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30-20 Game
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Probability
Parts
Part 1
Part 2

Two players, Philip and Brandon, have a 30-side and 20-side dice, respectively. Each player rolls their dice and the player with the highest role wins (Brandon also wins in the event of a tie). The loser of the game pays the winner an amount equivalent to the value of the winner's dice roll.

Part 1

What is the expected value for the payoff of Philip?