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How can the law of large numbers be applied to gambling? Many system reply on the theory that if one is backing red, say, in roulette and one gets behind because of an adverse run on black, the law of large numbers will ensure that red will eventually catch up. The probability of this can be assessed for any number of coups.

In throwing a die, the probability of throwing a 6 is 1/6. The more times the die is thrown, so the likelihood increases that the closer, in proportion, will be the number of 6s to 1/6 of the number of throw.

It is in the disregard of the words -in proportion- that most misconceptions arise. In 600throws of a die, we might expect a 6 to occur about 100 times. We would not be unduly surprised ie the deviation from our expectancy were 20 per cent, but we would if the number of 6s were 80 above or below the expected 100. In 600,000 throws, we would expect about 100,0006s. Conversely we would not be surprised if the deviation were 80, but would be astonished were the deviation 20 per cent. The larger the number, the smaller will be the likely deviation, in percentage term, but it will be larger in actual number.

In the law of large numbers, what is a large number? Paradoxically, whatever it is, it is never large enough. If the richest man in the world converted his fortune into pennies, and spun them all, would there be enough for him to be confident that he would get close to 50 per cent head/50 per cent tails? Yes, but he would probably be even closer if 100 other men with similar fortunes joined him in the experiments, although the actual number of 'odd' heads or tails over probably would be greater. If the two richest men in the world tossed a coin repeatedly and paid each other in pennies for a correct call, it is certain that one would eventually finish broke.

By poker.tj