You have the option to play (or not) a game of chance involving the toss of a fa

Question

You have the option to play (or not) a game of chance involving the toss of a fair coin. If it lands heads you win $10. If it lands tails you lose $10.

a.       Construct the pay off table for this game

b.      What is the expected value of playing this game?

c.       What is the expected value of perfect information for this game?

d.      Suppose you could purchase perfect information before each toss of the coin for $3, how much total return (profit) could you expect after 10 tosses of the coin?

e.      What is expected value of this game if it costs $1 to play for each toss of the coin?

Explanation / Answer

a)    Pay-off table

    Event    Probability    Pay-off     EV

      Head      0.5                $10         $5

      Tail          0.5               -$10       -$5

b) EMV=$5+ -$5= 0

c) The expected value of perfect information for this game is $5

d)After 10 tosses, cost of perfect information=10*$3=$30 and EMVPI=10*$5=$50

     Profit=$50-$30=$20

   e) The expected value of this game if it costs $1 to play for each toss of the coin (w/o perfect information)= -$10

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