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If the laws of probability can't guarantee you'll win, what good are they?

4 October 2010

Typical casino gamblers strike out blindly – or, worse, follow superstitions or myths – mind-lessly or even deliberately flouting tools that can aid them in making sound decisions in their punting pursuits. A major reason for this phenomenon is that folks in general want plain-English instructions saying "do this and you'll get that." Since gambling is characterized by uncertainty rather than cause-and-effect, the best guidance they can get is offered by the laws of probability. And these don't provide cookbook rules. Instead, they offer means of balancing factors such as risk and reward or effort and result. Less intuitively satisfying because they put the burden back on the individual. But extremely useful for bettors willing to fire-up their little grey cells.

The probabilities underlying casino gambling are straightforward. The basic quantities of interest are the chances of winning, pushing, or losing individual wagers. Finding these values essentially requires counting then comparing how many ways coups can be resolved and the sizes of groups of those results that win, push, or lose. When cases are numerous, and can occur in alternate combinations, the math gets trickier than addition and division, but the principles don't change.

The probability of an event such as a winning round is commonly expressed as a fraction. The form is "(ways to win) out of (total ways the coup can be resolved)" or, (ways to win) divided by (total ways the coup can be resolved) with the quotient converted to a percentage. Ambiguity occurs when pushes may be included or excluded as outcomes so it's critical to know which count was used in obtaining the figures for the totals.

Odds present the same information in a manner some solid citizens find easier to envision and more consistent with payoffs. Odds are stated as "(ways of winning)-to-(ways of losing)" or the converse "(ways of losing)-to-(ways of winning), depending on who they're "for" or "against." The numbers are usually simplified by cancellation, either so the figure on the right of "-to" equals 1 (e.g., 36-to-15 becomes 2.4-to-1) or to make both figures the lowest possible integers (e.g., 36-to15 becomes 12-to-5).

Beyond the probabilities associated with individual bets, gamblers should be interested in the chances of being ahead or behind by various amounts after extended play. Here, values can be interpreted as: 1) the frequency at which bettors can expect to reach a specified level under stated conditions or 2) the fraction of all bettors playing in a defined manner who can expect to reach a particular plateau. The calculations are based on the probabilities of the individual wagers but also include factors such as bet sizes, payoffs for success, numbers of decisions, and loss limits.

The operative word here is "expect." In probability analyses, the term implies averages over many cases rather than something any individual can plan on actually happening. It's therefore natural to ask how far above or below the average players should prepare to be when the dust settles. The laws of probability can answer this question, too, although the concept is applied surprisingly rarely. The associated calculations, admittedly more complicated than counting and dividing, yield figures that describe the volatility associated with expected values. That is, the likelihood of deviating from the average by varying amounts under given conditions.
Unfortunately, none of this spills secrets the casino bosses don't want anyone to know about bets, singly or in combination, that guarantee wins. That's because there are no such secrets. The laws of probability can, however, be helpful in establishing realistic goals and in choosing games and modes of play in line with achieving them. And they can provide insight into what's arguably the most common error casino gamblers make. That is, not recognizing that bet sizes, loss limits, and the chances associated with particular wagers are related to prospects of agony or ecstasy at the end of a session or casino visit.

Of course, this will all be irrelevant if you're bent on taking money you'd be well-advised not to treat cavalierly, and invest it on a shot at a big payday – figuring someone's gonna be in the right place at the right time and it could as well be you as anyone else. Further, if people think they can talk you out of this notion, they ignored that wise wordster, Sumner A Ingmark, when he wrote:
Those whose minds are made up and are itching to act,
Won't be swayed from their courses by contrary fact.

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.