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Why Luck Goes beyond the Law of Averages23 March 1998
Casino players can also use this concept to go beyond the law of averages. Doing so can help them understand luck - departures from "expected" results, why one machine or table seems hotter or colder than another despite identical odds and edges. Say a solid citizen is sure casino bosses set the slot machines by pushing buttons somewhere. The player "charts" several casinos on busy nights, counting how often jackpot bells ring during 10-minute intervals. The person will then play where the number is highest, thinking it's where the slots are currently the loosest. Make some assumptions for the sake of argument. 1) Each charted casino has 2,000 machines in action during the observations. 2) Players average four spins per minute. 3) Odds and payouts are the same everywhere, with jackpots being 40,000-to-1 longshots. And, what if the machines in one casino differed from those in the rest? Suppose the odds against a jackpot at one establishment were 50,000-to-1. The average there drops to 1.6 hits every 10 minutes; actual chances are 20.2 percent for none, 32.3 percent for one, 25.8 percent for two, 13.8 percent for three, and 7.2 percent for four or five. Down from the houses with 40,000-to-1 machines, but not by enough so that counting the number of bell-ringers in a 10-minute interval yields any useful information. Similar statistics govern other games. For instance, the probability that a blackjack dealer will "break" is roughly 28 percent. In an 18-round shoe, the dealer can be expected to break five times. But, what are the chances of a hot shoe in which the dealer breaks eight or nine times? Or of a cold shoe in which the dealer only breaks once or twice - or not at all? The answers, again provided by the Poisson Distribution, are as follows:
Here are examples of how to interpret these figures. The average number of dealer breaks during an 18-round shoe is five. However, the chance of exactly five breaks is only 17.5 percent. Moreover, there's a 1.8 percent chance the dealer will break 10 times - twice the expected rate. Likewise, there's a 3.4 percent chance the dealer will only break once during the shoe. And a small but real 0.7 percent chance the dealer won't break at all. Next time you're at BargainMart and the cashiers leave for lunch just as shoppers converge on the checkout aisles, consider this. Did you hit a normal but low-probability event, or did management ignore statistics in planning? And next time you're gambling and hit a hot streak, think about this. Are you experiencing the extremes of the Poisson Distribution, or did your 1-900-PSYCHIC advisor really know it would be your lucky day? Either way, remember the reasoning of that rational rhymer, Sumner A Ingmark:
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