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PLAYING IT SMART by ALAN KRIGMAN
You Can't Rely on Averages when You're Dealing with Small Chances. When casino outcomes have high or moderate possibilities of occurrence, it doesn't take a Methuselah's age of action before actual frequencies home in on statistically expected averages. As an example, there's around 21.5 percent chance of ending with a high pair at jacks-or-better video poker, so in 1,000 tries you'd expect 215 of 'em and would almost surely get between 200 and 230. A probability of a natural in multi-deck blackjack is about 4.75 percent. In 10,000 hands, this averages out to 475 -- and you'd likely see from 450 to 500 of the li'l devils. The situation is different for rare events, those with extremely low probabilities. Averages then become fickle forecasts. Progressive jackpots at Caribbean Stud offer good illustrations. The probability of a royal in Caribbean Stud is one out of every 649,740 hands. After this many hands without a grand slam, the jackpot would be around $160,000. But, it's common for jackpots to reach $250,000 or $300,000, indicating that nobody's scored in over two or three times 649,740 tries. It's also not unusual to notice totals under $20,000 or $25,000 on several successive visits to the same joint, suggesting that the jackpot's been hit and reset more than once during a relatively short interval. The following table shows the effect. The percentages are the probabilities of from zero to five and over five royals after enough hands for the expected number to be one, two, or three.
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