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Math The Almighty Buck Science

Researchers Create a Statistical Guide To Gambling 185

Posted by samzenpus from the crunch-the-numbers dept.
New submitter yukiloo writes "An early Christmas treat for the ordinary Joe who is stuck with a Christmas list that he cannot afford and is running out of time comes from two mathematicians (Evangelos Georgiadis, MIT, and Doron Zeilberger, Rutgers) and a computer scientist (Shalosh B. Ekhad). In their paper 'How to gamble if you're in a hurry,' they present algorithmic strategies and reclaim the world of gambling, which they say has up till recently flourished on the continuous Kolmogorov paradigm by some sugary discrete code that could make us hopefully richer, if not wiser. It's interesting since their work applies an advanced version of what seems to be the Kelly criterion."
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Researchers Create a Statistical Guide To Gambling More

Researchers Create a Statistical Guide To Gambling

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  • Do you even bother to edit submissions anymore? (Score:5, Interesting)

    by questioner ( 147810 ) on Sunday December 11, 2011 @04:50PM (#38337546)

    Half this submission makes no sense, grammatically or otherwise.

    • Re: (Score:2, Informative)

      by msauve ( 701917 )
      That's OK. It's not really a paper, it's just a way to sell Maple software.

    • Re: (Score:2)

      by jd ( 1658 )

      Gramatically looks fine. I see subjects, objects and verbs in all the right places. There are commas where they're not needed and no commas where they are, but comma rules are regularly broken. Just as s's is now considered acceptable (I consider it gross and a sign of mental fragility), comma rules aren't considered important any more outside of formal writing. Unless you know something about Slashdot the rest of us don't, formal writing doesn't really fit the description.

    • Actually, the grammar is pretty darn good. There are two compound, complex sentences. There is one compound sentence marred only by the lack of a comma between the words "interesting" and "since." There is no failure of subject-verb agreement. Pronouns are used correctly and with no confusion over attribution. Well above the usual standards here, I say.

    • Re:Do you even bother to edit submissions anymore? (Score:4, Interesting)

      by carnivore302 ( 708545 ) on Monday December 12, 2011 @04:01AM (#38340986) Journal

      I find anything related to the Kelly Criterion interesting. It made me a rich guy :-)

      To clarify, try this experiment: sit down with a group of friends and pretend you all have 100 dollars. Ask everybody what their stake will be for the following game: you throw a coin and if it ends up heads, everybody gets 1.5 times his stake, plus the initial stake returned. Tails means the stake is lost. First of all: this game has a positive expectancy so you should play. But the question of how much you should bet is an interesting one. It is easy to see why: bet nothing and you will not profit. Bet everything and sooner or later you will be wiped out. Try the game with a couple of friends who haven't heard of Kelly and chances are everybody has lost his stake in a couple of rounds.

        Once you find a profitable strategy that works, and scales to large large amounts, Kelly is really useful to know.

      Mark

  • Well.... (Score:5, Interesting)

    by jd ( 1658 ) <imipak@ y a hoo.com> on Sunday December 11, 2011 @04:51PM (#38337556) Homepage Journal

    The news story posted on Slashdot not that long ago on a casino successfully suing a gambler of all his winnings because the machine's system for preventing you from winning wasn't working tells me that the only paradigm in use is "give us your money... or else!"

  • Comment removed based on user account deletion

  • Conclusions (Score:5, Interesting)

    by Anonymous Coward on Sunday December 11, 2011 @04:56PM (#38337584)

    The three authors completely agree on the mathematics, but they have somewhat different views about the
    significance of this project. Here they are.

    Evangelos Georgiadis’ Conclusion
    We provided a playful yet algorithmic glimpse to a field that has up till recently flourished on the Kolmogorov,
    measure-theoretic paradigm [as evidenced by the work of Dubins and Savage [4] (see [7] for more recent
    developments]. The advent and omnipresence of computers, however, ushered an era of symbol crunching
    and number crunching, where a few lines of code can give rise to powerful algorithms. And it is the ouput
    of algorithms that usually provides insight (and inspiration) for conjectures and theorems. Those, in turn,
    can then be proven in their respective measure-theoretic settings. Additionally, a computational approach
    lends itself easily to more complex scenarios that would otherwise be considered pathological phenomena
    (and would be fiendishly time-consuming to prove – even for immortals like Kolmogorov and von Neumann).

    Doron Zeilberger’s Conclusion
    Traditional mathematicians like Dubins and Savage use traditional proof-based mathematics, and also work
    in the framework of continuous probability theory using the pernicious Kolmogorov, measure-theoretic, par-
    adigm. This approach was fine when we didn’t have computers, but we can do so much more with both
    symbol-crunching and number-crunching, in addition to naive simulation, and develop algorithms and write
    software, that ultimately is a much more useful (and rewarding) activity than “proving” yet-another-theorem
    in an artificial and fictional continuous, measure-theoretic, world, that is furthermore utterly boring.

    Shalosh B. Ekhad’s Conclusion
    These humans, they are so emotional! That’s why they never went very far.

  • is not to play.

  • Not a Useful Guide (Score:5, Informative)

    by Anonymous Coward on Sunday December 11, 2011 @05:03PM (#38337636)

    The paper is about how much to bet (your strategy) on a given round if you have x dollars and want to win N dollars. This is problematic for two reasons.

    First, their method only works when the probability of winning is >0.5, which never happens in any real casino.

    Second, almost nobody really bets this way. Most people don't go to a casino looking to win N dollars. Instead, they go to the casino hoping to play for time T without losing more than N dollars (although people might not be up front about that goal).

    Another problem is that they assume that the probabiilty is constant with each round. That's true for some games (roulette), but not for others (blackjack).

    • Mod parent up.

      First, their method only works when the probability of winning is >0.5, which never happens in any real casino.

      This is not quite true. In blackjack, there are times when you have p>0.5. That's the point of counting cards. Some games, like poker, are really games of skill. Others, like horse racing, involve non-random aspects.

      Another problem is that they assume that the probability is constant with each round. That's true for some games (roulette), but not for others (blackjack).

      Another thing that makes the paper not really applicable to real life is that it assumes you can choose to bet any amount. In reality, if you're in a casino playing blackjack, one of the most common ways for the management to detect that you're counting cards and throw you out i

      • Another thing that makes the paper not really applicable to real life is that it assumes you can choose to bet any amount. In reality, if you're in a casino playing blackjack, one of the most common ways for the management to detect that you're counting cards and throw you out is that they notice that you're varying your bets according to a certain pattern.

        I don't frequent casinos (there are few places more boring to me), but my understanding is that they generally allow, if not encourage card counting because most folks do it badly, and lose. The _hope_ of winning brings people in with their latest 'guaranteed winning scheme'. Card counting is hard, and as I understand it casinos have mostly changed their shuffling schedule and other things to make it harder. If, despite all these impediments, you appear to be doing too well, I suspect that they start to

      • Re: (Score:2)

        by N1AK ( 864906 )

        This is not quite true. In blackjack, there are times when you have p>0.5. That's the point of counting cards.

        Actually, it was as he specifically said he was talking about 'any real casino'. Blackjack as played in casinos is effectively impossible to game due to all the counter-measures in place now. If you gamble in a casino you are either part of an elaborate and complex attempt to cheat the house or like 99.99% of people playing chance is the only way you're coming away with a win.

    • Re:Not a Useful Guide (Score:5, Informative)

      by Tacvek ( 948259 ) on Sunday December 11, 2011 @05:34PM (#38337866) Journal

      Yeah. The title of the paper is a bit misleading.

      They are studying the case of some betting game with a fixed probability of winning p (with p>1/2) and a fixed 1:1 payout, using a discrete model of money, with no maximum bet, a minimum bet of $1, and all bets being constrained to a multiple of $1.

      It is already known that if you enter with x dollars and you have a target amount of N, your best strategy is to always bet the minimum. Needless to say always betting the minimum can take forever, so even under this very unlikely set of circumstances, you would not want to actually follow that strategy.

      So instead they introduce a round limit T, and introduce software that solves the relevant dynamic programming recurrence determine what you should bet given the probability p, your current balance x', your desired amount N, and the remaining number of rounds until the loan shark kills you T'.

    • Second, almost nobody really bets this way. Most people don't go to a casino looking to win N dollars. Instead, they go to the casino hoping to play for time T without losing more than N dollars (although people might not be up front about that goal).

      People usually go to a casino with as much money as they are willing to lose. I also think the idea of spending at least a given time wile losing a set amount is a bit absurd unless it involves the chance of winning.

      You could make a case for a fun casino evening involving maximizing your chances of winning N dollars within time T1 while still not going broke before time T2. A strategy of proportional betting (I assume the paper does that) will limit your chances of going broke regardless.

    • Re: (Score:3)

      by Kjella ( 173770 )

      First, their method only works when the probability of winning is >0.5, which never happens in any real casino.

      Against the house, no. Against other poker players for example, it's possible if you've identified weaknesses in the other players. But even if you've identified a 52% chance to win, how hard should you play to extract the most possible money while not getting yourself eliminated by bad hands? After all you still have a 48% chance of losing. The blinds going up means you have time pressure, you can't keep playing tiny bets forever. Not that I think poker players think this way, but it doesn't seem that usel

    • You're looking at the constraints wrong. Most games can fit the assumptions quite easily. For example, if you think of the rounds not during a game, but as repeated iterations of the same game.

      Take blackjack. Every time you play the game with a fresh set of cards, the ultimate probability of winning is the same, provided you use the same strategy each time. That counts as one round, with a winning probability p.

      Also, you're wrong about p >0.5, there are strategies for p 0.5 .

      Mathematics results a

    • No kidding (Score:5, Insightful)

      by Sycraft-fu ( 314770 ) on Sunday December 11, 2011 @07:56PM (#38338624)

      My guide to making the most money gambling: Don't.

      In any casino the odds are always, ALWAYS stacked against you. They don't hide this fact, either. The odds are published and you can easily notice that the payout is less than the probability of getting something. They are in business to make money, it has to be this way or they'd go broke.

      So don't gamble to make money. If you enjoy the thrill of it, if it entertains you, and you can afford it, then by all means. But don't try and find some way to gamble "quickly" that will make you money because it won't. Any money made is purely luck and your strategy of what you bet on will play very little in to it.

      Play the game for enjoyment.

    • http://wizardofodds.com/games/video-poker/ [wizardofodds.com]
      "Full-Pay Deuces Wild optimal strategy (return of 100.76%)"

  • How to lose all your money gambling during the holidays in a bad economy because you don't understand multivariate calculus. Accompanied by a Maple package on a separate site. Note: Do not attempt to eat the maple package after you've gambled away your grocery money.

  • Note about Ekhad (Score:5, Interesting)

    by werdnam ( 1008591 ) on Sunday December 11, 2011 @05:08PM (#38337668)
    I'm not sure if the original submitter had his tongue in cheek by describing the co-author Ekhad as a "computer scientist." Just in case he didn't, note that Shalosh B. Ekhad is actually Zeilberger's computer. Since most of Zeilberger's research depends heavily on computations, and (I think) as a nod to some of his philosophical positions, Zeilberger usually lists his computer as a coauthor on his papers. So I guess Ekhad is a computer scientist, but not quite in the way we usually mean. :)

  • According to the paper they are (initially) using a p=3/5 for an even return which to me is a hypothetical or illegal situation.

    Am i missing something here or is this just a paper for if you find your self in lucky situation where the house is loss leading?

    • In blackjack, watch the cards closely. Every time a 2-6 is dealt, add 1. Every time a 10, jack, queen, king, or ace is dealt, subtract 1. For example, if someone is dealt blackjack (A-10), subtract 2. If the running total since the last shuffle is at least four times the number of decks left in the shoe, the house is loss leading.

  • Shalosh B. Ekhad (Score:5, Interesting)

    by slasho81 ( 455509 ) on Sunday December 11, 2011 @05:30PM (#38337838)
    Shalosh B. Ekhad is not a person. From Wikipedia [wikipedia.org]:

    Zeilberger is known for crediting his computer "Shalosh B. Ekhad" as a co-author ("Shalosh" and "Ekhad" mean "Three" and "One" in Hebrew respectively, referring to the AT&T 3B1 model).

  • Continuous vs Discrete (Score:3, Interesting)

    by yukiloo ( 2527940 ) on Sunday December 11, 2011 @10:27PM (#38339520)
    After having read the paper it becomes evident that both authors have a liking for analyzing the problem in a discrete light. My degree is in mathematics, number theory so I am slightly biased myself. For that matter, I got intrigued by the fact that when dealing with the continuous version of gambling one does deal with unrealistic assumptions. One of which is ... money is indefinitely divisible which of course this is a bonkers assumption. Now assuming money has finite integral values, the analysis becomes much more difficult, particularly in the light of edge effects. So, that is why the authors seem to resort to heavy computer simulation.

  • All that work... (Score:4, Insightful)

    by AlienSexist ( 686923 ) on Sunday December 11, 2011 @11:48PM (#38339984)
    All of this effort and brainpower to produce a guide that might as well say "Don't gamble"

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