I'm stuck on this Probability?

Two players A and B play the following game: Initially, player A has n(sub)A pounds and player
B has n(sub)B pounds, both greater than zero. They toss a fair coin and if it turns HEADS, then player B gives one pound to
A. If it turns TAILS, then player A gives a pound to B. The game stops when one of the players loses
all his money. What is the average number of steps until the end of the game ?

(HINT: let m(sub)j be the expected number of steps required, when player A has j pounds and try to set up a recursive equation
for m(sub)j.)

Question

I'm stuck on this Probability?

Two players A and B play the following game: Initially, player A has n(sub)A pounds and player
B has n(sub)B  pounds, both greater than zero. They toss a fair coin and if it turns HEADS, then player B gives one pound to
A. If it turns TAILS, then player A gives a pound to B. The game stops when one of the players loses
all his money. What is the average number of steps until the end of the game ? 

(HINT: let m(sub)j be the expected number of steps required, when player A has j pounds and try to set up a recursive equation
for m(sub)j.)