Two players (player A and player B) are playing a game against each other repeatedly until one players wins all available money. When a player wins a game they take $1 from the other player. Suppose player A starts with $4 and player B starts with $2. If player A wins a game with probability 1/4 and player B wins a game with a probability of 3/4, what is the probability that player A eventually wins all the money? All plays of the game are independent and identical.

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