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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

The topic here several days ago about the ethics of teaching people to play gambling games got me thinking.

It seems that mathematicians are in the best position to understand the theoretical nature of gambling games. I wonder, then, whether you guys think that there is any positive value in any form of gambling at all, and what your attitude towards it is in general.

Personally I have spent a lot of time with a compulsive gambler, and I think I have gained a lot of insight into the gambling mindset (which is every bit as foolish as people imagine). The old cliche is very true: Most people bet on possibility, not probability.

The lottery is a good example of this. Whenever the odds of the lottery are brought up, I usually hear "You've got to be in it to win it" (to which I usually reply "Yes, and to lose it as well"). But nobody who truly understood their odds, and actually cared about the money, would respond in this way. When I looked into a common form of lottery here, I discovered two key facts:

1. If the jackpot is greater than about $55,000,000 then you have a mathematical edge

2. However, even if you were to buy three tickets every day, it would, on average, take you around 42,000 years to realise that edge.

Can you run a profitable business on the lottery? Absolutely! All you have to do is buy tens of millions of dollars worth of tickets on a high jackpot and hope for the best! (Double or nothing!)

There is a similar story about the card-based version of cra ps. I learned some time ago that, with rigorous study of the art and science of counting cards and abuse of the volatility index, this game can be beaten. All that is required is around 8 hours of intense mental concentration and tracking in order to take advantage of a statistical anomaly that will net you an average profit of 15 cents an hour!

On a more serious note, there have been a handful of very successful businesses exploiting the game of 21. This requires teams and a shared bank, however. The idea is to hit choice locations around the world, be in one venue no longer than 45 minutes, have some guys watching the volatility at tables with good rules and signal to another guy to come in pretending to be a high-roller when the deck is very favourable. This "profession" is infinitely more difficult than it was some decades ago, however.

Besides pokr and acting as the bookie for people to place sports or other bets, the only other financially favourable form I can think of is unpopular raffle tickets - but nobody wants to be looked down on for selling the prizes for a profit, lol

As a final note here, I think the best argument in favour of occasional gambling (besides enjoyment) is the idea of "nonlinear utility". This is the idea that, for example: Just because 100 one-cent coins make up a dollar does not mean having a dollar is worth 100x the amount that having a one-cent coin is worth; it is probably worth at least a million times more because a one-cent coin is practically useless (it doesn't even exist in a lot of countries; it is ignored in shopping transactions)! This concept seems to me to provide a (limited) basis for making bets with a negative expected value - intuitively, you are risking some "spare change" you do not care about for a slight chance of something you would very much care about (much more than the quotient of it and what you're risking would indicate).

Nevertheless, I do not have much of an opinion, and would like to know what you think (:

*Last edited by Relentless (2016-01-10 07:55:30)*

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Gambling can yield positive utility because not all players are rational.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

Do you mean: Gambling can benefit some people even though they lose the gambling games? That could make it rational for some people to gamble; rationality has to do with decision-making, not values.

I recall a study that showed that buying lottery tickets is a satisfying experience that could easily be worth the loss of money. The same may be true of many kinds of gambling, if the bankroll is not needed.

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Buying lottery tickets has a negative expectation and isn't rational.

To clarify, is this post about values?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

Yes, it is about gambling values. What are your gambling values?

Actually, buying lottery tickets may have a positive expectation if they are cheap and the jackpot is very high - but you will have to buy millions of tickets before you can expect a profit.

I was talking about expectation that includes things other than money, like satisfaction. What did you mean about positive utility?

*Last edited by Relentless (2016-01-18 04:41:03)*

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 135

People buying powerball tickets...

**The eclipses from Algol come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.**

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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

Haha, she had better be worth a million trips to Aspen with nine hours in the wrong direction, or roughly 4700 years of driving. Which is worth just over $500 million in fuel.

But, you know, you've got to be in it to win it!

*Last edited by Relentless (2016-01-21 18:36:28)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,668

He thinks Aspen is in France.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

I have recently analysed my local Keno. It turns out that, like the lottery, a positive expectation is possible - but making a profit with that edge is unrealistic.

Specifically, the player has an advantage in Keno when the jackpot for 10 out of 10 numbers is higher than about $4.1 million. But in order to get that jackpot, the player must play an average of over 8 million games, which, even if the player had the $4.1 million to stake, would take 220 years at 100 games per day.

If 100 players teamed up to play 50 games per day each, it could be done in 4 and a half years ... but then each player would have to stake $41k and spend a considerable amount of time for years to get an average of something like $1,000 per year.

I like these examples where gambling games can be beaten mathematically, but not practically. There are many of them. This is exactly how the lottery works ... it can mathematically be beaten with a jackpot over $55 million with my local ticket prices, but the sheer average number of tickets you would have to buy (about 46 million I think) before you win makes the idea ludicrous. Even if you somehow got 100,000 people to buy $600 worth of tickets with a shared bank and a particularly high jackpot, they would be unlikely to average more than $150 profit each; and that's before considering the chance that some other person wins as well and the entire prize has to be cut in half or thirds!

*Last edited by Relentless (2016-01-25 16:26:03)*

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