Marcus and Allen are playing Rock/Paper/Scissors. The first one to win 10 times does not have to do the dishes. The score is now 9 to 7 in favor of Marcus. If ties are ignored and not counted, what is the probabilty Marcus will not have to do the dishes?

Answer 1

He only needs to win one more time to watch TV instead of doing dishes.
Assuming he is not a pro, and everything being equal, and since history does not count, what is the probability for him to win the next one?