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]

Originally Posted by 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.

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

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]

Originally Posted by patnray

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]

Originally Posted by 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...

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]

Originally Posted by 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...

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]

Originally Posted by Badly Shaved Monkey

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]

Originally Posted by Dave1001

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]

Originally Posted by Jekyll

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]

Originally Posted by Dave1001

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]

Originally Posted by Jekyll

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]

Originally Posted by Dunstan

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]

Originally Posted by Dave1001

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]

Originally Posted by Dave1001

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]

Originally Posted by Dunstan

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]

Originally Posted by Pup

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 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]

Originally Posted by Dave1001

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 in 1654, in the context of gambling. I'd like to hear about earlier applications.

[anor277]

Originally Posted by 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.

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

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]

Originally Posted by 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?

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]

Originally Posted by Dunstan

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.
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.

Quote:

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]

Originally Posted by Dave1001

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:

Originally Posted by Pup

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]

Originally Posted by Cuddles

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]

Originally Posted by Dave1001

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]

Originally Posted by Jorghnassen

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]

Originally Posted by Jorghnassen

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]

Originally Posted by Pup

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..

Originally Posted by Huntsman

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]

Originally Posted by Dave1001

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