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Another backgammon puzzle: more serious effort

Posted By: Timothy Chow
Date: Saturday, 2 March 2013, at 11:00 p.m.

In Response To: Another backgammon puzzle: more serious effort (Steve Mellen)

There's an annoying technicality in probability theory which is that when dealing with a situation with an infinite number of possibilities, we have to distinguish between "happening with probability 1" and "always happening."

In your scenario, the walk terminates with probability 1, but it doesn't always terminate, because as you say, it could go back and forth in the middle forever.

We'd all be much happier if we could figure out how to set up the laws of probability so that this technical distinction could be eliminated. Unfortunately, there's no way to do so without violating other properties that we want our theory of probability to have.

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