Should you lay odds on Don't Pass and Don't Come bets at craps?

Say you bet on Don’t Pass or Don’t Come at craps. Your chances are 47.9 percent of ecstasy and 49.3 percent of agony; the remaining 2.8 percent is the probability of pushing.

Although the come-out involves just one roll, it’s the dark underbelly of Don’t Pass and Don’t Come wagers. At this stage of a hand you’re a serious underdog with a mere 8.3 percent chance of winning even money. The other possibilities are 22.2 percent of losing, 2.8 percent of pushing, and 66.7 of having the shooter establish a point and postponing the decision on the bet.

During the point phase of the game, you win if the shooter throws a seven before repeating the established number and lose if the converse occurs. Given that you’ve cleared the hurdle of the come-out, you’ve become conditionally favored to win even money on your base bet to a degree dependent on the point. On four or 10, the advantage is 6-to-3 – six ways to win versus three to lose. On five or nine, it’s a 6-to-4 lead – six ways to win versus four to lose. And on six or eight, the bias is 6-to-5 – six ways to win versus five to lose.

Combined, the joint prospects for the even-money bet on the come-out and the point rolls give you the overall 47.9 and 49.3 percent probabilities of winning and losing, respectively, and the house’s relatively modest 49.3 - 47.9 = 1.4 percent edge. But the casino bosses go further in their generosity. They let solid citizens inclined to do so increase their Don’t Pass and Don’t Come bets after points have been established, when the likelihood is greater of triumph than of tragedy.

There’s a little hitch, however. New bread bet when players know they’re more apt to succeed than fail pays less than even money; the payoffs are inversely proportional to the odds that bettors will win. Earnings on the auxiliary bets are therefore $1 for every supplementary $2 at risk on four or 10, $2 for every additional $3 up for grabs on five or nine; and $5 for every extra $6 on six or eight. Owing to the strict inverse relationship, neither bosses nor bettors have an edge on the secondary bet – and it’s accordingly known as “Free Odds” or, commonly, “Odds.”

Wagers on which casinos have no edge are not exactly ubiquitous. The list pretty much comprises the Odds at craps – on which edge is zero, as well as subsidiary bets to double or split properly at blackjack and a few circumstances like acting as Banker at pai gow poker – on all of which players have an edge. A neutral observer might assume that experienced gamblers would eagerly avail themselves of the opportunities these cases present. It doesn’t always happen.

For craps buffs on Don’t Pass or Don’t Come, one fly in the no-edge ointment is aversion to the idea of more cash being vulnerable to a loss than can be won on any single round. The hesitancy despite two key factors. 1) The bet is expected to win more frequently than it loses. 2) Although a base bet that gets to a point favors the player with a greater than even shot at picking up even money, the casino is still statistically on top when the wager is evaluated over the whole cycle, and laying Odds lowers the house’s effective edge on the gross at stake. Further, players with adequate bankrolls may feel at ease exposing an amount like $10 on the toss of the dice. But the same folks may be uncomfortable laying, say, $60 as triple Odds against a point of four – a $10 setback being one thing and a $70 loss something else entirely, probabilities notwithstanding.

A special situation arises from time to time. Occasionally, players on Don’t Pass or Don’t Come exercise the option to take down their wagers rather than follow through on the point portion of a hand. This is encountered most often when the point is six or eight. Bettors who do it usually figure that the odds of winning on one of these numbers is only 6-to-5, whereas going through the come-out roll again might yield a five or nine where they’d be favored 6-to-4, or a four or 10 where they’d be stronger yet at 6-to-3. This reasoning is specious because the uphill battle of the come-out more than wipes out the benefit enjoyed on the point.

If you do find players who take down Don’t Pass or Don’t Come bets on points, forget trying to explain the facts of life to them. Instead, offer to buy the bets they want returned. Just give them the dough for another come-out roll, and congratulate yourself for making a wager that gives you an advantage from the get-go. If you wish, you can lay Odds on it. You’d still be in the catbird seat with respect to chance of winning or losing the round, and would have been able to make a “fair” bet without paying the price for the privilege by going through the come-out. But now, instead of the Odds reducing what would be the house’s edge were you to have been in peril during the come-out, the extra money actually lowers your net advantage. So, should you lay the Odds under these conditions or not? Go for the moolah or with the math ? It’s a dilemma deftly described by the celebrated songspinner, Sumner A Ingmark, in this venerable verse:
Logic rarely is effective,
When decisions are subjective.