[BruceZ]

This will illustrate the difference between a probability of 1 and a dead certainty that someone was asking about earlier. If we can flip as fast as we please, we can flip an infinite number of times in 1 minute. We'll just take 30 seconds for the 1st flip, 15 seconds for the second flip, 7.5 seconds for the 3rd flip, etc. After 1 minute we will have flipped an infinite number of times, or else the game will have ended at some point. It is still possible that the game never ended, and the probability of that it never ended is 0. That is, for each flip we can assign a winner and a loser so that the game doesn't end. There is only 1 way to do this, that is the winners and losers must alternate. Since there are an infinite number of ways the flips can occur, the probability that the game never ends is 0. That is, the probability that the game does end is 1. But it is not a dead certainty that it will end, because there is 1 way that it will not end.