The Wizard And The Gambler's Fallacy

You know who you are. Yeah you. You are that guy who decides that just because the roulette has landed on red the last 200 times, black must be due. Well sir, you are wrong. Just plain wrong. And we here at Casino Snob have had enough of your logic. You know what else? We're not alone! The Wizard of Odds, that wise and powerful master of all things gaming-odds related, has also weighed in on your antics. Please do us all a favor, and heed his words:

I disagree with you when you said that if a roulette ball has landed on red 20 times in a row it is equally likely to land in red as black on the next spin.

This kind of comment never comes with any kind of mathematical reasoning or evidence behind it. Little metallic balls do not have a memory and can not defy the laws of physics by jumping in one color or the other. If you don't believe me please read any introductory book on probability. I don't have time to tutor the entire world on this one person at a time.

The probability of red winning 20 times in a row in roulette is (18/38)20 = 1 in 3,091,874. Thus, if red has already hit the last 19 spins the odds are that the next spin will almost certainly be black because of the long shot against 20 reds.

First, the odds of 19 reds in a row and then a black are the same as 20 reds in a row. The past does not matter. The probability of red after 19 reds is 18/38.

Still don't get it? Fine. Go take yourself a course in Combinatorics, then.. email the wizard, and perhaps he will grace you with some insight.

October 30, 2007

The Wizard And The Gambler's Fallacy