Question

MEDAL!!

(bill and larry toss two coins. if both coins come up heads, bill pays larry $4. larry pays bill $1 otherwise.)

What is the expected value of this game for bill?

Answer 1

There are four possibilities, each with a probability 0.5*0.5=.25 = 25%

HH = Bill pays Larry $6
HT = Larry pays Bill $1
TH = Larry pays Bill $1
TT = Larry pays Bill $1

Bill will have a positive expected payoff and Larry will have a negative expected payoff, but the value will be the same:

Bill's Payoff = -6*.25 + 1*.25 + 1*.25 + 1*.25 = -$0.75
Larry's Payoff = 6*.25 + -1*.25 + -1*.25 + -1*.25 = $0.75