When stepping into a casino, it can be useful to have a clear sense of how probability works and how it applies to the games that you're playing. In today's discussion about gambling however, we're reminded that a gambler's fortune can depend on more than just random odds.
Today's post on the Gambler's Fallacy relates the tale of one night in Monte Carlo when people lost millions of dollars thinking the next spin of the roulette wheel would surely land the ball on red. Some readers pointed out that when a roulette ball keeps landing on black, there may be certain biases at work. xyzzy12345 notes:
There are as many gamblers, probably more, who take the fallacy the other direction. The dice are hot. Ride the streak.
Sports fans (and the athletes themselves) believe that they are hot or that they are in a slump. Now it is possible the human beings do get "in the zone" and their shooting accuracy is actually better today. Certainly if a Basket ball player sinks 5 shots early in the game, his team mates will feed him the ball, and he will score more points over the course of the game. But most attempts to study "the zone" are unable to identify that such a phenomenon can be proven.
Bayesian probability gives more credence to the luck runs in streaks, but it does so through a back door. If the roulette wheel comes up black 20 times in a row, there may be some bias in the wheel that had not been previously accounted for, and so the Bayesian can adjust his priors with the new information.
mwhite66 adds that such biases have been observed in studies on gambling:
In the '70 a group of computer whiz-kids at UCSC decided to try to beat the Vegas casinos using the new microprocessors. They surveyed the games and learned that, most counterintuitively, roulette was the easiest to beat. They devised an algorithm that could beat the game with over 80% probability, coded it up and put the microprocessor in their shoes. Along the way they learned that experienced croupiers could drop the ball pretty much wherever they wanted by timing the flick of the ball along the race. This is all written up in a wonderful book called The Eudaemonic Pie (The Eudaemonic Pie).
Meanwhile, plenty of commenters offered their advice on gambling: don't do it—or at least go in knowing that you're going to lose a set amount of money.