clear cut :D.

[Dave1001]

Funny how rational and irrational (also what is "common sense" and what isn't) aren't so clear cut :D.

Yeah, I think most of us knew that going in. But I think a good short hand for rational is what maximizes the agent's odds of persistance as an agent. Because if it ceases to persist as an agent, it ceases to be a factor in future interactions. Sort of like the agents in the tit-for-tat game, and what drives persistance in natural selection environments.

[Dave1001]

It does not. The amount of psychological "lift" you get from the hope may not depend on the accuracy of the calculation -- or even on the existence of a calculation.

Well, I think this is just a difference in first principles and definitions of terms. Sort of like if you defined a prime number to be "multiples of two" and we're defining prime numbers to be "integers which are only divisible by 1 and themselves". We'd similarly end up arguing on parallel tracks.


It seems for your chosen definition rational is completely a function of an agent's action in any context. Why is the action rational? Because the agent did it. Is it rational to to pay a psychic $1000 to hear them tell you what their dead spouse wants you to do? Yes, because of the psychological lift you get from hearing their communication. Is it rational to tithe 10% of your gross income to an evangelical church? Yes, because of the psychological lift knowing that you're going to heaven. I won't say that it's a meaningless approach to ascertaining rationality. I just think it's a particular definition divorced from the analysis others of us are using. Sort of like if you chose to define rational as "whatever will give the agent the least hope". That's not a definition you're using, but I think it's just as arbitrarily different from ours.

I think the definition for rational choice we're using is reducible to that which most likely perpetuates the persistance of the rational agent. Hence the choice which leads to more resources to maximize persistance is more rational than the choice that reduces such resources. Thus, not maximizing returns from $1 invested is not the most rational choice. I think this is the same measure used in the Tit-For-Tat game and implied in most discussions about what is or is not rational. Although not generally spelled out in this level of detail (though I'm sure 100 more footnotes could be written), I think this is the default definition. Rather than "the rational choice is that which provides the most anticipatory happiness" or "the rational choice is that which provides the least anticipatory happiness".

[drkitten]

It seems for your chosen definition rational is completely a function of an agent's action in any context.

No.

Why is the action rational?

In broad terms, because it achieves a goal that the agent has (at reasonable cost).

Is it rational to to pay a psychic $1000 to hear them tell you what their dead spouse wants you to do?

Does it make you feel better? If so, then it's no less rational to pay a psychic $1000 to make you feel better than it is to pay $1000 for tickets to a sold-out show.



I think the definition for rational choice we're using is reducible to that which most likely perpetuates the persistance of the rational agent. Hence the choice which leads to more resources to maximize persistance is more rational than the choice that reduces such resources. Thus, not maximizing returns from $1 invested is not the most rational choice.

If you accept "returns" to be an extremely general concept, including things that we don't typically think of as financial, then, yes. But maximizing "returns" would then include things like the happiness you get from thinking about your possible lottery winnings, a happiness that does not seem to be dependent on expected value.

If you define "returns" to be purely financial, you just defined the entire entertainment industry out of existence, since going to a film costs you money and returns you nothing.

In presenting his development of game theory, Von Neumann and Morgenstern found it necessary to make the simplifying assumptions that all "returns" can be quantified and compared on a uniform scale. Even they weren't foolish enough to assume that this scale is a purely financial one.

[NobbyNobbs]

There is no force that acts on the coin to prevent it coming up heads a billion times in a row. That result is not prohibited, just extremely unlikely. So unlikely that we would question the "fairness" of such a coin or the toss.

Nothing "makes the predicted results happen". The landings do not "organize themselves". If they did then the Gambler's Fallacy would be true...

A coin toss is sufficiently complex that the result is random and either outcome has a probability of 0.5 every time the coin is tossed. The coin doesn't "know" about the previous tosses.

It is the randomness that causes the observed result. The upward force and induced spin rate varies slightly for each toss. The air currents are slightly different each time, etc. It is conceivable that someone could practice a particular flipping technique and acheive enough consistency to skew the results one way, but that wouldn't be a random event...

Another way to see it is that we know it is a random process precicely because the measured outcome, over a large number of trials, is 50/50. Any other result would be a strong indication that something non-random is happening... Then, and only then, does it make sense to seek a force acting on the coin (or other cause).

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

Ok, so I've been lazy and haven't read the whole thread, but I had to respond to this post. It seems to me that you're saying you get the results you do because the process is random, and you can prove the process is random because of the results that you get.

This is a circular argument. Did I read something wrong?

[Schneibster]

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen. ...

But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails? ...

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row? ...The conversation seems to me to have gotten a bit far afield.

The question here, and please correct me if I've misunderstood you, seems to be, "what characteristic of the universe forces probabilistic predictions to come out correct?"

The answer appears to me to lie behind the fact that it is an inherent characteristic of the universe that when a process (that is, a sequence of operations or events with a defined beginning and ending) has alternative potential results (endings), and the process can be repeated, there will be a potential for each alternative to occur at each repeated trial of the process. However, in each trial, only one of the alternatives will be observed (unless you are into alternative universes, and even then, the "you" that you will continue to think of as "you" will observe only one of them in any one universe). The details of the process (objects involved, forces that affect those objects, particular states chosen as the "beginning" and "ending" of the process) will determine not only the number and type of alternatives, but also how likely each alternative is with respect to the (presumably) unity probability that there will be some result. (Note that if this is not a unity probability, then you cannot clearly define an "ending" state, and discussion of probability would be moot.)

Now, note that we've invoked objects, forces, and states; clearly, we are discussing physics here. Thus, the process is governed by physical laws, which are, by and large, and as far as we have been able to observe, essentially immutable over both space and time (that is, over a long enough series of trials, I'll get the same number of heads and tails today as I will tomorrow, and I'll get the same number at home as I will at the bar). This has exceptions, but we know about most of those, too (for example, if my coin is brass on one side and iron on the other, and I flip it over a magnet, it will alter the probabilities).

So basically, what I'm saying is that the fact that such probability calculations work so well is a consequence of the fact that we live in a universe in which physical law determines the outcome of the overwhelming majority of, if not all, processes, and in which physical law is essentially immutable. This is borne out by the fact that we seem to be able to assign such probabilities to the behavior of the smallest constituents of matter/mass/material and force/energy/influence, and when we observe the behavior of these constituents, we never observe behavior in violation of these probabilities; when we do, we go looking for the new law that governs this unexpected behavior, modifying our earlier understanding.

This is a kind of determinism, but it is not philosophical determinism; at the quantum level, we can predict the probability that a process will attain various alternative states extremely accurately, but we cannot predict which alternative any particular trial will result in. Just as we cannot predict whether the coin will come up heads or tails, but we can predict that (absent some physical force that we are not aware of) it will come up heads half the time and tails the other half.

This appears to me, in other words, to be the result of two fundamental characteristics of the universe that exist a priori, that is, without any underlying "machinery" or "cause:"
1. The behavior of objects, systems, and processes is governed by immutable physical laws; and
2. These laws specify the probability that various fundamental processes will result in various alternatives.

Rather a long answer for what is actually a rather deep question, IMHO. Hope it was worth your while to read.

[Hellbound]

...Rather a long answer for what is actually a rather deep question, IMHO. Hope it was worth your while to read.

Yeah, what he said.

That's what I was trying to get at earlier, only mine wasn't as smart, or clear, or readable, or, you know, good.

:D

[Schneibster]

Thanks! :D

[Notrump]

There is no “force” of probability. It is a purely mathematical concept.

Let’s allow coin flips as a good representative for a wide variety of probabilistic events. With coin flips we are conceivably dealing with a deterministic process. But measuring the conditions and calculating the result of even a single flip is far beyond our capabilities. So we resort to the laws of probability, which are purely mathematical. Other than quantum mechanics (and some might argue even then), we only relate probabilistic laws to the physical world when actual measurements or calculations are difficult or impossible.

Assuming unbiased conditions, then according to the laws or probability, no matter what has been the result of previous flips, the next one is equally likely to be heads or tails. That also means that if after 100 flips, 60 heads occurred and 40 tails, either type is equally likely to show up the majority of the time in the next 100. Interestingly, if the result were 50-50 in the second 100, then the average number of heads per flip would decline from 0.60 after 100 flips to 0.55 after 200. If the result were 54-46 in favor of heads in the second 100, then the average number of heads per flip would decline from 0.60 after 100 flips to 0.57 after 200, despite a majority of heads during the second 100.

So in the long run the average for each type will likely approach 0.50, even if the absolute difference between the number of occurrences of each type remained nearly unchanged or slowly increased. Thus “reversion to the mean” does not mean that an event, which had been occurring less frequently than predictions, will then start outpacing predictions. Instead it means that the overall average will likely revert nearer to the predictions.

"Likely" is the key word. In actuality, anything can happen. But by employing the mathematical laws of probability, we can often make reasonable decisions and preparations for otherwise uncertain future events.

Again, it’s purely math. There's no “force” of probability. ;)

[born]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet. :)
How about you factor in the "tosser". Each of us have a certain degree of subconscious reflex action. If that same person keeps flipping the same coin, with their usual style of movement and spontanious force level, there should end up being some sort of pattern.

[lenny]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play....

chaos keeps going; each coin toss stops.

poincare' considered both types of systems about 100 years ago; hardly pseudoscience (overhyped in public no doubt, but strong mathematical core.)

[lenny]

How about you factor in the "tosser". Each of us have a certain degree of subconscious reflex action. If that same person keeps flipping the same coin, with their usual style of movement and spontanious force level, there should end up being some sort of pattern.

i do not know of an experiment testing individuals; however there was an experiment some time ago which, grouping many people together, came up with ~51% chance that a fair toss by a normal person (no magicians!) would land with the same side up facing up as was up when it was tossed...

(i can look for the reference if anyone wants it)

[Tarot_Is_A_Card_Game!]

There is no “force” of probability. It is a purely mathematical concept.
I was just going to post the same thing, but you beat me to it!:D

[fuelair]

Nothing drives probability. That is a meaningless concept. Probability is simply a mathematical statement of observed occurences. Actually, if things did not work out according to the mathematics there would be a need for an explanation. (The odds that two things that are able to happen randomly mean they will happen equally over a large number of opportunities. If they do not, they are not happening randomly and and explanation is in order)

[BillyJoe]

drkitten,

Ignorance may be bliss, but I would not say it is rational.

If someone plays lotto because of the "thrill of possibly winning", I would say I understand why he plays lotto, but I would not say it is rational for him to play lotto.

BJ

[BillyJoe]

Unless you are like me, and have a negative net worth...I would definately play that game. :)Yeah, but only because you won't be able to pay out when you win. ;)

[BillyJoe]

I agree that there is no force behind probability.
It is the result of the universe being able to be understood - and hence able to be codified into what we call "The Laws of Physics".
If anything or everything was possible, our concept of probability would not exist.

In a different universe, it could be quite possible that...
- the ratio H/T increases exponentially with increasing number of coin tosses.
- the ratio H/T tends towards 2.
- tossing H would necessarily cause T to be tossed next time.

[lenny]

Probability is simply a mathematical statement of observed occurences.
in fact "relative frequency" reflects observed occurences, probability is, as you say mathematical and cares not a dot for observations...

Actually, if things did not work out according to the mathematics there would be a need for an explanation.

take the forecast probability of rainfall in ,say, the 5 day ahead forecasts; coillect all the forecasts made over a year:

count the number of times it rained on a day when a 10% probability of rain was forecast. divide that number by the total number of times there was a 10% forecast probability of rain.

methinks you will find yourself in need of an explanation.

[Maenoon]

I'm not a physicist, but it seems to me that the Second Law of Thermodynamics may actually come into play. This is the concept that gives birth to entropy. Boiling it down into simple terms: The more complex a system is, the more that system wants to become disorganized.

So, flipping a coin is a relatively uncomplicated system where you only have three possible outcomes (heads, tails, or the coin lands on its edge). And, drawing on Heisenberg's Principle of Uncertainty, once you observe how the coin lands, you cannot possibly know if that is how it would have landed if you weren't actually watching it. It's rather like the Zen Buddhist koan, "If a tree falls in the woods and no one is watching, does it make a sound?"

But if you're talking about probabilities, the more complex a system is, the harder it would be to predict the outcomes. The only thing you can really expect is that a complex system will tend to become increasingly disorganized as time moves forward.

Brian Greene does a much better job of explaining it in his book "The Fabric of the Cosmos."

[T'ai Chi]

What force controls probability?

I personally dunno. But many people have thought about it, and think that god(s) gives some people motivation. For example


"When the Lord created the world and people to live in it - an enterprise which, according to modern science, took a very long time - I could well imagine that He reasoned with Himself as follows: 'If I make everything predictable, these human beings, whom I have endowed with pretty good brains, will undoubtedly learn to predict everything, and they will thereupon have no motive to do anything at all, because they will recognize that the future is totally determined and cannot be influenced by any human action. On the other hand, if I make everything unpredictable, they will gradually discover that there is no rational basis for any decision whatsoever and, as in the first case, they will thereupon have no motive to do anything at all. Neither scheme would make sense. I must therefore create a mixture of the two. Let some things be predictable and let others be unpredictable. They will then, amongst many other things, have the very important task of finding out which is which.'" -E.F. Schumacher


"To understand God's thoughts we must study statistics, for these are the measure of His purpose." -Florence Nightingale

[Jorghnassen]

take the forecast probability of rainfall in ,say, the 5 day ahead forecasts; coillect all the forecasts made over a year:

count the number of times it rained on a day when a 10% probability of rain was forecast. divide that number by the total number of times there was a 10% forecast probability of rain.


That's not how probability of precipitation works. IIRC, if it says there's a 30% chance of rain, it means 30% of the territory covered in the forecast will see some rain according to the model used. Weather forecast is still very much done deterministically (though things may be changing, see some of the works of, say, Adrian E. Raftery).

[BillyJoe]

So, flipping a coin is a relatively uncomplicated system where you only have three possible outcomes (heads, tails, or the coin lands on its edge). And, drawing on Heisenberg's Principle of Uncertainty, once you observe how the coin lands, you cannot possibly know if that is how it would have landed if you weren't actually watching it. It's rather like the Zen Buddhist koan, "If a tree falls in the woods and no one is watching, does it make a sound?"I am finding it difficult to see the analogy between a Coin Flip, Heisenberg Uncertainty, and the Zen Koan. :(

[Hellbound]

It's rather like the Zen Buddhist koan, "If a tree falls in the woods and no one is watching, does it make a sound?"

Yes :D

[Meffy]

And, drawing on Heisenberg's Principle of Uncertainty, once you observe how the coin lands, you cannot possibly know if that is how it would have landed if you weren't actually watching it.

My understanding of Heisenberg is that his principle applies strictly at the quantum mechanical level -- that only via fairly extraordinary contrivances can it be made to affect events at the macroscopic level. (If that was intended as a joke, beg pardon.)

[Maenoon]

My understanding of Heisenberg is that his principle applies strictly at the quantum mechanical level -- that only via fairly extraordinary contrivances can it be made to affect events at the macroscopic level. (If that was intended as a joke, beg pardon.)

What can I say? I'm incurably facetious.

Seriously, though, I do realize that Heisenberg's principle applies to particles.

However, the study of particle behavior is cogent to a discussion about probabilities. Numerous experiments have shown that particle behavior is directly associated with probability waves.

The probability waves associated with any given particle theoretically stretch across the entire expanse of the universe, but the waves spike the strongest near the vicinity of the particle. So, you can expect that a particle will remain near the spot where you last saw it, but it could just as well dart off across to the other side of the universe without any warning. It's not likely, but it is supposedly possible. It's one of the freakier ideas associated with physics.

This is probably an unsatisfactory explanation. If you want to learn more, once again, I refer you to Brian Greene's books.

[Meffy]

What can I say? I'm incurably facetious.

You're not the only many-faceted member of the forums. I'll skip the books, as the starship Heart of Gold already provides an excellent demonstration of the power of the improbability drive.

[jayrev]

drkitten,

Ignorance may be bliss, but I would not say it is rational.

If someone plays lotto because of the "thrill of possibly winning", I would say I understand why he plays lotto, but I would not say it is rational for him to play lotto.

BJ

Sure it is, as long as he values (the enjoyment of playing + the odds of winning) more than the cost of the lotto ticket. In fact, I would say it must be so.

[BillyJoe]

Sure it is, as long as he values (the enjoyment of playing + the odds of winning) more than the cost of the lotto ticket. In fact, I would say it must be so.What is the value of (the enjoyment of playing + the odds of winning)?

First of all, the (the odds of winning) are practically zero.

So then, what is the value of (the enjoyment of playing)?

In fact, it doesn't really matter because "the enjoyment of playing" is based on the misconception that he has a real chance of winning. But we know his actual chance of winning is practically zero. So, it doesn't matter how highly he values the "the enjoyment of playing", it is still irrational.

----------------------------

If you are saying that it is rational because of the mere fact that he enjoys it, regardless of the fact that his enjoyment is based on an irrational assessment of his chances of winning, then I think we have a disagreement about the meaning of the word "rational".

[Loss Leader]

In fact, it doesn't really matter because "the enjoyment of playing" is based on the misconception that he has a real chance of winning. But we know his actual chance of winning is practically zero. So, it doesn't matter how highly he values the "the enjoyment of playing", it is still irrational.

In grad school, we used to say that the lottery is a tax on stupidity.

[Cuddles]

What is the value of (the enjoyment of playing + the odds of winning)?

First of all, the (the odds of winning) are practically zero.

So then, what is the value of (the enjoyment of playing)?

In fact, it doesn't really matter because "the enjoyment of playing" is based on the misconception that he has a real chance of winning. But we know his actual chance of winning is practically zero. So, it doesn't matter how highly he values the "the enjoyment of playing", it is still irrational.

----------------------------

If you are saying that it is rational because of the mere fact that he enjoys it, regardless of the fact that his enjoyment is based on an irrational assessment of his chances of winning, then I think we have a disagreement about the meaning of the word "rational".

If someone spends £5 in an hour gambling, is this any less rational than spending £5 on a film in the cinema? There is no logical scientific reason to enjoy either of these, but I doubt many people would argue the cinema is irrational, so why should gambling be? If people understand that they are not likely to win, but are just gambling as a fun way of spending a couple of hours with some friends I see nothing irrational about this at all. It only becomes irrational when people actually believe they have a better chance of winning than in reality, despite all evidence to the contrary.

[BillyJoe]

If someone spends £5 in an hour gambling, is this any less rational than spending £5 on a film in the cinema? There is no logical scientific reason to enjoy either of these, but I doubt many people would argue the cinema is irrational, so why should gambling be? If people understand that they are not likely to win, but are just gambling as a fun way of spending a couple of hours with some friends I see nothing irrational about this at all.I believe I was talking specifically about the lotto.

It only becomes irrational when people actually believe they have a better chance of winning than in reality, despite all evidence to the contrary.We agree then.

[Roboramma]

I believe I was talking specifically about the lotto.
I don't see why it should be impossible to enjoy playing the lotto without being misguided as to your actual chances of winning...

[BillyJoe]

I don't see why it should be impossible to enjoy playing the lotto without being misguided as to your actual chances of winning...You know that the chances of you winning lotto are practically zero and yet, week after week, you enter the lotto and, week after week, you watch the draw to see yourself not winning yet again.
Sound like fun to you?

[jayrev]

What is the value of (the enjoyment of playing + the odds of winning)?

First of all, the (the odds of winning) are practically zero.

So then, what is the value of (the enjoyment of playing)?

In fact, it doesn't really matter because "the enjoyment of playing" is based on the misconception that he has a real chance of winning. But we know his actual chance of winning is practically zero. So, it doesn't matter how highly he values the "the enjoyment of playing", it is still irrational.

----------------------------

If you are saying that it is rational because of the mere fact that he enjoys it, regardless of the fact that his enjoyment is based on an irrational assessment of his chances of winning, then I think we have a disagreement about the meaning of the word "rational".

No, rationality is absolute. I think we have a disagreement about the meaning of "practically zero", as well as the relativity of money. It would be irrational for me to invest my 401K in lotto tickets. It is not at all irrational for me to buy 1 lotto ticket if the cost has "practically zero" affect on my life, while the potential payoff could have a drastic affect.

[BillyJoe]

I think we have a disagreement about the meaning of "practically zero"..."practically zero" means "for all intents and purposes, zero". It means you can assume it will not happen.

It is not at all irrational for me to buy 1 lotto ticket if the cost has "practically zero" affect on my life, while the potential payoff could have a drastic affect.One lotto ticket? The average lotto player plays eight games every week. That is not "practically zero" affect on the player's life. It is a considerable investment (wrong word, of course) of time money and effort. And the payoff will not come even if he plays eight games a week, every week for the rest of your life. With no payout, it is irrational to play.

[jayrev]

"practically zero" means "for all intents and purposes, zero". It means you can assume it will not happen.

One lotto ticket? The average lotto player plays eight games every week. That is not "practically zero" affect on the player's life. It is a considerable investment (wrong word, of course) of time money and effort. And the payoff will not come even if he plays eight games a week, every week for the rest of your life. With no payout, it is irrational to play.

So is it still irrational when the expected value of the lottery ticket exceeds the cost?

[Almo]

Well, the glib answer is that there are 2 or 3 choices: hidden variables, nothing and God.

Hidden Variables has been disproven, to my knowledge.

[Almo]

So is it still irrational when the expected value of the lottery ticket exceeds the cost?

The expected value of a lotto ticket is never higher than its cost. Or there wouldn't be a lottery.

[BillyJoe]

jayrev,

The expected value of a lotto ticket is never higher than its cost. Or there wouldn't be a lottery.If you are not sure about this check http://en.wikipedia.org/wiki/Expected_value

BJ

[jayrev]

The expected value of a lotto ticket is never higher than its cost. Or there wouldn't be a lottery.

I agree that is true for someone who plays every drawing. But if you only play lottos that "rollover" when there is no winner, and the payout exceeds the probability of winning, doesn't that specific ticket have a +EV?

[plouton]

What did Einstein mean when he said that God did not play dice in reference to quantum physics? And what does it mean that the scientific community today believes that he was wrong about that? Does that mean that randomness, random chance exist in the universe?


Dave 1001 was correct. Einstein made that remark because he did not think there was any randomness in the universe. I think he went to his grave trying to disprove this idea he had done so much to develop. Physically, we are unable to predict the outcome of a coin toss because it involves differential equations in fluid dynamics among other things. Those of you that have taken a course in differential equations know that most of them cannot be solved, only approximated. I believe, as indicated above, that Chaos theory rules here.

[Meadmaker]

I agree that is true for someone who plays every drawing. But if you only play lottos that "rollover" when there is no winner, and the payout exceeds the probability of winning, doesn't that specific ticket have a +EV?


In very, very, rare cases, the size of the jackpot is such that the dollar value of the jackpot is greater than $1 * number of possible tickets. However, that doesn't mean a positive EV. If multiple winning tickets are sold, then the jackpot gets divided among the winners. So, when calculating EV, you have to take into account that there is a chance multiple winning tickets will be sold.

And then of course, there's taxes.

I seriously doubt that there has ever been a lottery game where the EV was positive.



I actually buy an occasional ticket, or did when my disposable income was higher, prior to marriage. I don't think it was irrational. I'm guessing I bought about 20 tickets per year. The most I ever won was 50 dollars. Like most people, I am sure that if I added up all the winners, and subtracted the losers, I would end up a net loser. However, since I had disposable income, the occasional dollar didn't bother me in the least to lose, but the occasional 20 or 50 dollar win was way cool. So, my net enjoyment was positive.

I realize that is not the typical buying pattern that generates the revenue for the state.

[jayrev]

In very, very, rare cases, the size of the jackpot is such that the dollar value of the jackpot is greater than $1 * number of possible tickets.

Actually it's not that rare at all, it happens a few times a year here in Georgia. But I tend to agree that when you consider the possibility of a jackpot split and taxes it does become less likely for the EV to truly be positive.

[lenny]

That's not how probability of precipitation works. IIRC, if it says there's a 30% chance of rain, it means 30% of the territory covered in the forecast will see some rain according to the model used.
the method you suggest has the drawback that it cannot be determined empirically. whether or not it rained is usually defined by a bucket in a rain gauge (but even the definition of "rained" can [?used to?] vary within Europe).

Weather forecast is still very much done deterministically (though things may be changing, see some of the works of, say, Adrian E. Raftery).

monte carlo style probabilistic methods have been operational in both the US and Europe since 1992...

http://www.ecmwf.int/services/dissemination/3.1/Forecast_Probability_products.html

[DeviousB]

Actually it's not that rare at all, it happens a few times a year here in Georgia. But I tend to agree that when you consider the possibility of a jackpot split and taxes it does become less likely for the EV to truly be positive.

Play the European lotteries, they're tax-free.
;)

PS. Checking out the Euromillions lotto, I see that a 2 euro ticket has a 1 in 76 million chance of winning 140 million euros. Factoring in the other prize tiers and I wouldn't be surprised if the EV was positive in this case

PPS. I also see that there have been 10 jackpot rollovers so far. After 12 draws without a jackpot winner the top prize is instead distributed between the second prize winners (who face 5 million to 1 odds). Now that's when I buy my ticket!

[BillyJoe]

What's the probability that someone would find this thread again after two months?

[DeviousB]

Hidden Variables has been disproven, to my knowledge.

More or less. See Bell's Inequality (http://en.wikipedia.org/wiki/Bell's Inequalitym).

[DeviousB]

What's the probability that someone would find this thread again after two months?

1.

Old threads never die...

They just repeat the arguments from 3 pages ago ad infinitum.

[Cuddles]

eight[/I] games every week. That is not "practically zero" affect on the player's life. It is a considerable investment (wrong word, of course) of time money and effort. And the payoff will not come even if he plays eight games a week, every week for the rest of your life. With no payout, it is irrational to play.

So would you agree that it is irrational to go to the cinema? As I said before, if I spend £5 on the lottery and don't win, or £5 on the cinema, either way I have lost £5 and gained nothing. But while playing the lottery I had the excitement and adrenaline from knowing that I might win, and while in the cinema I had the excitement and adrenaline from watching imgainary things get blown up. By your arguments both are irrational, but if I do both purely for the enjoyment at the time, and not with the expectation that either one will change my life, I would say neither are irrational.

[nimzov]

So would you agree that it is irrational to go to the cinema? As I said before, if I spend £5 on the lottery and don't win, or £5 on the cinema, either way I have lost £5 and gained nothing. But while playing the lottery I had the excitement and adrenaline from knowing that I might win, and while in the cinema I had the excitement and adrenaline from watching imgainary things get blown up. By your arguments both are irrational, but if I do both purely for the enjoyment at the time, and not with the expectation that either one will change my life, I would say neither are irrational.

I Agree. I don't know about adrenaline but I think hat people play loto for the dream of winning something. This is not very different than going to the movies and not more irrational.

Of course people who believe that their chance of winning is different from their objective or statistical chance of winning are thinking irrationally.

nimzo

[lenny]

What's the probability that someone would find this thread again after two months? Old threads never die...

They just repeat the arguments from 3 pages ago ad infinitum.
in fact, this one returned to life addressing open issues on rainfall.
that said, those issues were not what grew!

[BillyJoe]

So would you agree that it is irrational to go to the cinema?No.

if I spend £5 on the lottery and don't win, or £5 on the cinema, either way I have lost £5 and gained nothing.
If you are descriminating about what you see at the cimema, you could gain a great deal in ongoing enjoyment, education, discussion etc etc. On the other hand, playing the lottery is a dead loss.

But while playing the lottery I had the excitement and adrenaline from knowing that I might win...Your "excitement and adrenalin" are based on a false premise - that you might win. The odds (zero for practical purposes) are such that it does not justify your "excitement and adrenaline". Your "excitement and adrenaline" are, therefore, irrational.

..if I do both purely for the enjoyment at the time, and not with the expectation that either one will change my life, I would say neither are irrational.The only reason that you can enjoy playing lotto is that you don't know that it is irrational. Ignorance may be bliss but that doesn't stop it from being irrational. :cool:

BJ

[BillyJoe]

I Agree. I don't know about adrenaline but I think hat people play loto for the dream of winning something. This is not very different than going to the movies and not more irrational.I disagree :D

Of course people who believe that their chance of winning is different from their objective or statistical chance of winning are thinking irrationally.I agree ;)

BJ

[Cuddles]

Your "excitement and adrenalin" are based on a false premise - that you might win. The odds (zero for practical purposes) are such that it does not justify your "excitement and adrenaline". Your "excitement and adrenaline" are, therefore, irrational.

Irrelevant. It doesn't matter why you are excited, the fact that you are is enough reason to play. People jump off hundred foot cliffs. They enjoy it, but there is no rational reason for the enjoyment. However, the fact that they experience the enjoyment provides a rational reason for jumping, therefore jumping is rational. Of course, someone who doesn't enjoy cliff-diving would be irrational for jumping off since they don't gain anything from it at all. Just because you don't enjoy the lottery doesn't mean others don't, so while it may be irrational for you to play, it doesn't make it irrational for others to do so.

[DeviousB]

Equally, though, it would be rational to visit a homeopath if it made you feel better. Or drop a couple of K on pyschic hotlines because you enjoy the calls.

In fact most personal enjoyments aren't rational (from Encarta, "governed by, or showing evidence of, clear and sensible thinking and judgment, based on reason rather than emotion or prejudice"); they are just enjoyable.

You do something you enjoy because you enjoy it. Even if it makes no sense whatsoever (http://en.wikipedia.org/wiki/Bonsai).

[nimzov]

Your "excitement and adrenalin" are based on a false premise - that you might win. The odds (zero for practical purposes) are such that it does not justify your "excitement and adrenaline". Your "excitement and adrenaline" are, therefore, irrational. BJ
I disagree. :D

Chances of winning "something" are not zero. Some people get excited for winning 50$.

nimzo

[BillyJoe]

It doesn't matter why you are excited, the fact that you are is enough reason to play. People jump off hundred foot cliffs. They enjoy it, but there is no rational reason for the enjoyment. However, the fact that they experience the enjoyment provides a rational reason for jumping, therefore jumping is rational.I think it is irrational to define "rational" the way you have, because now you have to find another word to stand in place of what the rest of us define "rational" to be And that's a waste, because we already have a perfectly good word for that :D

In other words, I agree with DB.