Vegas gambling guide: How the law of averages works

vegas signUSA Today – Ask a mathematician or a casino owner if you can win gambling in a casino, and the truthful answer is yes, but almost always only in the short run. Unless you’re a professional player who only plays with the long-term edge on your side, the longer you play, the more certain it is that you will lose.

People get funny ideas about the way gambling works. In casinos there are games of chance (roulette, craps, keno, bingo, slots, baccarat) and games of chance and skill (poker, blackjack, video poker).

A game of chance is like flipping a coin or spinning a wheel with 10 numbers. What happens is what happens. A player can guess what the outcome will be but cannot influence it. Games of chance operate according to the law of averages. If you have a fair coin and flip it 10 times, the law of averages leads you to expect that approximately half of the tosses will come up heads and the other half tails. If a roulette wheel has 38 slots, the law of averages suggests that the ball will fall into a particular slot one time in 38 spins.

The coin, the roulette ball, and the dice, however, have no memory. They just keep doing their thing. If you toss a coin and come up with heads nine times in a row, what are your chances of getting heads on the tenth toss? The answer is 50%, the same chance as getting heads on any toss. Each toss is completely independent of any other toss. When the coin goes up in the air that tenth time, it doesn’t know that tails has not come up for a while, and certainly has no obligation to try to get the law of averages back into whack.

Though most gamblers are familiar with the law of averages, not all of them understand how it works. The operative word, as it turns out, is “averages,” not “law.” If you flip a coin a million times, there is nothing that says you will get 500,000 heads and 500,000 tails, no more than there is any assurance you will get five heads and five tails if you flip a coin 10 times. What the law of averages does say is that, in percentage terms, the more times you toss the coin, the closer you will come to approximating the predicted average.