Winning Contest

Alice and Bob challenged each other to‚Äč 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
AAA
AABAA
ABABBAAAA

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.

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