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Tags lotteries , math puzzles , probability , probability puzzles

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Old 25th February 2012, 02:01 PM   #121
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Originally Posted by Dan O. View Post
5.5% of lottery jackpot winners go bankrupt.

If you want to get rich you need to learn to manage your money and invest in yourself. get an education, develop your work skills and advance your career. A small investment made early in life comperable to buying a lottery ticket every week will grow exponentially into a significant life style change that also gives you the skills needed to avoid the bankruptcy trap when your boat does come in.
I am middle aged, closing in on elderly. Looking back on how I was raised, I think the most important lesson my parents taught me was to live within my means. In America, I realize that I am a minority because I believe being in debt because of overspending is far more embarrassing than driving a 10-year-old car with a dent and a scratch.
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Old 25th February 2012, 06:06 PM   #122
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Originally Posted by jasonpatterson View Post
What is true, however, is that any set of 6 numbers with a simple pattern is less likely to occur than one of the sets of 6 numbers with no obvious pattern.
Indeed, but they occur just as often as expected. The House always wins.

Quote:
Obvious might not be the best adjective ...
It works for me, but obvious can vary - in some cultures, for instance, the digit 8 is especially lucky while in others 7 is favoured.
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Old 25th February 2012, 06:29 PM   #123
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Originally Posted by Ladewig View Post
I am middle aged, closing in on elderly. Looking back on how I was raised, I think the most important lesson my parents taught me was to live within my means.
With reference to gambling, I was taught only to gamble in games where you might have an edge (roulette and lotteries do not qualify), and to gamble with slightly more than you can afford. Not your rent, not enough to be left taking out a PayDay Loan, certainly not money you're transporting from point A to Big Vinnie (who's expecting you), but enough to get a flame from the significant other and a dull couple of months.

It was a teacher who taught me that, as it happens, not my family . My family were dead set against gambling, but doing the Football Pools somehow didn't count.

Debt (other than a home mortgage well within your means) was an absolute no-no. Up there with Divorce .
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Old 26th February 2012, 04:22 AM   #124
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Originally Posted by Ladewig View Post
If the chances of turning a 34-cent ticket into a $7600 payout consisted of a one in fifty billion chance, then would it suck?
ETA: if such a lottery offered that payout for those odds would it be, in your opinion, a suckers' game designed to separate rubes from their money?
The words 'pulling' and 'teeth' come to mind! In answer to your questions: yes, of course, because you're weighing up the situation before the event. Standing at the teller paying in a cheque for $7,600 on the back of a $0.34c bet after the event far from sucks. Get it?!

Originally Posted by Dan O. View Post
It's a fool's game for anyone that plays.
However, in the U.S. we make them into even bigger fools by taking back at least 30% of the jackpot winnings through taxes.
Originally Posted by vladi View Post
And gambling is for fools, anyway
I'd question whether the majority of lottery winners would agree!

Originally Posted by Dan O. View Post
If you want to get rich you need to learn to manage your money and invest in yourself. get an education, develop your work skills and advance your career.
I'd hazard that not many people get rich following this philosophy compared to those that do and don't. In my humble opinion, except for the fortunate few who inherit wealth, those who get rich take massive risks - not continuously - but at significant points in their lives.

Originally Posted by Dan O. View Post
A small investment made early in life comperable to buying a lottery ticket every week will grow exponentially into a significant life style change that also gives you the skills needed to avoid the bankruptcy trap when your boat does come in.
Not necessarily true. What sort of 'investment' are you alluding to, and what do you mean by 'small'!?

Originally Posted by Ladewig View Post
I am middle aged, closing in on elderly. Looking back on how I was raised, I think the most important lesson my parents taught me was to live within my means. In America, I realize that I am a minority because I believe being in debt because of overspending is far more embarrassing than driving a 10-year-old car with a dent and a scratch.
I think you're right that embarrassment from debt isn't an issue for most, bred by lack of responsibility founded in a seeming lack of ramification.

Originally Posted by CapelDodger View Post
With reference to gambling, I was taught only to gamble in games where you might have an edge (roulette and lotteries do not qualify) ...
What does, then?

Originally Posted by CapelDodger View Post
... and to gamble with slightly more than you can afford. Not your rent, not enough to be left taking out a PayDay Loan, certainly not money you're transporting from point A to Big Vinnie (who's expecting you), but enough to get a flame from the significant other and a dull couple of months.

It was a teacher who taught me that, as it happens, not my family . My family were dead set against gambling, but doing the Football Pools somehow didn't count.
Probably because they could afford it, just like they could afford the occasional meal out?!
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Old 26th February 2012, 05:20 AM   #125
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Originally Posted by Southwind17 View Post
Standing at the teller paying in a cheque for $7,600 on the back of a $0.34c bet after the event far from sucks. Get it?!
So your point is that it doesn't suck to win the lottery? Well... okay, yeah, that's true.

It doesn't tell us anything about whether or not it's worthwhile to play however.
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Old 26th February 2012, 06:16 AM   #126
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I was involved with a compulsive gambler.

She believed in her heart of hearts that 1,2,3,4,5,6 was a stupid bet* because of the unlikelihood that those numbers could ever come up.

Nothing could sway her.

One of her arguments was, "Fine. Just show me one lottery where those numbers have ever come up".

I think it indicates a flaw in how our brains process probability, which is often counterintuitive.


*as other have indicated, it is a stupid bet, but only because if it did hit you'd be sharing the winnings with hundreds or thousands of others.
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Old 26th February 2012, 06:42 AM   #127
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Even the great Tommy Cooper (http://www.mkccc.com/humour/t.htm) had problems with odds.

"Apparently, 1 in 5 people in the world are Chinese. And there are 5 people in my family, so it must be one of them. It’s either my mum or my dad. Or my older brother Colin. Or my younger brother Ho-Cha-Chu. But I think it’s Colin".
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Old 26th February 2012, 08:59 AM   #128
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Originally Posted by Southwind17 View Post
The words 'pulling' and 'teeth' come to mind! In answer to your questions: yes, of course, because you're weighing up the situation before the event. Standing at the teller paying in a cheque for $7,600 on the back of a $0.34c bet after the event far from sucks. Get it?!
Actually, no. I keep trying to use your example. I am up to the point were I have the $7600 check in my hand and I am in line at the bank, but I keep imagining all the people who lost money in line ahead of me.

Putting aside the joking - because humans are so bad at deciding what is a good or bad bet, mathematicians developed "expected value" as a way to compare bets. Unless one plays a 6/42 parimutuel game that has rolled over for 25 consecutive drawing, then one is statistically looking at a terrible, terrible bet.
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Old 26th February 2012, 10:51 AM   #129
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What does it cost to play the lottery. Over a lifetime of playing $1 per week for 70 years you would spend about $3600. If that were saved and earned a modest 5% interest per year it would accumulate to over $30,000.

If we condense the lifetime of lottery play into a single draw, 30% gets paid out in minor prizes that would return $9000. So you would be putting up the net of $21,000 for a one chance in 1500 to win a jackpot worth about $9 million. That's like convincing a small town to all give up their cars so that the mayor can live on a small yacht.
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Old 26th February 2012, 01:37 PM   #130
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Originally Posted by Roboramma View Post
So your point is that it doesn't suck to win the lottery? Well... okay, yeah, that's true.

It doesn't tell us anything about whether or not it's worthwhile to play however.
Again, ask a selection of jackpot winners that question. And don't forget that for most players the emotional hope of winning each week and the anticipation when checking the result is well worth the modest stake.
Originally Posted by Ladewig View Post
Actually, no. I keep trying to use your example. I am up to the point were I have the $7600 check in my hand and I am in line at the bank, but I keep imagining all the people who lost money in line ahead of me.
... and you don't have a wry smile on your face?!

Originally Posted by Dan O. View Post
What does it cost to play the lottery. Over a lifetime of playing $1 per week for 70 years you would spend about $3600. If that were saved and earned a modest 5% interest per year it would accumulate to over $30,000.
Which would be worth what, exactly, in net present value terms at, say, average 8% p.a. discount?!
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Old 26th February 2012, 01:43 PM   #131
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Originally Posted by Dan O. View Post
What does it cost to play the lottery. Over a lifetime of playing $1 per week for 70 years you would spend about $3600. If that were saved and earned a modest 5% interest per year it would accumulate to over $30,000.
When the UK lottery first started I picked my six numbers, but I've never bought a ticket. I just used to check the winning numbers in the paper each week, and keep track of how much money I'd saved by not playing the lottery. I got 3 right numbers several times and 4 numbers once, but I was still about £200 up when I finally stopped bothering. I used to buy myself little treats with the money I'd saved.
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Old 26th February 2012, 02:32 PM   #132
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Originally Posted by Pixel42 View Post
When the UK lottery first started I picked my six numbers, but I've never bought a ticket. I just used to check the winning numbers in the paper each week, and keep track of how much money I'd saved by not playing the lottery. I got 3 right numbers several times and 4 numbers once, but I was still about £200 up when I finally stopped bothering. I used to buy myself little treats with the money I'd saved.
So, so sad!
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Old 26th February 2012, 02:50 PM   #133
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Originally Posted by Southwind17 View Post
Again, ask a selection of jackpot winners that question. And don't forget that for most players the emotional hope of winning each week and the anticipation when checking the result is well worth the modest stake.
I occasionally buy a ticket although it is a stupid thing to do. While it is possible to enjoy the anticipation leading up to the drawing, I have found that if one disciplines oneself, it is possible to enjoy all the anticipation without actually buying the ticket. And even if one cannot convince oneself to enjoy that type of anticipation, one could instead buy a ticket for a drawing in the future. That way, the price of a single ticket provides weeks or months of anticipation.

Originally Posted by Southwind17 View Post
... and you don't have a wry smile on your face?!
While I am the kind of person who does enjoy wry humor, dark humor, and life's little (and big) ironies, I don't know if I would be smiling. I've never stood at the end of a line with tens of thousands of people in it so it might be difficult to manage any kind of smile.


ETA: Despite my lack of smileys, I do consider these exchanges friendly banter instead of a dramatic argument or condescending oneupsmanship.

Last edited by Ladewig; 26th February 2012 at 03:01 PM.
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Old 26th February 2012, 03:05 PM   #134
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Originally Posted by Southwind17 View Post
Which would be worth what, exactly, in net present value terms at, say, average 8% p.a. discount?!
Present value is trivial to compute. For an infinite series of fixed payments, the question becomes: what present value would earn sufficient interest in one period to equal the payment. The interest rate was specified for an annual period so this needs to be converted to the periodic rate for 1 week which is the 52nd root of 1.08 minus 1 or about 0.148%. The principle required to earn $1 at this rate is $1 / .00148 = $675.

In my example, the fixed payments ended after 70 years. To adjust for this, we need to subtract the present value of principle 70 years in the future which is -$675 / 1.08^70 = -$3.

The NPV of 70 years of $1 weekly payments with an anuallized rate of 8% is therefore $672.
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Old 26th February 2012, 03:06 PM   #135
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Originally Posted by Dan O. View Post
What does it cost to play the lottery. Over a lifetime of playing $1 per week for 70 years you would spend about $3600. If that were saved and earned a modest 5% interest per year it would accumulate to over $30,000.

If we condense the lifetime of lottery play into a single draw, 30% gets paid out in minor prizes that would return $9000. So you would be putting up the net of $21,000 for a one chance in 1500 to win a jackpot worth about $9 million.
May I see your calculations? I am ashamed to admit that (at first glance) a ticket that costs $21,000 and yields a one in 1500 chance of $9 million does sound more tempting to me than the one ticket for a one in 5 million chance at $3 million.


ETA: oops, I just ran the numbers on the $21,000 option that they are painful.
But I still want to know where 30% came from.

Last edited by Ladewig; 26th February 2012 at 03:08 PM.
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Old 26th February 2012, 03:31 PM   #136
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Originally Posted by Ladewig View Post
May I see your calculations? I am ashamed to admit that (at first glance) a ticket that costs $21,000 and yields a one in 1500 chance of $9 million does sound more tempting to me than the one ticket for a one in 5 million chance at $3 million.


ETA: oops, I just ran the numbers on the $21,000 option that they are painful.
But I still want to know where 30% came from.

For the lottery payments part, I was just using a typical lotto payment schedule of "Prizes equal 50% of sales" and a distribution of 40% of the prize pool to the grand prize. This will of course vary for individual lottery games.
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Old 26th February 2012, 09:48 PM   #137
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Originally Posted by Dan O. View Post
For the lottery payments part, I was just using a typical lotto payment schedule of "Prizes equal 50% of sales" and a distribution of 40% of the prize pool to the grand prize. This will of course vary for individual lottery games.
But where did the "30% gets paid out in minor prizes " come from?
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Old 26th February 2012, 11:26 PM   #138
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Originally Posted by Ladewig View Post
I occasionally buy a ticket although it is a stupid thing to do.
Unless it wins you the jackpot, of course. Oh ... hang on ... we've already been there haven't we!

Originally Posted by Ladewig View Post
While it is possible to enjoy the anticipation leading up to the drawing, I have found that if one disciplines oneself, it is possible to enjoy all the anticipation without actually buying the ticket.
By 'disciplines oneself' you must surely mean something along the lines of flagellation, right? In which case I can perfectly understand how one might then derive blissful euphoria from watching a lottery draw with absolutely no prospect of winning! Seriously, am I missing something in you psyche here?!

Originally Posted by Ladewig View Post
And even if one cannot convince oneself to enjoy that type of anticipation, one could instead buy a ticket for a drawing in the future. That way, the price of a single ticket provides weeks or months of anticipation.
Or alternatively convert to a diet of banana cake, thereby providing weeks or months of constipation!

Originally Posted by Dan O. View Post
Present value is trivial to compute ...

The NPV of 70 years of $1 weekly payments with an anuallized rate of 8% is therefore $672.
... and how, I wonder, does that compare to, say, the NPV of what you're likely to spend on completely wasteful trivialities that have absolutely no possible prospect of betterment; indeed more than likely detriment, over the same years? I suppose smoking (and possibly drinking?!) aren't fair comparisons, but I wouldn't mind seeing the figures!
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Old 26th February 2012, 11:54 PM   #139
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Originally Posted by Southwind17 View Post
By 'disciplines oneself' you must surely mean something along the lines of flagellation, right?
No, I am talking about disciplining one's mind. You don't really have to have an actual lottery ticket in your hand to fantasize about winning the lottery. One could spend one's coffee break time surfing the internet looking at exotic destinations and fantasizing what it would be like to travel there without actually making the lottery ticket purchase.

As for watching the drawing, I'd just skip that bit; but if one wants to, one could write down six numbers and when they don't win the big jackpot, one could smile wryly about what a sucker's game the lottery is and how easy it is to not play it.
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Old 27th February 2012, 01:28 AM   #140
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Originally Posted by Ladewig View Post
But where did the "30% gets paid out in minor prizes " come from?
50% of the income is the prize fund. 40% of the prize fund goes to the major prizes, i.e. 20% of the income. That leaves 60% of the prize fund for the minor prizes, or 30% of the income.
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Old 27th February 2012, 03:37 AM   #141
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Originally Posted by Southwind17 View Post
... and how, I wonder, does that compare to, say, the NPV of what you're likely to spend on completely wasteful trivialities that have absolutely no possible prospect of betterment; indeed more than likely detriment, over the same years?

Yep, that pretty much sums up a gambling habit.
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Old 27th February 2012, 03:58 AM   #142
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Originally Posted by Ladewig View Post
No, I am talking about disciplining one's mind.
You don't say!

Originally Posted by Ladewig View Post
You don't really have to have an actual lottery ticket in your hand to fantasize about winning the lottery. One could spend one's coffee break time surfing the internet looking at exotic destinations and fantasizing what it would be like to travel there without actually making the lottery ticket purchase.
You don't say!

Originally Posted by Ladewig View Post
As for watching the drawing, I'd just skip that bit ...
Skip it enroute to what/where?!

Originally Posted by Ladewig View Post
... but if one wants to, one could write down six numbers and when they don't win the big jackpot, one could smile wryly about what a sucker's game the lottery is and how easy it is to not play it.
I can imagine you're a real hoot to have around!

Originally Posted by Dan O. View Post
Yep, that pretty much sums up a gambling habit.
What? How? How does boozing constitute gambling? There's a real and direct return on investment!
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Old 27th February 2012, 08:08 AM   #143
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Originally Posted by Southwind17 View Post
I can imagine you're a real hoot to have around!
Actually, I am. I do not understand why you interpreted my comment as an issue with my being a hoot.

The bottom line is that it is a sucker's game designed to separate rubes from the money.

Spending money for anticipatory pleasure of lottery fantasies is a waste of money, because as I have shown, people who do not or cannot buy tickets can still fantasize about suddenly becoming independently wealthy. People in jail, people too young to buy tickets, people too poor to buy tickets - many of these people do engage in anticipatory fantasies about winning the lottery. You don't have to have an actual ticket in your hand to fantasize about winning.

I mentioned that I occasionally buy tickets, but because I know enough math to accurately calculate the odds, I am willing to admit that I am participating in a suckers' game.

Last edited by Ladewig; 27th February 2012 at 08:09 AM.
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Old 27th February 2012, 10:18 AM   #144
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Originally Posted by Ladewig View Post
You don't have to have an actual ticket in your hand to fantasize about winning.
But you do to have a chance at winning.
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Old 27th February 2012, 11:28 AM   #145
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Originally Posted by alfaniner View Post
But you do to have a chance at winning.
Ah, yes. I see the mistake I was making.
I was rounding off the calculations to five decimal places.

The chance of winning with one ticket = 0.00000
The chance of winning with no ticket = 0.00000
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Old 27th February 2012, 03:32 PM   #146
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Originally Posted by Ladewig View Post
Ah, yes. I see the mistake I was making.
I was rounding off the calculations to five decimal places.

The chance of winning with one ticket = 0.00000
The chance of winning with no ticket = 0.00000
Do people ever win lottery jackpots?!
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Old 27th February 2012, 04:11 PM   #147
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Even for one of the biggest drawings in the powerball lottery, the expectation that there would be a winner was only about 42% (link). If that's the best they can do then the answer is no.


ETA: the actual number of winers was this value rounded to the nearest whole number.

Last edited by Dan O.; 27th February 2012 at 04:14 PM.
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Old 27th February 2012, 04:11 PM   #148
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Originally Posted by Southwind17 View Post
What does, then?
Games in which you might have an edge include poker, backgammon, horse- and dog-racing, bridge, cribbage. Football Pools Any gamble in which your judgement might be better than others. Zero-sum games are best, of course.

Quote:
Probably because they could afford it, just like they could afford the occasional meal out?!
Football Pools were part of their culture, whereas meals out weren't. When they broke through into the middle classes (bless 'em) that barely changed.

My great-gran believed all card-games to be sinful except cribbage and rummy (and rummy was a bit risque). She had a theology all of her own.
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Old 27th February 2012, 04:13 PM   #149
CapelDodger
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Originally Posted by Ladewig View Post
Ah, yes. I see the mistake I was making.
I was rounding off the calculations to five decimal places.

The chance of winning with one ticket = 0.00000
The chance of winning with no ticket = 0.00000
Are you going to round your whole life down to 5 decimal places? Take a walk on the wild side from time to time!
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It's a poor sort of memory that only works backward - Lewis Carroll (1832-1898)

God can make a cow out of a tree, but has He ever done so? Therefore show some reason why a thing is so, or cease to hold that it is so - William of Conches, c1150
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Old 27th February 2012, 05:50 PM   #150
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Originally Posted by Dan O. View Post
From the cited link
Even for very large jackpots, the expected value of a ticket is still less than the price of the ticket.
A 50% house advantage?! If a casino slipped weighted dice into a craps game, the house advantage would still not be that high.

Keno has only a 30% house advantage! Keno!

There is no table game in any [ETA legal] casino anywhere in the U.S. with a house advantage even close to that.

The house advantage in lotteries is twice as bad as the house advantage at a casino's big six wheel (aka circus wheel, wheel of fortune, money wheel).1 And that game is the archetypal rubes' game.

A suckers' game designed to separate rubes from their money.
Or as was stated in some of the several other lottery threads in JREF, a voluntary tax on people who cannot do math.


ETA
1) I am talking about American big six. Australian big six has few slots resulting in a house advantage of only 8%

Last edited by Ladewig; 27th February 2012 at 06:09 PM.
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Old 27th February 2012, 07:19 PM   #151
Southwind17
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Originally Posted by CapelDodger View Post
Games in which you might have an edge include ...
Important word that: "might"!

Originally Posted by Dan O. View Post
Even for one of the biggest drawings in the powerball lottery, the expectation that there would be a winner was only about 42% (link). If that's the best they can do then the answer is no.
Would you like me to prove you wrong, or shall we take that as a given?!
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Old 27th February 2012, 07:28 PM   #152
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I'm sure you could cherry pick a few outliers and claim that proves your point. But the statistics will consistently show that the people playing the state lotteries will loose on average 50% of what they put in.
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Old 27th February 2012, 11:02 PM   #153
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Originally Posted by Southwind17 View Post
... and how, I wonder, does that compare to, say, the NPV of what you're likely to spend on completely wasteful trivialities that have absolutely no possible prospect of betterment; indeed more than likely detriment, over the same years? I suppose smoking (and possibly drinking?!) aren't fair comparisons, but I wouldn't mind seeing the figures!
It depends on how much you spend but the NPV of any annuity is a simple multiple of the annuity.

If you spend $W every year on "completely wasteful trivialities" and the interest rate is 8% then the NPV of your "wasteful" expenditure is $W/0.08 or 12.5 x $W.
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Old 28th February 2012, 01:13 AM   #154
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Originally Posted by Southwind17 View Post

Originally Posted by Southwind17 View Post
I think what jp means is that a combination of patterned numbers is less likely than a combination of un-patterned numbers, which, of course, is correct. He just didn't word it very well.


Can it be put more simple than that?!
I don't get why this is important. We could divide the available lottery numbers into any major and minor grouping: Say the set of numbers that include even numbers (A), and the set that doesn't (B).
And we can make the observation that the winning combination is more likely to come from set A than set B.
But this observation is useless. As soon as you actually make your choice, whether it is from set A or set B, the chances of that particular combination winning is the same as any other, whether from set A or set B: 1 in N!/(N - 6)!
There's no way to translate the fact that the winning numbers are more likely to come from one arbitrarily chosen division or another, into an increased chance of winning.
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Old 28th February 2012, 01:28 AM   #155
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Originally Posted by CapelDodger View Post
Games in which you might have an edge include poker, backgammon, horse- and dog-racing, bridge, cribbage. Football Pools Any gamble in which your judgement might be better than others.
I'd agree with some of that, but certainly not UK football pools. As I recall some 30% is skimmed in 'commissions', and I seriously doubt an individual's skill will overcome that kind of rake.

Horse and dog-racing? Dunno. High St bookies typically run an 'over-round' of about 15% I believe. Hard to beat that, and you're up against unkown opponents who are effectively setting the odds. Even the racing-paper pro tipsters are routinely shown to be losers in those published 'tipster leagues'.

As to those other games, finding opponents known to be weaker can be a skill in itself
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Old 28th February 2012, 01:38 AM   #156
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Originally Posted by Southwind17 View Post
About 15 million to 1, which is greater than the odds of my true anecdote, and which, hence, trumps yours:

I took a vacation in Rome. One afternoon I bought a circular 'coin-like' pendant from a market stall to put on my existing neck chain. Unfortunately, however, it didn't have a metal split ring on it, only a hole in it, so I determined to locate a small split ring later, possibly from a jewellers.

After returning to the hotel, however, whilst heading to the bathroom to take a shower, I stood on something with my bare foot on the hard wooden floor boards. Upon examination it was, of course ... a metal split ring, perfectly sized.

What are the odds? Around 20 million to 1, I'd say, give or take.
You shuffle a deck of cards seven times (In Shuffling Cards, 7 Is Winning Number) then lay the cards out on a table. The outcome you're witnessing has a probability of:
1 in 80,658,175,170,943,878,571,660,636,856,403,766,975 ,289,505,440,883,277,824,000,000,000,000
Are you amazed by this?
Do you think you just witnessed a miracle?
Hopefully not!
It would certainly be amazing if the outcome had been predicted before the shuffle, but after the event, well, no one's going to get excited, despite the fact that we might care to look at the numbers and call them staggeringly improbable.
Your anecdote would be remarkable if while buying the pendant, you had said to yourself, no I won't worry about the missing ring because I'm going to find one later on the floor of my hotel bathroom. (And just as a further insight, if you had found the ring at any point between Rome and Australia wouldn't you have counted that as just as remarkable?)
No, as it stands your 20 million to 1 is far less numerically impressive than that 80 unvigintillion to 1 cards shuffle...

Wikipedia: The law of truly large numbers
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Old 28th February 2012, 02:34 AM   #157
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Originally Posted by Alex Cured View Post
You shuffle a deck of cards seven times (In Shuffling Cards, 7 Is Winning Number) then lay the cards out on a table. The outcome you're witnessing has a probability of:
1 in 80,658,175,170,943,878,571,660,636,856,403,766,975 ,289,505,440,883,277,824,000,000,000,000
Are you amazed by this?
Do you think you just witnessed a miracle?
Hopefully not!
It would certainly be amazing if the outcome had been predicted before the shuffle, but after the event, well, no one's going to get excited, despite the fact that we might care to look at the numbers and call them staggeringly improbable.
Your anecdote would be remarkable if while buying the pendant, you had said to yourself, no I won't worry about the missing ring because I'm going to find one later on the floor of my hotel bathroom. (And just as a further insight, if you had found the ring at any point between Rome and Australia wouldn't you have counted that as just as remarkable?)
No, as it stands your 20 million to 1 is far less numerically impressive than that 80 unvigintillion to 1 cards shuffle...
You're wrong. The fact that I identified the need for a split ring before I stumbled upon one coincidentally makes it amazing. If I'd stumbled upon it without any predicated context then thought: "Actually, I could use that.", well that would be different. But that's not what happened.

Last edited by Southwind17; 28th February 2012 at 02:36 AM.
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Old 28th February 2012, 04:14 AM   #158
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Originally Posted by Alex Cured View Post
I don't get why this is important. We could divide the available lottery numbers into any major and minor grouping: Say the set of numbers that include even numbers (A), and the set that doesn't (B).
And we can make the observation that the winning combination is more likely to come from set A than set B.
But this observation is useless. As soon as you actually make your choice, whether it is from set A or set B, the chances of that particular combination winning is the same as any other, whether from set A or set B: 1 in N!/(N - 6)!
There's no way to translate the fact that the winning numbers are more likely to come from one arbitrarily chosen division or another, into an increased chance of winning.
It's not important; it's trivial, but true nonetheless.
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Old 28th February 2012, 05:14 AM   #159
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Originally Posted by Alex Cured View Post
But this observation is useless. As soon as you actually make your choice, whether it is from set A or set B, the chances of that particular combination winning is the same as any other, whether from set A or set B: 1 in N!/(N - 6)!
There's no way to translate the fact that the winning numbers are more likely to come from one arbitrarily chosen division or another, into an increased chance of winning.
In Florida, there is a publication called "Bargain Trader". I don't know if they still do, but they used to print a complete history of Fl Lotto winning numbers and a count of how many times each number had hit.

Some people would look at the most frequently drawn numbers and bet them because they were "hot". Some people would look at the least frequently drawn numbers and bet them because they were "due".

The reasoning in both cases is, of course, fallacious*. I think there's both a Gambler's Fallacy and an Inverse Gambler's Fallacy that apply here, though I always forget which is which.

*assuming a random draw, of course. If certain balls were weighted or otherwise favored, the "hot" number would in fact be a better bet.

Last edited by Fast Eddie B; 28th February 2012 at 05:19 AM.
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Old 28th February 2012, 07:16 AM   #160
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Originally Posted by Alex Cured View Post
1 in N!/(N - 6)!
that should be: 1 in N!/(N - 6)!/6!

To see that this is true, just ask how many possible combinations of N-6 balls are left after 6 balls have been removed.
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