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# Would Craps be Craps with Eight-Faced Dice?

3 May 2004

What if dice had eight identical faces instead of six? It's certainly feasible. Think of an Egyptian pyramid with a square base and four matched triangular faces. Now join two pyramids base-to-base and you get an octahedron with eight identical faces. Engrave the faces with from one to eight dots and presto. Call the casino game played with these objects pharaoh craps.

How would you design pharaoh craps to be analogous to the standard game with six-faced cubes, but modified to account for the two extra numbers on each die? The basis for specifying the features of the game lies in the fact that instead of 36 possible ways the dice can land, there would be 64. And the totals would be from two to 16 rather than two to 12. The accompanying table shows how many ways out of the 64 each total could be formed.

Distribution of totals on
two eight-faced dice

 total number of ways 2 1 (1-1) 3 2 (1-2, 2-1) 4 3 (1-3, 2-2, 3-1) 5 4 (1-4, 2-3, 3-2, 4-1) 6 5 (1-5, 2-4, 3-3, 4-2, 5-1) 7 6 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) 8 7 (1-7, 2-6, 3-5, 4-4, 5-3, 6-2, 7-1) 9 8 (1-8, 2-7, 3-6, 4-5, 5-4, 6-3, 7-2, 8-1) 10 7 (2-8, 3-7, 4-6, 5-5, 6-4, 7-3, 8-2) 11 6 (3-8, 4-7, 5-6, 6-5, 7-4, 8-3) 12 5 (4-8, 5-7, 6-6, 7-5, 8-4) 13 4 (5-8, 6-7, 7-6, 8-5) 14 3 (6-8, 7-7, 8-6) 15 2 (7-8, 8-7) 16 1 (8-8)

The first design decision would be to select the "miss-out" number. Logically, it's the most likely total, the sum that can be formed in the most ways. In hexahedral craps, this is seven, which can occur six out of 36 possible ways. In the pharaoh variation, the distinction goes to the nine, at eight out of a possible 64, so it would undoubtedly serve this function.

Next to be determined would be the totals having action on the come-out and becoming the one-roll "propositions." Suppose Pass bets lost coming out with two, three, and 16, and won with nine and 15. The boxes would then be four to eight and nine to 14.

Pass line bettors would be favored on the come-out by 10-to-4. Much stronger than the 8-to-4 in traditional craps. But not strong enough if the flat portion of the bet paid even money on the point because house edge overall would be a whopping 6.8

percent. Worse than many slots. No rational person would play. Making the payout on the point 6-to-5 would swing this too far down. The house would still have an edge, but it would only be 0.6 percent. Casinos wouldn't offer a new game at this level.

Another option would be to leave winners on the point at 1-to-1 but pay more than even money on the come-out. At 3-to-2 on the come-out, players would have 1 percent edge overall, a ticket to the unemployment window for any casino boss who implemented it. At 7-to-5 on the come-out, overall house advantage on a flat line bet would be 0.5 percent -- not enough profit for the house. A payout of 6-to-5 would get the edge to 3.7 percent. This would be a curse to the cognoscenti but in the same ballpark as the carnival games to which solid citizens are flocking nowadays.

You'd also have to set the payouts for Place bets. Take the four or 14 as an example. Each has three ways to win and eight to lose, so you're fighting odds of 8-to-3. If the bet paid what might seem an attractive 12-to-5, the edge would be an excessive 7.3 percent. Bringing this to 13-to-5, edge drops to 1.8 percent, which wouldn't be out of the question. As for the inside, Place bets on eight or 10 have seven ways to win and eight to lose.

Even-money payoffs would give the house a high 6.7 percent edge. Greater payoffs on these numbers, 6-to-5 or 7-to-6 for instance, wouldn't work because they tip the scales to favor the player.

Maybe we should just forget innovation for the sake of change and stick with the hexahedrons dice doyens have learned to love and hate so passionately all these years. For, as the reactionary rhymer, Sumner A Ingmark, reminded readers:

Tradition, honed by sands of time,
Transcends from crudeness to sublime.