Geometric distribution problem

I am am trouble with the following homework problem.

(Note:This is exactly how the problem is stated)

Two players each put one dollar into a pot. They then decide to throw a pair of dice alternately. The first one who throws a sum of 5 wins the pot. How much should the player who starts add to the pot to make this a fair game?

I think it is a geometric distribution.

Which is defined as p(x)= p(1-p)^x and the mean is (1-p)/p.

I also know the probability of 2 dice summing to 5 is 4/36 or approx. .1111.

I can determine the probability that player A wins when P{X=1}, P{X=3}...

Similarly, for player B P{X=2}, P{X=4}

The professor also gave the following clues:

P{A wins}=? P{B wins} =?

E[A's reward]=P{A wins}*1

E[B's reward]=P{B wins}*(1+$x)

But I am lost.

Any help would be greatly appreciated.