In a game a player pays ₹10 to roll a fair die once. If a six appears the player receives ₹x, and if any other number appears the player receives nothing. For what value of x is the game fair, that is, the player's expected gain is zero?

Question

Accepted Answer

60. The player receives ₹x with probability 1/6 and nothing with probability 5/6, so the expected receipt is x/6. A fair game needs this to equal the ₹10 stake, giving x = 60. Setting x = 10 returns the stake only one time in six and loses about ₹8.33 per game in the long run.

In a game a player pays ₹10 to roll a fair die once. If a six appears the player receives ₹ $x$ , and if any other number appears the player receives nothing. For what value of $x$ is the game fair, that is, the player's expected gain is zero?

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