Winning Contest
Alice and Bob challenged each other to a duel with at most 30 rounds. A person will win when they have won precisely 3 more rounds than the other. In how many different sequences can Alice win?
Denote the round where Alice or Bob wins as A
and B
respectively. Some winning sequences for Alice are as follows:
1 2 3 

Note that the sequence BBBAAAAAA
is not a winning sequence for Alice because Bob already won on the third round and the game would have ended.