Can You Get an Edge at Craps by Controlling the Dice?

2 January 2007

By Alan Krigman

Edge in gambling depends on the offset between the chance of an event and the payoff when it happens. Normally, going into new rounds, offsets are such that the house has an advantage.

As an example, say you Place the four at craps for $10. Six combinations (1-6, 2-5, 3-4, 4-3, 5-2, 1-6) lose and three (1-3, 2-2, 3-1) win. With unbiased dice, all faces have the same chance of finishing on top. This means you're bucking odds of 6-to-3 (which everyone who remembers cancelling from arithmetic in the 4th grade knows is 2-to-1). Absent an edge either way, the payoff would also be 2-to-1; $10 would win $20. But you only get $18. Averaged over many coups, the house pockets the difference.

For you to have an edge on the four, the payoff would have to exceed $20 or the shot at winning be better than 18-to-10 (1.8-to-1). Other than on progressive payouts culled from previous action for future winners, casino bosses who relish job security don't let such situations arise on any bets they offer.

Still, edge can be reversed in some cases. With no hanky-panky. Most famously in blackjack. Cards are set aside after being dealt, so the make-up of a shoe – and therefore probabilities of various situations – change during the game between shuffles. Players who track the cards used can accordingly identify when high ranks are more or less likely to be drawn than average. A surplus of 10s and aces favors the solid citizens. Betting exclusively, or raising wagers, when shoes are rich in high cards gives players an edge. A half to one percent is not uncommon.

Craps shooters could have an edge if they could influence the probabilities of various totals. It's a popular and contentious topic among players. Focus is usually on getting certain sets of faces to appear together when the dice come to rest.

Dice control might be more feasible based on faces you don't want, rather than on combinations you do. This could conceivably be achieved by aligning dice side-by-side with unwanted faces along the "axle," and throwing so they tend to roll end-over-end and not twist while in motion. The accompanying table shows edge for Place bets, were the two dice to roll independently with the indicated faces completely eliminated.

Edge on Place bets with indicated opposing faces of each die eliminated. Negative values favor the house, positive the player.

The data project the best overall results by eliminating 1 & 6 on one die and 3 & 4 on the other. All the Place bets would be hugely advantageous, especially four and 10. Eliminating 1 & 6 and 2 & 5 would work for bets on five, six, eight, and nine but not on four and 10. Similarly, 2 & 5 and 3 & 4 would be strong on five and nine, less so on six and eight, and bad on four and 10.

Even a highly skilled shooter couldn't expect to completely avoid certain faces. Say the controlled throw for the elimination of 1 & 6 and 3 & 4 were 25 percent effective. Edge would be marginally positive on the six or eight but would favor the house on the other numbers. At 51.2 percent efficiency, it would favor players across the board – by 0.02 percent on five or nine, 2.07 percent on six or eight, and 5.57 percent on four or 10. With 75 percent success, players would be favored by 19.58 percent on four or 10, 7.56 percent on five or nine, and 4.60 percent on six and eight.

Can the dice be controlled? Some are sure they can, others sure they can't. Empirical evidence is lacking. Anecdotal evidence describes people who apparently do it. If you're going to play craps at a certain level anyway, it won't hurt to try. However, anyone considering betting the farm on what may be more fancy than fact, more coincidence or wishful thinking than proof, might first mull this memorable muse by the immortal Sumner A Ingmark:

A dollar is easier lost than won,
On schemes that are easier said than done.

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