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#9
04-05-2003, 11:38 PM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 1,636
Re: creating a 2:1 shot with a fair coin

There's a slight problem with that Ray. He said a finite number of flips. Your coinflip freeze out can go on forever. Now you're saying, that's ridiculous, of course it will always end. But for fair coins with exactly a 50% chance of heads, it can be proven that the average value of the length of the game is infinite! What is true is that it becomes very unlikely that the game will last more than N flips when N becomes very large, but this probability never goes to zero for any N, and it turns out that N gets large faster than the probability approaches zero, so the expected value of the length of the game is infinite.

Now you'll say you're still not swayed because I sense you're a practical kind of guy, and that is what you say about such things, and you will say you'll play this freeze out, and you will have every confidence that the game will end every time, and most likely it will end very quickly. You would be right to be as confident as you please, as long as you're not exactly 100% confident. You can be 99.99999% certain that it will end within a certain period of time, but never 100% certain that it will end within any period of time no matter how long. It will almost always end in a short time, but on average it will take forever.