How much should I pay to play?

 If your chance of winning 100 in a game is 0.05, a fair price for playing is 0.05 x 100 = 5

 Similarly, if you win 50 for a head and lose 40 for a tail. the fair price would be 

  x 50 -   x 40  =  5. 

The Problems : 

1.         What should you pay to play a game where you win 10 for every spot showing when a die is thrown once?

 2.         What should you pay to play a game where you win 10 for every spot showing when two dice are thrown once?

 3.        This next game is supposed to have been played at St Petersburg:  

            A coin is tossed until a head appears.  If it appears on the first toss, you win 1.  If it first appears on the second toss, you win 2.  If it appears for the first    time on the third toss, you win 4, and so on, doubling each time.

 (a)       What is the probability that you will win exactly 32?  That you will win more than 32?  That you will win less than 32?

(b)       If the game stops after 10 throws, what would be a fair price to pay?

(c)        If it is to go on, regardless of how long the game takes, what would be a fair price to pay?  How can you explain the answer you get?

(d)        If the rules are changed so that the Bank will not pay if the winning total is more than 1,000,000, what is a fair price to pay?

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Last modified: June 18, 2007