Here are all 36 rolls. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) Here are all the rolls with a combined value of '9' or over: (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6,4) (6,5) (6,6) There are 10 of them, so the probability of getting a roll with a combined value of '9' or over isor Here are the rolls of '7' or '8': (1,6) (2,5) (2,6) (3,4) (3,5) (4,3) (4,4) (5,2) (5,3) (6,1) (6,2) There are 11 of them, so the probability of getting a roll with a '7' or '8' is . Here are the rolls less than a '7': (1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (4,1) (4,2) (5,1) There are 15 of them, so the probability of getting a roll less than a '7' is or . Rolls | Probability | Winning | Expectation ------------------------------------------------------------------------ '9' or over | 10/36 | $1.05 | (10/36) × $1.05 = $0.29 1/6 '7' or '8' | 11/36 | -$3.00 | (11/36) × -$3.00 = -$0.91 2/3 less than '7'| 15/36 | $0.60 | (15/36) × $0.60 = $0.25 ------------------------------------------------------------------------ Totals | 36/36=1 | | -$0.37 1/2 The expectation is cents. That means if you play the game many times, you will average losing cents per game. Edwin