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The following dice game is offered to you. You may simultaneously roll one red die and...

The following dice game is offered to you. You may simultaneously roll one red die and three blue dice. The stake is $1. If none of the blue dice matches the red die, you lose your stake; otherwise, you get anyway paid k + 1 dollars if exactly k of the blue dice match the red die. In the case that exactly one blue die matches the red die, you get paid an additional $0.50 if the other two blue dice match. What is the expected payoff of the game?

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