Pedro Martínez: I did, lol, 10 messages ago in Re: 100% vs 0%.

ChessM challenged my 5-5 example:
[playBunny: Both sides roll 5-5 ad infinitum]

1st)The probability that both sides will roll a 55 an infinite number of times is exactly zero!

2nd)Even if the game will continue with an infinite number of 55 (although this can never happen as i said), that game would be one single game and this doesn't help us in the question of how many Backgammon games exist? Finite or infinite?

This is correct when considering the production of the sequence but if you look at it from the viewpoint that you already have the infinite set of sequences then the sequence already exists, then you have a single infinitely long game.

Then, given that for each roll there are alternate sequences of rolls which will result in the same position (ie. one piece on the 5-point and one on the bar), there are an infinite number of games.

Wil and Abigail have already said much the same thing.