Monday, March 01, 2004
Mathematics
This might be of interest to all the craps players out there. It can be shown that two 6-sided dice with sides labeled [1,2,2,3,3,4] and [1,3,4,5,6,8] (called Sicherman dice) will present the exact same probabilitistic makeup as standard 6-sided dice. You can check all of it, but by way of further explanation, notice that standard dice have roll totals of 2 through 12, as do the Sicherman dice. Furthermore, for standard dice, there are 4 ways to get a roll total of, for example, 5: [1,4], [2,3], [3,2], and [4,1] For Sicherman dice, there are also 4 ways to get a roll total of 5: [1,4], [2,3], [2,3], and [4,1]
I suppose, though, that mentioning craps wasn't exactly correct since playing with Sicherman dice you lose the side bets of "boxcars" and the like.
This might be of interest to all the craps players out there. It can be shown that two 6-sided dice with sides labeled [1,2,2,3,3,4] and [1,3,4,5,6,8] (called Sicherman dice) will present the exact same probabilitistic makeup as standard 6-sided dice. You can check all of it, but by way of further explanation, notice that standard dice have roll totals of 2 through 12, as do the Sicherman dice. Furthermore, for standard dice, there are 4 ways to get a roll total of, for example, 5: [1,4], [2,3], [3,2], and [4,1] For Sicherman dice, there are also 4 ways to get a roll total of 5: [1,4], [2,3], [2,3], and [4,1]
I suppose, though, that mentioning craps wasn't exactly correct since playing with Sicherman dice you lose the side bets of "boxcars" and the like.
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