I got the same answer as Varun. But I think it's easier to do in terms of a tree. Start with (0,0) and then two possible nodes (0,1) and (1,0). If either team reaches a 4, it is a terminal state, with value -100 or +100. You'll end up with a tree that widens and then narrows to (3,4) and (4,3). Now use backward induction. Label each node with Value|Bet.

You immediately bet 100$ that A will win the series and - that's it.