P(A wins|A rolls 10) = P(B and C roll lower than 10) + P(B and C both roll 10)*P(A wins next round vs all three) + P(B or C rolls a 10, the other rolls lower)*P(A wins next round vs either B or C)

There are six ways to roll a 10 or above: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6), so there is a

chance of rolling less than 10.

P(B and C both roll lower than 10) =

P(B and C both roll 10) =

In general, all three players start with equal chances of winning, so

P(B or C rolls a 10 and the other rolls lower) = P(B rolls 10, C rolls lower)+P(C rolls 10, B rolls lower) =

In general, if there are only two players left, they have equal chances, as well, so

Hence,