More Coin Tossing

You have the opportunity to play a game with a biased coin, where $P(H)=\frac{1}{2}+b$ and $P(T)=\frac{1}{2}-b$. In each round of the game, you toss the coin and win or lose one dollar. The game is played as follows. 

On the first toss: receive a dollar regardless of the outcome. 
On all other tosses: if you won (lost) a dollar on the prior toss, you win (lose) a dollar if the current toss comes out heads and lose (win) a dollar if it comes out tails.

What would you pay to play this game with a coin of bias $b$ for exactly $n$ rounds? Why?