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# Which is preferable, big bets or small?

2 August 2010

Say you want to win big at a casino, starting with a bankroll you consider realistic. Assume you're willing to go for broke, bag the bonanza or bust out trying. There are two basic approaches.

You can strike it rich betting low at games with high payoffs, like the slots or tables with bonus side action. The problem is that the more the payoff, the less the chance of achieving it.

The other method is to bet high on propositions with low payoff ratios but good probabilities of success. Banker at baccarat, for instance, has a greater likelihood of winning than losing. As another example, on Pass bets at craps, chances are close to 50-50 -- 49.29 percent of winning and 50.71 percent of losing.

Suppose you start with \$100 and bet it all, flat, on Pass at craps. Rounding to whole numbers, the chance of winning \$100 is close to one out of two. If you keep parlaying the bet -- adding the last payoff to what you had previously, chances at successive levels are one out of four -- \$300, one out of eight -- \$700, one out of 17 -- \$1,500, one out of 34 -- \$3,100, one out of 70 -- \$6,300, one out of 141 -- \$12,700, one out of 287 -- \$25,500, one out of 582 -- \$51,100, one out of 1,181 -- \$202,300.

Is one chance out of 1,181 to win \$202,300 on a \$100 bankroll too remote? How does it jibe with prospects of a jackpot in this range on a slot machine at \$1 per pull? There's no easy answer because you don't know the probabilities on slots with these kinds of high-end returns. But, for comparison, the chance of winning a mere \$1,000 with a Royal at jacks-or-better video poker, betting \$1.25 per pull, is worse -- one out of 40,000.

Alternately, you could start with a \$100 stake and bet \$25 per hand on Pass at craps. You'd double your money with four wins in a row, the chance of which is one out of 17. Win three and lose one and you're \$50 ahead. Win two and lose two and you're even with \$100 still in your rack. Win one and lose three and you're down \$50, with \$50 left to keep playing if you wish.

Inquiring minds will want to know how betting bigger improves the chance of reaching a lofty win goal before depleting a given size stake. Every case is unique because propositions have different chances of success, and players may keep wagers constant or vary them in a myriad of ways. But you can see the trend using a flat Pass bet at craps with the same amount at risk in every round.

Pretend you're willing to risk \$500 for a \$1,000 profit. Your chance of success for several amounts bet is shown in the second column of the accompanying table. If this is your sole incentive for gambling, the data suggest betting the most you can per coup.

Chances associated with variously-sized flat Pass bets at craps starting with a \$500 bankroll
```bet     chance of earning \$1,000     chance of surviving for
before busting out       at least 25 decisions
\$5                          0.3%                        100%
\$10                         4.5%                        100%
\$25                        17.0%                        100%
\$50                        24.4%                         95%
\$100                       27.7%                         66%
\$500                       32.4%                         15%
```

Reaching a win goal as opposed to going down in a blaze of glory isn't the only gambling criterion, however. There's also an issue of the chance of still being in the game, ahead or behind but not belly-up, after a session of reasonable duration. Sure, you want to win a lot of money. But, do you want to trust your destiny to a single shot, notwithstanding the odds? Here, increasing your bets cuts rather than raises your prospects. This is evident in the probabilities presented in the third column of the table for 25 decisions on flat Pass bets at craps.

Is there an optimum crossover? Bets large enough to help you reach a win goal yet small enough to keep you in the running if fate doesn't smile on you right away? There may well be, although it'll differ among players. And you'll undoubtedly keep changing your mind about it whenever the other way of playing would have turned out better on any particular day. For, as that Chaucer of chance, Sumner A Ingmark, metrically muttered:

If I knew before what I knew later,
Then my bank account would be much greater.

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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.