Craps Systems

Craps players love systems, trying to mix and match bets in hopes of finding the magical formula that will beat the casino.

Just about any system will work sometimes, and when a player wins with a system, it encourages another try, and another, and another. In the long run, of course, the casino comes out on top.

When readers send me systems, the challenge isn't so much in determining whether the formula gives the player and edge, but deciphering why it doesn't.

So it goes with a system e-mailed to me recently by a player called Chuloco:

"What if someone played $10 on pass, $10 don't pass, $10 field simultaneously, then kept doing that from the come and don't come lines? Wouldn't you either win the field or lose the field on a 6 or 7 or 8? The 6 or 8 would give you a strong come number and the 7 would break even (except for the field bet)."

There are several weaknesses in this system. First, pass and don't pass--and come and don't come on later rolls--don't perfectly offset. If a point is established, every pass loser is a don't pass winner, and vice versa. And on the comeout, don't pass losers on 7 and 11 win on pass, and pass losers on 2 and 3 win on don't pass.

So far so good, but then we have to account for the 12. On the comeout, 12 loses on pass but doesn't win on don't pass. Once every 36 comeout rolls--the frequency with which 12 is rolled--this system loses $10 on pass without an offsetting win on don't pass.

The bigger problem is that the field is a one-roll bet, with a house edge (5.56 percent if 12 pays 2-1, 2.78 percent if 12 pays 3-1) that is far higher than the 1.41 percent on pass or 1.4 percent on don't pass. If we are continually replenishing the field bet, we bet most of our money on the weakest part of the wager.

Let's walk through the results of this system for each number rolled on the comeout, with $30 at stake on each trial. For the moment, we'll assume that just one field bet is made per trial:

2. Win $20 with 2-1 payoff on field; pass and don't pass offset. Overall: win $20 on the one roll of 36 that is a 2.

3. Win $10 on field; pass and don't pass offset. Overall: win $10 for each of the two rolls of 36 that is a 3, for a total of $20.

4. Win $10 on field; pass and don't pass offset. Overall: win $10 for each of the three rolls of 36 that is a 4, for a total of $30.

5. Lose $10 on field; pass and don't pass offset. Overall: Lose $10 for each of the four rolls of 36 that is a 5, for a total loss of $40.

6. Lose $10 on field; pass and don't pass offset. Overall: Lose $10 for each of the five rolls of 36 that is a 6, for a total loss of $50.

7. Lose $10 on field; pass and don't pass offset. Overall: Lose $10 for each of the five rolls of 36 that is a 7, for a total loss of $60.

8. Lose $10 on field; pass and don't pass offset. Overall: Lose $10 for each of the five rolls of 36 that is an 8, for a total loss of $50.

9. Win $10 on field; pass and don't pass offset. Overall: win $10 for each of the four rolls of 36 that is a 9, for a total of $40.

10. Win $10 on field; pass and don't pass offset. Overall: win $10 for each of the three rolls of 36 that is a 9, for a total of $30.

11. Win $10 on field; pass and don't pass offset. Overall: win $10 for each of the two rolls of 36 that is an 11, for a total of $20.

12. Win either $20 for 2-1 payoff or $30 for 3-1 payoff on the field; lose $10 on pass; break even on don't pass. Overall: win either $10 or $20 for the one roll in 36 that is a 12.

Add all that up, and you get either $170 or $180 worth of wins on 2, 3, 4, 9, 10, 11 and 12, but $200 worth of losses on 5, 6, 7 and 8. So for an average 36 betting sequences, the player loses either $20 or $30, depending on the field bet payoff on 12.

That calculates to house edges of 2.78 percent if the field pays 2-1 on 12 or 1.85 percent if the payoff is 3-1. Either way, the player is spotting the house more of an edge than if he or she stuck to pass or don't pass. That's just what we should expect--the overall house edge falls between the highest and lowest.

But it gets far worse than that if the player keeps making field bets after a point is established, as Chuloco suggests. On two-thirds of the sequences--those that start with 4, 5, 6, 8, 9 or 10--the player will make at least two field bets and possibly many more before the pass and don't pass bets are decided. As more and more money is invested in the worst bet in the combination, more and more money goes to the house side of the table.

Another reader e-mailed a system he was told is a surefire money-maker. We'll look at that one next week.