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# Who Cares If Numbers Have to Roll Twice to Pay on Come Bets?

3 June 2003

Craps players have lots of reasons for making Place rather than Come bets. They want chips all over the layout as soon as a shooter establishes a point, for fear of missing the start of a hot roll. Their daughter was born at 5:55 on 5/5/55 so five is their lucky number. They can't afford to take odds when the Come bet moves to a box and worry that dealers might snicker at them for not doing so. They had a premonition the nine was gonna hit. These explanations aren't exactly illative, but they don't pretend to be. They're admittedly matters of personal conviction.

None of these is the rationale you hear most often, however. The honor here goes to "a number only has to show once to win on a Place bet; it has to hit twice to pay on a Come." This argument differs because it's not based on faith, which nobody can really gainsay; it implies logic, but is more pseudo than scientific.

Temporarily ignore the payoffs for the various options and consider only the chance of winning one or another of the wagers.

Place bets on the six or eight have five ways to win and six to lose, so the probability of winning is 5/(5+6) or 45.45 percent. The five and nine each boast four ways to win and six to lose so the likelihood of euphoria is 4/(4+6) or 40 percent. And on the four or 10, it's three ways to win and six to lose, providing a prospect of profit equal to 3/(3+9) or 33.33 percent.

Figuring Come bets gets a bit tougher. The bets win on come-out rolls of seven or eleven; that's eight ways out of 36, and 8/36 is 22.22 percent. Money moves to the four three ways out of 36, then subsequently has three ways to win and six to lose; overall, the chance of reaching then winning on a four is (3/36)x(3/(3+6)) or 2.78 percent. For a five, it would be (4/36)x(4/(4+6)) or 4.44 percent. The six is (5/36)x(5/(5+6)) or 6.31 percent. Eight, nine, and 10 mirror six, five, and four, respectively. Adding it all up, winning on the come-out or establishing and repeating the possible points, gives a probability of 49.29 percent.

Taking the complete cycle into account, a Come bet is more apt to win than any Place bets. Its success rate is 49.29 percent versus 45.45, 40, and 33.33 percent for Place bets on six or eight, five or nine, and four or 10, in that order. This, despite Come bets requiring the number to hit twice. Solid citizens who rely on recurrence theory are forgetting instances when a Come bet scores before getting to a point, especially those involving a seven when the Come bet wins but Place money would lose.

Dauntless dice doyens doubtless discern that the chance of winning isn't the whole story in comparing strategies. Place bets pay more than even money: 7-to-6 for the six and eight, 7-to-5 for the five and nine, and 9-to-5 for the four and 10. Come bets without odds pay only 1-to-1 regardless of the point.

Edge or expectation is a measure of bet quality that combines and jointly characterizes payoffs and probabilities of winning. The values represent the commission earned by the casino or the players' theoretical loss per dollar at risk. For Place bets, expectation is for players to lose 1.51 cents/dollar on six or eight, 4 cents/dollar for five or nine, and 6.67 cents/dollar for four or 10. For Come bets with no odds, the expectation is to lose 1.41 cents/dollar. By this measure, as with probabilities alone, Come bets are more attractive than any Place alternatives.

Taking odds on a Come bet after it's moved to a number doesn't affect the probability of winning. But it alters the payoffs. The effect is to reduce the theoretical loss per dollar, making Come bets even more attractive relative to their Place parallels.

Still want to make Place instead of Come bets? Go ahead, if your daughter's birthday means that much to you, or if you trust your hunches more than you do the laws of the universe. But bettors who think they're a wiser choice because they have to hit once and not twice to win should reconsider. For, as Sumner A Ingmark, the rollers' rhymer, reminded those punters of poetic proclivity:

Beware the expert demagogic,