The fields bet in caraps is a one roll bet that the next rol

The fields bet in caraps is a one roll bet that the next roll will be in {2, 3, 4, 9, 10, 11, 12}. Payoff odds (in most casinos) are 2 to 1 on {2, 12} and 1 to 1 on {3, 4, 9, 10, 11}. Calculate the house advantage H_0(B, X).

Solution

Over 36 rolls the expected return is

3+4+6+0+0+0+0+8+6+4+3 = 34 for every 36 bet making the house advantage

2/36 = 1/18 = 0.05555555555555555555555555555556 = 5.5555555555555555555555555555556%