Semi-wall stochastic game

The semi-wall game is a Gridworld game played on a 3x3 grid. With player $A$ starting in the bottom left corner and player $B$ starting in the bottom right. The goal of the game is to arrive at the money in the centre top - whoever does that first gets a point. If two players try to enter the same spot with even odds one player moves in and the other stays where they are. There is a semi-wall above each player to start with which has a 50% chance of letting them through, otherwise they stay where they are. The game looks as follows: