4 ms·

The math of gambling

18 points by peter123 17y ago

jvdh 17y ago
The way she describes winning at roulette is bogus. First of all, if your money is doubled when you hit the right colour, you don't make any profit in the long run. You will stay on the same amount. Second of all, there is a 0, and often also a 00 on the roulette wheel, which is neither red nor black. This means that the chance you're correct is less than 50%, so you stand to make a loss in the long run. There is no way to win at roulette, without using a computer to predict where the ball is going to be, based on the movement and spinning of the wheel. And I seriously doubt that even that is possible using just human observation and a trigger in your foot. [edit: the author is female, sorry about that]
- tokenadult 17y ago
  The way he describes winning at roulette is bogus. New Scientist appears to be in serious decline.
- deleted 17y ago
  [deleted]
- splat 17y ago
  I think you're misinterpreting the author's point about roulette. She never claimed that you could profit off of roulette in the long run. You can, however, almost certainly profit off of it in the short run. The strategy she describes has one double one's bet if one loses. If you bring enough money to cover 7 losses (which means you would have to have roughly 100 times your initial bet), then you have a >98% chance of coming out ahead. You won't be ahead by much, and the strategy won't work in the long run (i.e. you can only do it a couple of times--when you inevitably end up with 7 consecutive losses it will more than wipe out any earnings you make), but it is nevertheless a legitimate strategy to "beat" roulette in the short term.
  - jvdh 17y ago
    True, I did misinterpret that. And she does own up to it that after 7 streaks you'd need 1280 pounds if you initially start with 10. Still, the article states that there's a 50:50 chance of landing on black or red, which is simply not true.
    - splat 17y ago
      Fair enough. The article also claims that the outcome of a coin flip is 50:50, which is also not true.
      - req2 17y ago
        You're mixing theoretical odds and practical odds, which might be considered sloppy. Additionally, unfair coins can trivially be used as fair coins, but unbalanced roulette wheels cannot easily be used as fair roulette wheels.
        splat 17y ago
        A fair coin has a roughly 51% chance of landing with the same side up as it started with. See the paper by Diaconis et al. "Dynamical Bias in the Coin Toss."
        req2 17y ago
        A fair coin is one on which p = 0.5. A coin that has a 51% chance is clearly not a fair coin. This isn't even what I was talking about, but is still equally easy to turn into a fair coin. In this case, caller calls in the air after flipper hides the side that starts up. 0.5 * 0.51 + 0.5 * 0.49 = 0.5 For any other case, flip a coin twice. Assign one person HT and the other person TH, reflipping TT and HH. Since p * (1 - p) = (1 - p) * p, the dual flip is a fair flip. Please don't mention the possibility of sleight of hand next.
  - bigwill 17y ago
    I hear what you're both saying. But I wouldn't call beating roulette in the short term a legitimate strategy exactly because it only works in the short run--strategies are supposed to work for longer than that! The only legitimate value I can see is that if you actually enjoy the experience of playing roulette that it's worth paying for it. Anyone who's willing to buy volatility can win in the short term. Otherwise, stick to a game of skill and get some money on the table while you do it. If you're good you can get some vol. and some positive EV.
- huangm 17y ago
  re: roulette What the author is describing is a 'Martingale' strategy, and it is indeed a surefire way of making a profit (with one critical caveat: you need an unlimited bankroll). After each win, you always earn a profit of X (where X is your base bet), regardless of how many rounds you have lost before. Without a sufficiently large bankroll relative to X, however, probability of bankruptcy is high.
  - burnout1540 17y ago
    And this is why casinos always have a table minimum AND a table maximum.
    - mynameishere 17y ago
      No, it isn't. The house can only lose the initial amount. I bet 50, and lose. I bet 100, and lose. I bet 200, and lose. I bet 400, and lose. I bet 800, and lose 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, and then... ...I lay 819,200 dollars on the table and WIN! 50 dollars. The reason they have limits is so that Sheik Abudab can't come in and lay down 500 million dollars and bust them. That is one valid reason to take bad odds: If you can destroy something as a side effect, without really being in danger yourself.
      - burnout1540 17y ago
        In your Martingale example, the table maximum would most likely be set around $2000. So if you lose 6 times (on your $50, $100, $200, $400, $800, and $1600 bets), you can't double your bet anymore. You'll be stuck with betting $2000 at most, which means you can longer guarantee yourself a profit. But now that I think about it, you could always just move to another table with a higher limit. Of course, if you're going through all this trouble to make $50, you probably don't have the bankroll to keep going. Maybe another reason for tables having different limits is that the pit bosses don't trust the dealers (or security?) in the low-roller areas to handle money above a certain amount?
        deleted 17y ago
pyre 17y ago
One way that I would 'win' at roulette in Grand Theft Auto: San Andreas was to always bet equal amounts on red/black and even/odd. My reasoning was that there are 4 possible outcomes. I have a 50% chance of breaking even, a 25% chance of winning, and a 25% change of losing. You probably can't 'win big' with such a strategy, but you've at least minimized the probability of a loss from 50% to 25%. You've also minimized the probability of a win by as much too, though. I'm no stats guru so I don't know how well this would work out on an actual roulette table... {edit} I should mention that I worked at a casino for a while, and roulette is the game with the highest probability in favor of the house. Blackjack is the lowest. Casinos really only have Blackjack tables because patrons want them, or else they would probably get rid of them pretty quickly. {/edit}
- deleted 17y ago
  [deleted]
- jvdh 17y ago
  Casinos really only have Blackjack tables because patrons want them, or else they would probably get rid of them pretty quickly. True, even with a simple strategy you can cut your theoretical loss to about 1-2% (without counting cards). But casinos have blackjack because most players don't know how to play. Most people don't follow that simple strategy (they often have leaflets explaining it too!). With counting cards you can make it profitable for you. But casinos will make life very difficult for you if they find out you're counting cards. See also the movie about the MIT Blackjack team: http://en.wikipedia.org/wiki/21_(2008_film) http://en.wikipedia.org/wiki/21_(2008_film)
  - pyre 17y ago
    The casino I worked at used some formula to generate the number of 'points' you would earn towards free stuff based partially on the risk of the game that you were playing. They used the ~1-2% number for blackjack (or whatever the low number of when you play what blackjack players call 'the perfect game') rather than a larger number that might be closer to the 'average' skill of players. This signaled to me that the casinos -- or at least the one I worked at -- in general treat the overall risk of blackjack as the low risk that skilled (non-counting) players can achieve, regardless of the number of people that might come in and ignore the simple, effective strategies to the game. Personally I think that the casinos would rather reduce the risk to themselves from skilled players as well as card counters and just remove all the blackjack tables, sending all those inexperienced gamblers onto games like roulette where they might lose a larger portion of the money they brought with them.
deleted 17y ago
[deleted]
TriinT 17y ago
I never, ever learned anything from a newscientist.com article. Those articles are cute, but one learns nothing deep. I say we go directly to the source! Here is it, Ed Thorp's The Mathematics of Gambling: http://www.bjmath.com/bjmath/thorp/tog.htm http://www.bjmath.com/bjmath/thorp/tog.htm which is the true "bible" of scientific betting. For the mathematically-inclined, I also recommend: http://en.wikipedia.org/wiki/Gambling_and_information_theory http://en.wikipedia.org/wiki/Gambling_and_information_theory http://en.wikipedia.org/wiki/Kelly_criterion http://en.wikipedia.org/wiki/Kelly_criterion and if you still have some energy left, try this: A Markov Chain Analysis of Blackjack Strategy http://www.ece.rice.edu/~crozell/courseproj/MCBJ.pdf http://www.ece.rice.edu/~crozell/courseproj/MCBJ.pdf Have fun! And remember: life is too short to read crappy articles!
mattheww 17y ago
Incidentally, if I wanted to put my math skills to work in a casino, I would play poker. This game is one where the odds have not been stacked against me and a little math drastically alters my expected values.

18 points by peter123 17y ago

jvdh 17y ago

The way she describes winning at roulette is bogus. First of all, if your money is doubled when you hit the right colour, you don't make any profit in the long run. You will stay on the same amount. Second of all, there is a 0, and often also a 00 on the roulette wheel, which is neither red nor black. This means that the chance you're correct is less than 50%, so you stand to make a loss in the long run. There is no way to win at roulette, without using a computer to predict where the ball is going to be, based on the movement and spinning of the wheel. And I seriously doubt that even that is possible using just human observation and a trigger in your foot. [edit: the author is female, sorry about that]

tokenadult 17y ago
The way he describes winning at roulette is bogus. New Scientist appears to be in serious decline.
deleted 17y ago
[deleted]
splat 17y ago
I think you're misinterpreting the author's point about roulette. She never claimed that you could profit off of roulette in the long run. You can, however, almost certainly profit off of it in the short run. The strategy she describes has one double one's bet if one loses. If you bring enough money to cover 7 losses (which means you would have to have roughly 100 times your initial bet), then you have a >98% chance of coming out ahead. You won't be ahead by much, and the strategy won't work in the long run (i.e. you can only do it a couple of times--when you inevitably end up with 7 consecutive losses it will more than wipe out any earnings you make), but it is nevertheless a legitimate strategy to "beat" roulette in the short term.
- jvdh 17y ago
  True, I did misinterpret that. And she does own up to it that after 7 streaks you'd need 1280 pounds if you initially start with 10. Still, the article states that there's a 50:50 chance of landing on black or red, which is simply not true.
  - splat 17y ago
    Fair enough. The article also claims that the outcome of a coin flip is 50:50, which is also not true.
    - req2 17y ago
      You're mixing theoretical odds and practical odds, which might be considered sloppy. Additionally, unfair coins can trivially be used as fair coins, but unbalanced roulette wheels cannot easily be used as fair roulette wheels.
      - splat 17y ago
        A fair coin has a roughly 51% chance of landing with the same side up as it started with. See the paper by Diaconis et al. "Dynamical Bias in the Coin Toss."
        req2 17y ago
        A fair coin is one on which p = 0.5. A coin that has a 51% chance is clearly not a fair coin. This isn't even what I was talking about, but is still equally easy to turn into a fair coin. In this case, caller calls in the air after flipper hides the side that starts up. 0.5 * 0.51 + 0.5 * 0.49 = 0.5 For any other case, flip a coin twice. Assign one person HT and the other person TH, reflipping TT and HH. Since p * (1 - p) = (1 - p) * p, the dual flip is a fair flip. Please don't mention the possibility of sleight of hand next.
- bigwill 17y ago
  I hear what you're both saying. But I wouldn't call beating roulette in the short term a legitimate strategy exactly because it only works in the short run--strategies are supposed to work for longer than that! The only legitimate value I can see is that if you actually enjoy the experience of playing roulette that it's worth paying for it. Anyone who's willing to buy volatility can win in the short term. Otherwise, stick to a game of skill and get some money on the table while you do it. If you're good you can get some vol. and some positive EV.
huangm 17y ago
re: roulette What the author is describing is a 'Martingale' strategy, and it is indeed a surefire way of making a profit (with one critical caveat: you need an unlimited bankroll). After each win, you always earn a profit of X (where X is your base bet), regardless of how many rounds you have lost before. Without a sufficiently large bankroll relative to X, however, probability of bankruptcy is high.
- burnout1540 17y ago
  And this is why casinos always have a table minimum AND a table maximum.
  - mynameishere 17y ago
    No, it isn't. The house can only lose the initial amount. I bet 50, and lose. I bet 100, and lose. I bet 200, and lose. I bet 400, and lose. I bet 800, and lose 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, and then... ...I lay 819,200 dollars on the table and WIN! 50 dollars. The reason they have limits is so that Sheik Abudab can't come in and lay down 500 million dollars and bust them. That is one valid reason to take bad odds: If you can destroy something as a side effect, without really being in danger yourself.
    - burnout1540 17y ago
      In your Martingale example, the table maximum would most likely be set around $2000. So if you lose 6 times (on your $50, $100, $200, $400, $800, and $1600 bets), you can't double your bet anymore. You'll be stuck with betting $2000 at most, which means you can longer guarantee yourself a profit. But now that I think about it, you could always just move to another table with a higher limit. Of course, if you're going through all this trouble to make $50, you probably don't have the bankroll to keep going. Maybe another reason for tables having different limits is that the pit bosses don't trust the dealers (or security?) in the low-roller areas to handle money above a certain amount?
      - deleted 17y ago

pyre 17y ago

One way that I would 'win' at roulette in Grand Theft Auto: San Andreas was to always bet equal amounts on red/black and even/odd. My reasoning was that there are 4 possible outcomes. I have a 50% chance of breaking even, a 25% chance of winning, and a 25% change of losing. You probably can't 'win big' with such a strategy, but you've at least minimized the probability of a loss from 50% to 25%. You've also minimized the probability of a win by as much too, though. I'm no stats guru so I don't know how well this would work out on an actual roulette table... {edit} I should mention that I worked at a casino for a while, and roulette is the game with the highest probability in favor of the house. Blackjack is the lowest. Casinos really only have Blackjack tables because patrons want them, or else they would probably get rid of them pretty quickly. {/edit}

deleted 17y ago
[deleted]
jvdh 17y ago
Casinos really only have Blackjack tables because patrons want them, or else they would probably get rid of them pretty quickly. True, even with a simple strategy you can cut your theoretical loss to about 1-2% (without counting cards). But casinos have blackjack because most players don't know how to play. Most people don't follow that simple strategy (they often have leaflets explaining it too!). With counting cards you can make it profitable for you. But casinos will make life very difficult for you if they find out you're counting cards. See also the movie about the MIT Blackjack team: http://en.wikipedia.org/wiki/21_(2008_film) http://en.wikipedia.org/wiki/21_(2008_film)
- pyre 17y ago
  The casino I worked at used some formula to generate the number of 'points' you would earn towards free stuff based partially on the risk of the game that you were playing. They used the ~1-2% number for blackjack (or whatever the low number of when you play what blackjack players call 'the perfect game') rather than a larger number that might be closer to the 'average' skill of players. This signaled to me that the casinos -- or at least the one I worked at -- in general treat the overall risk of blackjack as the low risk that skilled (non-counting) players can achieve, regardless of the number of people that might come in and ignore the simple, effective strategies to the game. Personally I think that the casinos would rather reduce the risk to themselves from skilled players as well as card counters and just remove all the blackjack tables, sending all those inexperienced gamblers onto games like roulette where they might lose a larger portion of the money they brought with them.

deleted 17y ago

[deleted]

TriinT 17y ago

I never, ever learned anything from a newscientist.com article. Those articles are cute, but one learns nothing deep. I say we go directly to the source! Here is it, Ed Thorp's The Mathematics of Gambling: http://www.bjmath.com/bjmath/thorp/tog.htm http://www.bjmath.com/bjmath/thorp/tog.htm which is the true "bible" of scientific betting. For the mathematically-inclined, I also recommend: http://en.wikipedia.org/wiki/Gambling_and_information_theory http://en.wikipedia.org/wiki/Gambling_and_information_theory http://en.wikipedia.org/wiki/Kelly_criterion http://en.wikipedia.org/wiki/Kelly_criterion and if you still have some energy left, try this: A Markov Chain Analysis of Blackjack Strategy http://www.ece.rice.edu/~crozell/courseproj/MCBJ.pdf http://www.ece.rice.edu/~crozell/courseproj/MCBJ.pdf Have fun! And remember: life is too short to read crappy articles!

mattheww 17y ago

Incidentally, if I wanted to put my math skills to work in a casino, I would play poker. This game is one where the odds have not been stacked against me and a little math drastically alters my expected values.