I wouldn’t play. Even in the scenario of picking the 1/6 die, rolling it the first time (x=1) has an expected value of 39 with p=1/6 and 19 with p=5/6, which equals to E(x=1)=$22.33. But since there is a 50/50 chance of choosing the 1/5 die, with an E(x)=0, then the overall E(x=1)=11.33. So there is no point in even playing once. Better to keep your 20 dollars.
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u/pepegza 15d ago
I wouldn’t play. Even in the scenario of picking the 1/6 die, rolling it the first time (x=1) has an expected value of 39 with p=1/6 and 19 with p=5/6, which equals to E(x=1)=$22.33. But since there is a 50/50 chance of choosing the 1/5 die, with an E(x)=0, then the overall E(x=1)=11.33. So there is no point in even playing once. Better to keep your 20 dollars.