Craps and Betting Systems
Date: 03/17/2003 at 11:10:28 From: Cliff Thomas Subject: The game of Craps In craps, can I bet on the 7 and win (more than I lose) if I assume a seven normally comes up within 32 rolls? I plan to only start betting after I have not seen a seven for 5 rolls so I start betting on roll #6. (I know that the past doesn't influence future dice rolls.) Then I gradually increase my bets to ensure a profit of about $10 when I finally hit. The confusing part is whether over the long term I can win my bankroll amount before losing it all to when that stretch of no 7 extends beyond 32 rolls. And the fact that I am not betting for 5 rolls after a 7, which means when a 7 comes up sometimes and I am neither winning or losing. Not being a gambler I found that if I hop the 7 in bets of multiples of $3, I could increase my returns and allow myself to extend my rolls to 34 rolls still using my $6k bankroll. I am still trying to find math that can clue me in as to whether I am likely to win my bankroll back before losing it all to a streak of no 7 for 34 or more rolls. Is there a formula to help me figure this out?
Date: 04/11/2003 at 13:20:31 From: Doctor Achilles Subject: Re: The game of Craps Hi Cliff, Thanks for writing to Dr. Math. There is a house edge on every bet in the casino. Craps is actually one of the games with the smallest house edge, if you stick to the pass line and lay odds on every bet. Laying odds on your pass and come bets is actually the only place in the casino where you can make a bet where there is no house edge. In other words, the payoff on laying odds is exactly equal to the probability that the outcome will occur. My personal favorite site for gambling rules and advice is The Wizard of Odds http://www.wizardofodds.com/ The author of the site is extremely methodical and mathematical and he does an outstanding job of explaining in mathematically sound ways how each game works and the pros and cons of different strategies. You can go directly to the craps page at: http://wizardofodds.com/games/craps/ The problem with doubling your bet (or multiplying it by 3, or by 1.5, or using some other strategy of increasing your bet every time you lose) is something that you hinted at already: you stand to lose your entire bankroll for the potential of a small profit. You can put a couple of thousand dollars on the line at a $10 craps table and double your bet on the "don't pass" line every time you lose. If you start with, say, $1000 and you double your bet on the don't pass line until you either win once (and come out $10 ahead) or lose all your money, then you have a little less than a 99% of coming out ahead $10. If you start with $10000 and do the same thing, then you have a little less than a 99.9% chance of winning. If you turn that around, you have just over a 1% chance of losing in the $1000 case and just over a 0.1% chance of losing in the $10000 case. If you lose, then you are down either $1000 or $10000. A little more than 1% multiplied by $1000 is equal to a little more than $10 and a little more than 0.1% multiplied by $10000 is equal to a little more than $10. So, on most trials you will win $10, but you have a small chance of losing a whole lot of money. And, on average, you will lose a bit more than you win. If you do this only once, then you will probably win $10, but you may be unlucky and lose it all. If you keep trying this over and over, then your odds of winning every time drop significantly. Let's say that you start with $1000 and play a $10 table, doubling your bet until you win, then you start over at $10 and repeat. If you keep doing this until you are either up to a total of $2000 or down to nothing, then the odds that you will win are EXACTLY the same as if you just sat down at a $1000 craps table and laid all your money down on the first shooter. In other words, on average, you expect to lose just as much as anyone else, using any betting strategy (assuming you put the same amount of money on the table). You can find a more complete explanation of betting strategies and the problems with them back at the Wizard of Odds: http://wizardofodds.com/gambling/scam.html It sounds like a great idea to sit at home with an Excel spreadsheet and plan out betting strategies with which you increase your bet. I've done it more than once. I once took one of my betting strategies (which involved multiplying my bet) to a casino. At one point while I was doing the strategy, I ran into a run of bad luck and had to double my bet 6 times in a row on a $5. All of a sudden, I had over $300 riding on a $5 table. At that point, things didn't look quite as good as they did on my Excel spreadsheet. Because the dice don't remember how many times you've lost, you're no more likely to win after doubling your bet 6 or 7 times than you are the first time. So here I was with over $300 bet, and slightly less than a 50% chance of ending $5 ahead of where I started and slightly more than a 50% chance of ending several hundred dollars lower than where I started. Fortunately, I won that bet (and walked away with my $5 profit), but the experience taught me that betting systems are the sort of thing that look nice on paper, and are fine before you start using them. If you're lucky and conservative, they can be fun and (with enough luck) even profitable. But increasing your bet when you're down will occasionally leave you in a position where you either have to give up or bet more money than you want to lose so that you can have a few more dollars when you leave the casino than when you entered it. Hope this helps. If you have other questions or you'd like to talk about this some more, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
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