Developing the Players Edge with the Mathematical Strategy and Combinations of Rolling the Dice in Sic Bo

Sic Bo

 

Sic BoYou must have understood in the previous post as how scientifically calculations are done to calculate the house edge in the game of Sic Bo. Here you will find the ways to have the player’s edge for the various betting options in sic-bo. Player’s edge is used as opposed to the house edge because it is more simpler to think of strategies from the player’s point of view. The player’s edge will always be negative, to get the house edge just multiply by -1. The general formula for the player’s edge is the dot product of all possible returns and their respective probability. Remember that there are 63=216 possible combinations of the throw of three dice in the game of Sic Bo

Let us understand the possible  betting combinations and their probability calculated mathematically

Rolling a Low Bet

This bet would have no house edge if it were not for the triple exception. The probability of a triple 1, 2, or 3 is 3/216. The probability of any total between 3 and 10 is 1/2, or108/216. 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%.

Rolling with the High Bet

You will have the same probability as above mentioned in the Low bet.

Rolling with a Specific Number

The probability of rolling zero of a specific number is (5/6)3 =125/216.
The probability of rolling one of a specific number is 3*(1/6)1*(5/6)2 = 75/216.
The probability of rolling two of a specific number is 3*(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%.

Rolling with the Total of 4

There are 3 ways to roll a 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%.

Rolling with the Total of 5

There are 6 ways to roll a 5: (1+1+3, 1+3+1, 3+1+1, 1+2+2, 2+1+2, 2+2+1). The player’s edge is thus 6/216*(+30) + (210/216)*(-1) =-30/216 = -13.889%.

Rolling with the Total of 6

There are 10 ways to roll a 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%.

Rolling with the Total of 7

There are 15 ways to roll a 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%.

Rolling with the Total of 8

There are 21 ways to roll a 8: (1-6-6 * 3 ways, 1-2-5 * 6 ways, 1-3-4 * 6 ways,2-2-4 * 3 ways, 2-3-3 * 3 ways). The player’s edge isthus 21/216*(+8) + (195/216)*(-1) = -27/216 =-12.500%.

Rolling with the Total of 9

There are 25 ways to roll a 9: (1-2-6 * 6 ways, 1-3-5 * 6 ways, 1-4-4 * 3 ways,2-2-5 * 3 ways, 2-3-4 * 6 ways, 3-3-3 * 1 way). Theplayer’s edge is thus 25/216*(+6) + (191/216)*(-1) =-41/216 = -18.982%.

Rolling with the Total of 10

There are 27 ways to rolla 10: (1-3-6 * 6 ways, 1-4-5 * 6 ways, 2-2-6 * 3 ways,2-3-5 * 6 ways, 2-4-4 * 3 ways, 3-3-4 * 3 ways). Theplayer’s edge is thus 27/216*(+6) + (189/216)*(-1) =-27/216 = -12.500%.

Rolling with Total of 11

It is same as rolling with the total of 10

Rolling with the Total of 12

It is same as rolling with the total of 9

Rolling with the Total of 13

It is same as rolling with the total of 8

Rolling with the Total of 14

It is same as rolling with the total of 7

Rolling with Total of 15

It is same as rolling with the total of 6

Rolling with the Total of 16

It is same as rolling with the total of 5

Rolling with the Total of 17

It is same as rolling with the total of 4

Rolling with Two numbers

Lets suppose the two numbers chosen are 1 and 2. There are 30 combinations featuring a 1 and a 2: 1-2-1 * 3 ways, 1-2-2 * 3 ways,1-2-3 * 6 ways, 1-2-4 * 6 ways, 1-2-5 * 6 ways, 1-2-6 * 6ways. The player’s edge is thus 30/216*(+5) +(186/216)*(-1) = -36/216 = -16.667%.

Rolling with Specific triplet

There is only 1 way to roll a specific triplet. The player’s edge is thus1/216*(+180) + (215/216)*(-1) = -35/216 =-16.20%.

Rolling with Any triplet

There are 6 ways to rolla triplet. The player’s edge is thus 6/216*(+30) +(210/216)*(-1) = -30/216 = -13.889%.

Rolling with a Specific pair

Let’s assume the pair chosen is ones. There are 16 ways two or three of that number 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. The player’s edge is thus 16/216*(+10) + (200/216)*(-1) = -72/216 = -18.52%.