You play a game of chance with the probability of winning at each play equal to 1/3.

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You play a game of chance with the probability of winning at each play equal to 1/3. You bet $1 and quit if you win. If you lose, you bet $2 and quit whatever happens. Find the expected value of your profit. Will this figure change, if you first bet $2, and then $1 (if you lose at the first time)? Guess and then check your guess.

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