Roll the Dice

Introduction

Roll the Dice is a simple game of luck betting whether the total of the roll of two dice will be over or under any chosen number by the player.

Two ordinary six-side dice are used.
The player may choose a number from to 2 to 12.
The player may all choose whether the next roll is over or under his chosen number, except he can't bet on impossible events, namely under 2 and over 12.
Ties LOSE

The following table shows the number of winning combinations, probability of winning, and return for all Under bets.

Total	Pays	Winning Combinations	Probability	Return
3	35.28	1	0.027778	0.980000
4	11.76	3	0.083333	0.980000
5	5.88	6	0.166667	0.980000
6	3.53	10	0.277778	0.980556
7	2.35	15	0.416667	0.979167
8	1.68	21	0.583333	0.980000
9	1.36	26	0.722222	0.982222
10	1.18	30	0.833333	0.983333
11	1.07	33	0.916667	0.980833
12	1.01	35	0.972222	0.981944

The following table shows the number of winning combinations, probability of winning, and return for all Over bets.

Total	Pays	Winning Combinations	Probability	Return
2	1.01	35	0.972222	0.981944
3	1.07	33	0.916667	0.980833
4	1.18	30	0.833333	0.983333
5	1.36	26	0.722222	0.982222
6	1.68	21	0.583333	0.980000
7	2.35	15	0.416667	0.979167
8	3.53	10	0.277778	0.980556
9	5.88	6	0.166667	0.980000
10	11.76	3	0.083333	0.980000
11	35.28	1	0.027778	0.980000

The best bets are on under 10 and over 4 at a return of 98.33%.