Someone gives you two dice. They offer to pay you \$37 if you roll two 6s. However, it will cost you \$1 a roll. What is the EV of this wager?
My work:
1/36 = 35:1 = 0.0277 for \$37 = 1.027
35/36 = 1:35 = 0.972 for -\$1 = -0.972
EV: 0.055
This is what the answer page shows:
1/36 = .028
Other rolls: 35/36 = 0.972
.028(\$36) + 0.972(-\$1) = x
\$1.008 – \$0.972 = \$.036
EV = \$0.036
I've stared at this for an hour now and I can't figure out why my answer differs. Please take me out of my misery!
You multiplied .0277 * 37.
The solution multiplied it by 36 (you need to pay 1 dollar). Plus the solution rounded 0.0277 to 0.028.
UPDATE: You assumed that the payout would be 37 dollars. However, you have to pay 1 dollar. So the net payout is 36 dollars.