Two players compete against each other in a game of chance where Player A wins with probability 1/ 3 and Player B wins with probability 2/ 3. Every time Player A loses he must pay Player B $ 1, while every time Player B loses he must pay Player A $ 3. Each time the two play the game, the results are independent of any other game. If the two players repeat the game 10 times, what is the expected value of Player A’s winnings?
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