Players A and B each have $10 at the beginning of a game in which each player bets at each play, and the game continues until one player is broke. Suppose that Player A wins on a single bet with probability p = 0.45

What is the average duration of the game?

What is the probability that Player B wins the game?

So far I have created a diagram assuming that it doesn't matter how much is being bet per round ($10 per round in the diagram)

And the associated transition matrix

I do not know how to proceed from here to answer the questions that are being asked. I would appreciate any help in this matter.