 In some of these possible futures the game will actually have been decided in fewer than formula_1 rounds, but it does no harm to imagine the players continuing to play with no purpose.Considering only equally long futures has the advantage that one easily convinces oneself that each of the formula_3 possibilities is equally likely.Fermat was thus able to compute the odds for each player to win, simply by writing down a table of all formula_3 possible continuations and counting how many of them would lead to each player winning.