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Peter Ruchman has been published in a number of casino and gaming publications. He is the author of "After the Goldrush," a three-volume definitive history of gambling in Las Vegas, and is regularly featured on HBO, ESPN and the Discovery Channel.



Sunday, April 29, 2001

Standard Deviation, Part II

By Peter Ruchman

In making my way through casino life over the years, I encountered some truisms. Some can be verified by pure math. Others I embrace instinctively from an experiential sense. Whether they can be quantified and measured is irrelevant. I simply hold these truths to be self-evident -- all casino players and situations are not equal.

For players, major differences lie in skill level, ability and experience. From a situational standpoint, in a casino, things change constantly, forever in flux. When the blackjack or table player converges in specific circumstances you have an outcome, not predetermined like a slot machine, but one in which there is a human decision involved. This is particularly true in blackjack, where you decide how much money to bet, then determine what you will do with your two cards versus the dealer's single visible card. Depending on the situation, with another card possible or splits and doubles, there may be more decisions ending in a single or series of outcomes.

You have only seconds to arrive at these choices. Dawdle and other folks at your table will tend to irritable restlessness. What factors are weighed to resolve your direction? Do you recognize opportunity when it shows? And once you've evaluated circumstances to be positive, are you willing to take the next important step and risk your money.

Today's topic at hand is standard deviation. Using the old cliche of the 100 coin flips, you probably will not get a perfect 50-50 heads/tails ratio. The sample is too small. Most likely you will get a slightly skewed result one way or another, say 53 heads to 47 tails -- a deviation of six from the expected. Now flip the coin again and you might get a result closer to 50-50 OR, you may get one that contains a larger spread or deviation than the first result.

In matters of probability and chance, the issue of a variance from expected theoretical performance, or deviation is a matter of course. And for the experienced gambler, these areas present a window of opportunity worth seeking, then acting upon. For instance, you might expect that you could win two hands of blackjack, one after the other. Three wins in a row and you're thrilled and four is an old fashioned delight. Winning and losing streaks of a longer duration are real life representations of deviations from the norm. In the casino they happen all the time.

Play in a casino long enough and you'll experience both sides, winning and losing streaks longer than you dreamed or feared. The entire basis of "money management" theory is derived from the thought one might be ensnared in a prolonged losing streak with the inherent danger of depleting valuable funds. It is the awesome unpredictable nature of these streaks or deviations makes them so confounding -- they rise up like waterspouts from a relatively calm sea, churning the waters, throwing debris in every direction.

Casino veterans learn to fear and loathe losing streaks, treating them with enormous respect. That same respect holds true for winning streaks -- only the true pros recognize them, then act. The essence of gambling lies in these winning streaks in that they contain the true opportunities to make hay while the sun shines.

The unwitting public's tactic is to bet, then if a loss is suffered, bet more. Historically speaking, "systems" have been devised with names like Martingale, Fibonacci, D'Alembert and others, many based on a principle of multiplying an original bet until there is a win. This is called "chasing your losses."

No one wants to leave a loser -- casinos counts on this matter of life to make their own hay. Most people chase and bet more as their losses increase. This is the exact opposite of professional play. Experienced players bet more when they win and back off entirely or reduce to a table minimum when they lose -- a simple but very effective way to enhance your chances of enlarging your coveted bankroll.

How often have I seen a player win three, four, five hands and more without pressing or adding to his/her bet, choosing to "flat-bet" the entire sequence? Or worse, bet less with each successive win? The worst all-time example of this might be a man at the old Desert Inn playing craps who held the dice for almost three hours. While many around him parlayed his hot hand into thousands in the 1950s, he kept betting his original $5 on the pass line, risking only odds. When he finally "sevened-out,"he walked away to thunderous applause, clearing a grand total of $700! Some in the crowd had cleared thousands.

Standard deviation IS a mathematical term with an accompanying formula considering binomial distribution, etc.. Come by Gambler's Book Shop and we feature any number of probability books containing the specific information. The most critical and meaningful aspect for gamblers is one should EXPECT a variation, the UNEXPECTED. The larger the variation, the greater the chance for failure or success -- opportunity doesn't come knocking often. It's up to you to hear the door, then, open it wide.