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# Playing It Smart: Setting rational goals for your next playing session

10 February 2009

Casinos are built on the laws of large numbers that validate the veracity of averages. The theoretical models and the associated math are rock-solid. With enough bets over enough time, on propositions whose probabilities are known precisely, the bosses and their bean counters know what fraction of the action they'll keep. It's the edge multiplied by the gross wager.

Variations do occur in the financial figures you occasionally see. A game may "hold" 15 percent one month and 18 percent the next. This doesn't undercut the underlying principles. These apparent anomalies generally result from small numbers of events that are, separately, of sufficient magnitude to distort totals and render averages meaningless.

One such aberration might involve the rare "whale" who comes to a casino with \$10 or \$15 million, bets \$25,000 or \$50,000 per round, and either takes the joint for a bath or becomes Donald Trump's new best friend based on a few lucky or unlucky coups. Another might be one of the few-and-far-between monster jackpots.

Players, in contrast, rarely get in enough action for the laws of large numbers to apply. That whale, for instance, might bet a total of \$5 million in 100 or so rounds of blackjack. At 0.4 percent edge, the casino's theoretical "take" is \$20,000. But the bettor might well walk with a million or two profit or loss.

Individual solid citizens are always in the realm of small numbers. Jane or Joe might start at 8-5 video poker with \$100, and by recycling intermediate payoffs bet \$1,000 during an 800-spin session at \$1.25 per round. House advantage in this game is 2.7 percent. Multiply 2.7 percent by \$1,000 to find a theoretical loss of \$27. But \$27 is an average over thousands of 800-spin sessions. There's no way to predict how much Jane or Joe will actually win or lose during such a statistically short game.

Several things of interest can be determined about sessions of reasonable duration, however. For video poker and other games that are highly skewed because of top-heavy payoff schedules, computer simulations are ideal tools for obtaining this information. A computer is programmed to run thousands, maybe millions, of virtual short sessions. It then applies laws of large numbers to data from phenomena involving small numbers.

Players should be interested in the chance they'll get to finish some number of rounds on a given stake. They needn't be gambling gurus to guess that the bigger their bankrolls, the better their ability to outride the normal and inevitable downswings of any game. Simulation zeroes in on the probabilities for the video poker example. Players have about 70 percent chance of completing 800 spins with a \$100 bankroll. This falls to around 31 percent on a \$50 stake. At \$200, the chance is over 99 percent.

As for wins or losses, averages don't mean much in the session context. But bettors should want to know their potentials to reach alternate profit levels before sneaking over to a cash machine for a fix. Using the video poker example, if the objective is to start with \$100 and quit when \$50 profit is reached or exceeded, simulation gives the chance of success as roughly 32 percent. Shooting for double-or-nothing turning \$100 into \$200 or busting in the attempt, prospects of joy drop to 14 percent. And, those who are willing to down in a blaze of glory if they don't triple their money have only 6 to 7 percent likelihood of victory.

The figures, of course, will differ depending on the detailed parameters of each game. Practiced punters tend to know what to expect from expensive experience. But, in the heat of the action, even they still may tend to underestimate their bankroll needs or overestimate their profit potential. It's natural enough to remember instances when living dangerously in this manner panned out. But it's also a modus operandi packed with peril. As the parsimonious poet, Sumner A Ingmark, perspicaciously penned:

Though oft said didactically,
Approach gambling tactically,
By setting sights practically.

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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.