17 August 2009


Remember when we talked about Blackjack a while back? The main theme of the post was that, unlike most casino games, the odds in blackjack are continuously changing. Every card that is dealt in blackjack changes the overall odds in the game of your pulling any specific card.

Today we we will talk about games where the odds are fixed; which is a fiendishly difficult concept for some people to grasp. To do this, we'll use a very popular casino game, roulette (I'd use craps, but it deserves a post all its own). On any given roulette wheel there are 37 numbers. One through thirty-six and a '0' number. Some will also have a '00' (most American ones do), but for our purposes we will use a 37 number wheel.

Okay, it's payday, you got a decent bonus, you're heading to the casino to try your luck. At the roulette table, you notice that your lucky number, '4', has just landed. Being a mathsy kind of person, you know the chances of a the same number coming up twice in a row on a roulette wheel is 1 in 1,369. So, you bet your birthday instead and lo and behold, a '4' lands again, defying all the odds. It's a mathematical miracle!

Isn't it?

Well, sort of. Before any spin, the chances that any given number will come up twice in a row is in fact 1 in 1,369. However, once the number lands the first time it has no effect on the next spin. To put it more simply, every spin has a 1 in 37 chance of hitting any given number regardless of what the previous spin was.

Let's put it in more extreme terms. The chance that a number will be spun nine times in a row is 129,961,739,795,077 to 1. Or, if you like words, a bit over 129 trillion to one. Those are some pretty high odds. To put it in perspective, your chances of winning the lottery are about 200 million to one; or 645,000 times better. In my hypothetical, this has just happened. The world is abuzzing with the news. So, what are the chances of a number being spun ten times in a row? Well, from a fresh start, the chances are 4,808,584,372,417,849 to 1. So after our nine spins, the chances of the next spin being the same are 4.8 quadrillion (a word I had to look up) to one... right? No, the chances are 1 in 37. Previous rolls have no effect on the next one.

[Actually, at this point, there is a reasonable suspicion that the game has been compromised and there is a statistically higher chance of the same number rolling. We'd have probably shut the game down by the sixth roll or so.]

In the long run... all numbers will come up equal amounts of time; but this is in the life of the game. Just becuase the last twelve spins have been red does not make it statistically more likely it will spin black next. In the long run, the red and black spins should average out to about 48/48 (not 50/50 because the '0' number is green, which throws the red/black odds off). The odds one any given number is 2.7%. The odds of red/black (or odd/even) are 48.6%. Odds on the green '0' are (again) 2.7%.

These odds (say it with me) do not change.

So when you do head to Vegas and hear someone prattling on about how they've been keeping track and a '14' is due... well, in a way it is. But it may not show up until next week and do so fourteen times in a row.

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