PLAYING IT SMART by ALAN KRIGMAN

The house may have the edge, but you can have the odds

Although it's fun to fantasize about a big score, seasoned gamblers know that such strokes are rare. You needn't be a statistical scholar to deduce that when a payout is high, the associated probability must be low. Happily, for those who care to utilize the effect, the converse also holds.

To some players, the whole idea of a casino visit is to go for broke. Grab the brass ring or fall off the horse in the attempt. This isn't necessarily bad for those who can afford what they lose, consider the excitement and perks worth the money, and don't take their frustrations out on the dog when they get home.

Many solid citizens, however, prefer to seek frequent moderate profits rather than huge but elusive hauls. Such goals appeal particularly to those who gamble regularly. The good news is there are strategies conducive to runs of this type. The bad news is there's nothing magic about them and, in the long run, multiple small wins will usually be offset by a few big losses.

The general principle is that bettors can adjust the odds of triumph on a broad range of individual wagers, and on all sessions, despite the house advantage. Simply stated, you're more apt to win than lose as long as the total you're willing to risk is enough above the amount you're looking to gain.

Double-zero roulette offers straightforward illustrations at the bet level. Pretend you put $1 on each of 20 individual numbers. You have 20 ways to win and 18 to lose. You're favored to prevail with odds of 20-to-18. In probability parlance, that's 20 out of 38 or 52.6 percent. A hit on any of your choices pays $35 but you lose $1 each on the 19 misses so your net revenue is $16. That is, you risk $20 for a 52.6 percent chance of a $16 payoff.

You have even greater chance of success with $1 on each of 30 numbers. Now you're favored to win with odds of 30-to-8. That's 30 out of 38 or 78.9 percent. A hit pays $35 minus $29, so you're venturing $30 on a strong 78.9 percent chance of picking up $6.

Analogous reasoning pertains to sessions, albeit with trickier arithmetic. Say you're a blackjack buff who adheres rigorously to basic strategy. You hazard a $200 stake, play for $10 per round, and have the discipline to quit as soon as your earnings reach $100. Your chance of success is 64.0 percent. Risk the same $200 to win $50 and the probability you'll prevail is 78.4 percent.

A similar technique improves your prospects of winning more often in multiple tries. To do so, raise your chances on individual bets, sessions, or visits by lowering your monetary target.

Representative figures are shown in the accompanying table. The data give the chance of winning up to 10 times in 10 tries, when the likelihood of any single victory is 40, 50, or 60 percent.

Chance of multiple successes in 10 tries for alternate probabilities of winning in each instance

number of wins probability of winning in each instance in 10 tries 40% 50% 60% 0 0.60% 0.10% 0.01% 1 4.03% 0.98% 0.16% 2 12.09% 4.39% 1.06% 3 21.50% 11.72% 4.25% 4 25.08% 20.51% 11.15% 5 20.06% 24.61% 20.06% 6 11.15% 20.51% 25.08% 7 4.25% 11.72% 21.50% 8 1.06% 4.39% 12.09% 9 0.16% 0.98% 4.03% 10 0.01% 0.10% 0.60%

As an example of interpreting the figures, if the probability of a winning session is 40 percent, your shot at eight successes in 10 tries is 1.06 percent. This rises to 4.39 percent when the session probability is 50 percent. And, with a 60 percent shot at session success, your chance of eight out of 10 is 12.09 percent.

The bosses may have an advantage on the bets they book. But you can tailor strategies so you're favored to come out ahead in particular situations as well as series of instances. Not by luck alone, although this helps. But by understanding and applying some of the basic principles underlying games of chance. As the mathematical muse, Sumner A Ingmark, was motivated to mutter:

Wise players seeking gambling treasures,
Know edge and odds are different measures.

(c) 2008, ICON/Information Concepts Inc

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