Two people are playing a game, one round after another. Let the probability of person A winning be p, and the probability of person B winning be q, wherein 0<p<1, p+q=1.
There is no draw, and person A will gain 1 point when they win one round, person B will gain 1 point when they win one round, neither will lose points.
The game will stop when one of the two has two more points than the other player. What's the average number of rounds before the game stops?
The answer I have is $2/(p^2+q^2)$, I thought that I should try to make it into a probability distribution since that's the topic I'm currently on, but I'm not sure where to start... Thank you!