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Best of Alan Krigman
Setting the Dice is One Thing; Achieving Results Is Another6 August 2001
So it is with setting dice. There's more than one way to do it. And, setting the dice is one thing but getting the desired numbers to appear is another matter entirely.
Simple setting schemes start with preferred or unwanted results on one or more sets of faces, hoping they will or won't finish the same way, respectively. The former might have 2-2 on top, 3-3 on the front, 5-5 on the bottom, and 4-4 on the back. The latter might put 2-5 on top and bottom with 3-4 on front and back.
Fancier systems entail trying to reduce the chance of certain faces showing when the dice come to rest. One procedure involves placing the dice side by side with the proscribed faces on the "axles," like hubcaps. Then trying to throw in a way that the dice rotate around the axles, keeping the hubcaps on the ends.
Assume for the sake of argument this can be done. Then, a throw no longer has 36 possible outcomes -- six faces of one die times six on the other -- with the probability distributions on which the payouts for the game are predicated. Instead, a throw will have 16 possible outcomes -- four faces on one die times four on the other -- and an entirely different probability distribution.
The accompanying chart shows the distribution of results for random throws, and for the six ways the dice can be set to exclude pairs of faces. Probabilities are given as fractions -- the number of ways a result can appear out of 36 for a random throw and out of 16 for a successful axial set.
Probability Distributions for Alternate Axial Dice Settings
Use the chart to find settings that might favor one or another group of outcomes during come-out and subsequent rolls. You can get the idea without doing any math. A solid citizen shooting from the pass line might set 1-6/1-6, trying to avoid a craps on the come-out while retaining a good shot at a natural seven and having incrementally increasing chances of inside numbers for the point. An alternative might be 1-6/3-4 coming-out. This sidesteps the two or 12; the three is allowed but is offset by the 11. All other results have equal 2/16 chances.
After the come-out, a switch-up might be appropriate depending on the point and other bets. For instance, pretend you'd like a four or 10. Setting 1-6/3-4 gives you the most ways to hit these numbers while also minimizing the combinations that total seven. When you're looking for a six or eight, the 1-6/2-5 setting would offer more ways to succeed while still holding down the seven.
If you're numerically-inclined, you can use the chart to find the edge with various settings. Make believe you place the four for $10 and use the 1-6/3-4 setting. The probabilities are each 2/16 of winning $18 and losing $10. So you're the favorite, with an edge of 10 percent, calculated as (1/10)x[(2/16)(18)-(2/16)(10)].
Is the "axle" approach the only way to set the dice? Does this or any other method work? Am I recommending this practice or merely explaining it? Well, remember the aphorism, the allegory ... and these mutterings of the eminent muse, Sumner A Ingmark:
Approach with apprehension,
Best of Alan Krigman