I tackle the following game analysis: 2 players, two 6-sided dice. Bigger sum of points win. First roller has an advantage, as he wins even if 2nd player's dice sum equals to his. As the game is played with doubling cube (potentially increasing the odds before any roll), I tried to enumerate the list of possible sequences. For instance, if P1 rolls 12, the game ends (1 roll) However, the. sequences like 2,3,6,12 4,5,8,9,12 etc are plausible. I tried brutal force calculation and came up with 938 distinct sequences all of them ending with 12, obviously. I am just trying to double check my calculation and learn at the same time, how to calculate the number of sequences without brutal force? Any ideas?