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anonymous
 5 years ago
5 coins are tossed simultaneously. it costs nothing to play. if 1,2,3,4 heads occur, you will be paid 1 dollar for each head. if all heads or all tails occurs, you lose 20 dollars.
is it possible to adjust the pay amounts to make the game "fair" to both the dealer and the challenger if the expected payoff is 1.093?
anonymous
 5 years ago
5 coins are tossed simultaneously. it costs nothing to play. if 1,2,3,4 heads occur, you will be paid 1 dollar for each head. if all heads or all tails occurs, you lose 20 dollars. is it possible to adjust the pay amounts to make the game "fair" to both the dealer and the challenger if the expected payoff is 1.093?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sure, charge that much to play.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0probability of all head or all tails is 1/32+1/32=2/32 P(1 H) = 5/32 P(2 H) = 10/32 P(3 H)= 10/32 P(4 H)= 5/32 expected value is 1*5/32 +2*10/32 +3*10/32+4*5/3220*2/32

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but question is not clear since obviously you can adjust your payoff in infinite number of ways. numerator of that fraction is 5+20+30+2040 and when you divide by 32 you get 1.093 rounded. fair would mean the numerator was 0, so perhaps the easiest thing to do it so write 752x = 0 and solve for x as what you lose if you get all heads or all tails. this would make the game fair.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in other words instead of losing $20 you would lose $37.5 for all heads or tails. then game would be fair.
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