Tonight at dinner, a couple of colleagues and I were discussing the agenda for a meeting we’ll have next week in Las Vegas. When you’re a statistician in mixed company and Vegas comes up in conversation it’s impossible to avoid talking about gaming. It would seem like the most natural topic in the world to discuss with a statistician…but I don’t gamble. But neither can I resist a good probability puzzle. So the conversation turned to gambling strategy. My strategy (not to play at all) wasn’t very popular so we started to break down a few of the most popular games but ended up mostly talking about Roulette.
Roulette is a game that seems like it might be impossible to “beat,” but we came up with a strategy that just might work. I’m open to suggestions/criticism. Let’s assume that the last 15 outcomes are listed above the table. There are those who can’t resist betting Red after a string like this: BBRBRRBRBBBBBBB. But by now, most people realize that there is no such thing as a color being “due.” Every roll is independent and every pattern of colors is equally likely…if the house is honest.
A statistician might look at the past 15 outcomes as a sample from which to estimate the true proportion of Black rolls. In the above example, classical statistics would say that the probability of Black is 11/15 which could then be used to test if the probability of Black is greater than 0.5. But you might also know something about the integrity of the casino itself. Are you playing in Vegas or Bangkok, for example? If there is reason to suspect that the house is crooked (maybe the only safe bet when talking casinos), the best bet would actually be Black. While the suckers keep betting Red because one is surely “due,” the house cleans up. And you’ll have a better chance of taking the house by betting Black.
But the most important thing to consider is what it might mean to beat a dishonest casino. The good fellas running a crooked house are not the types of people I’d want to cross.