Alice and Bob play chess, if one of them can win three times then the other will be lost the game.
How many different results are possible between them on the chess game?
I guess there are 3 different conditions,
1. one of them achieve a triple-win : 2
2. one of them win 3 times and lost 1 time : 2 * C(3,1)=6
3. one of them win 3 times and lost 2 times : 2 * C(3,2)=6
So there are 14(2+6+6) possible results on the chess game.
Is it right? I hope someone can check it.thanks
[UPDATE]
Suppose draws don't happen.
Also, AABBA is the DIFFERENT result as ABABA.