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Sic Bo Appendix
Image take from the Claridge Hotel/Casino rule book. Click on the image to see the rules on the next page.
 Low:
This bet would have nohouse edge if it were not for the triple exception. Theprobability of a triple 1, 2, or 3 is 3/216. Theprobability of any total between 3 and 10 is 1/2, or108/216. So the probability of a winning triple is108/216  3/216 = 105/216. The player's edge is thus(105/216)*(+1) + (111/216)*(1) = 6/216 =~2.78%.
 High: See Low.
 SpecificNumber:
The probability ofrolling zero of a specific number is (5/6)^{3} =125/216.
The probability of rolling one of a specific number is3*(1/6)^{1}*(5/6)^{2} = 75/216.
The probability of rolling two of a specific number is3*(1/6)^{2}*(5/6)^{1} = 15/216.
The probability of rolling three of a specific number is(1/6)^{3} = 1/216.
The player's edge is thus (125/216)*(1) + (75/216)*(+1)+ (15/216)*(+2) + (1/216)*(+3) = 17/216 =~7.780%.  Total of4:
There are 3 ways to rolla 4: (1+1+2, 1+2+1, 2+1+1). The player's edge is thus3/216*(+60) + (213/216)*(1) = 33/216 =15.278%.
 Total of5:
There are 6 ways to rolla 5: (1+1+3, 1+3+1, 3+1+1, 1+2+2, 2+1+2, 2+2+1). Theplayer's edge is thus 6/216*(+30) + (210/216)*(1) =30/216 = 13.889%.
 Total of6:
There are 10 ways to rolla 6: (1+1+4, 1+4+1, 4+1+1, 1+2+3, 1+3+2, 2+1+3, 2+3+1,3+1+2, 3+2+1, 2+2+2). The player's edge is thus10/216*(+17) + (206/216)*(1) = 36/216 =16.667%.
 Total of7:
There are 15 ways to rolla 7: (1+1+5, 1+5+1, 5+1+1, 1+2+4, 1+4+2, 2+1+4, 2+4+1,4+1+2, 4+2+1, 1+3+3, 3+1+3, 3+3+1, 2+2+3, 2+3+2, 3+2+2).The player's edge is thus 15/216*(+12) + (201/216)*(1) =21/216 = 9.722%.
 Total of8:
There are 21 ways to rolla 8: (166 * 3 ways, 125 * 6 ways, 134 * 6 ways,224 * 3 ways, 233 * 3 ways). The player's edge isthus 21/216*(+8) + (195/216)*(1) = 27/216 =12.500%.
 Total of9:
There are 25 ways to rolla 9: (126 * 6 ways, 135 * 6 ways, 144 * 3 ways,225 * 3 ways, 234 * 6 ways, 333 * 1 way). Theplayer's edge is thus 25/216*(+6) + (191/216)*(1) =41/216 = 18.982%.
 Total of10:
There are 27 ways to rolla 10: (136 * 6 ways, 145 * 6 ways, 226 * 3 ways,235 * 6 ways, 244 * 3 ways, 334 * 3 ways). Theplayer's edge is thus 27/216*(+6) + (189/216)*(1) =27/216 = 12.500%.
 Total of 11: Seetotal of 10
 Total of 12: Seetotal of 9
 Total of 13: Seetotal of 8
 Total of 14: Seetotal of 7
 Total of 15: Seetotal of 6
 Total of 16: Seetotal of 5
 Total of 17: Seetotal of 4
 Twonumbers:
Lets suppose the twonumbers chosen are 1 and 2. There are 30 combinationsfeaturing a 1 and a 2: 121 * 3 ways, 122 * 3 ways,123 * 6 ways, 124 * 6 ways, 125 * 6 ways, 126 * 6ways. The player's edge is thus 30/216*(+5) +(186/216)*(1) = 36/216 = 16.667%.
 Specifictriplet:
There is only 1 way toroll a specific triplet. The player's edge is thus1/216*(+180) + (215/216)*(1) = 35/216 =16.20%.
 Anytriplet:
There are 6 ways to rolla triplet. The player's edge is thus 6/216*(+30) +(210/216)*(1) = 30/216 = 13.889%.
 Specificpair:
Lets assume the pair chosen is ones. There are 16 ways two or three of thatnumber can be rolled: 1+1+1, 1+1+2 * 3 ways, 1+1+3 * 3 ways, 1+1+4 * 3 ways, 1+1+5 * 3 ways, 1+1+6 * 3 ways. Theplayer's edge is thus 16/216*(+10) + (200/216)*(1) = 72/216 = 18.52%.
Following is a formula for s spots over n dice, taken from The Theory of Gambling and Statistical Logic by Richard A. Epstein, formula 514.
For example, let's look at the number of ways to get 11 spots over 3 dice.
int[(sn)/6] = int[(113)/6] = int[1.33] = 1
The total would be 6^{3} * [1^{0}*combin(3,0)*combin(116*01,31) + 1^{1}*combin(3,1)*combin(116*11,31) ] =
1/216 * [1*1*combin(10,2) + 1*3*combin(4,2)] =
1/216 * [1*1*45 + 1*3*6] =
1/216 * [4518] = 27/216 = 12.5%
Written by: Michael Shackleford