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Best of Alan Krigman
How does edge on Pass and Come bets at craps change during the game?9 July 2012
If you play craps and bet Pass or Come, which are identical except for the stage of a hand when they’re made, the edge you’re fighting is among the lowest in the casino. Blackjack with decent rules has less of a house advantage, assuming you follow Basic Strategy reasonably closely or, better, get a leg up on the bosses by counting cards. Once in an increasingly great while, you may also find a video poker game that gives you more of a break than you get on these craps wagers.
Overall, the probabilities of a win or loss on Pass or Come – from the come-out roll through the final resolution – are 49.29 and 50.71 percent, respectively. The edge on the flat portion of a bet of size B, the amount you initially wager on the come-out and which pays even money whether it wins on that roll or after a point is established, is therefore [0.4929 x B - 0.5071 x B]/B = -0.0142 or -1.42 percent (the minus sign indicating the house is favored). You can reduce this, however.
The edge on Pass and Come changes during the course of the action. Part of the change is inherent in the structure of the game. The rest results from actions taken by the player.
During the come-out, these bets win on sevens or 11s and lose on twos, threes, or 12s. Six dice combinations can form a seven six (1-6, 2-5, 3-4, 4-3, 5-2, 1-6) and two an 11 (5-6, 6-5) so there are eight ways the bet can win; a two can be formed with one combination (1-1), a three with two (1-2, 2-1), and a 12 with one (6-6) so there are four ways the bet can lose. The probabilities of winning are therefore eight out of a total of 12, and of losing are and four out of 12. With $10 on the line, effective edge during the come-out can accordingly be found as [(8/12) x 10 - (4/12) x 10]/10 = +(4/12), which is a huge +33.33 percent, the plus sign indicating the player is favored.
Unfortunately, you can’t stop there and take down the bet. Offsetting the big advantage players get on Pass and Come bets during come-outs, edge shifts to the house after the point is established. The size of the house’s hammer during the point phase of the roll depends on:
the point established by the come-out, which bettors can’t control, the amount, if any, added to the flat bet in the form of Odds – which, subject to the limits imposed by the casino – craps aficionados can specify as they wish and can afford.
Flat bets continue to pay even money during point rolls. Odds pay in proportion to the difficulty of winning – 6-to-3 (2-to-1) on the four or 10, 6-to-4 (1.5-to-1) on the five or nine, and 6-to-5 (1.2-to-1) on the six or eight. Amounts at risk and payoffs for $10 flats for representative choices of single, double, and 10X Odds multiples on the various points are as follows:
single Odds would augment the $10 flat with another $10, putting a total of $20 at risk; payoff for the $20 would be $10 + 2 x $10 = $30 on the four or 10, $10 + 1.5 x $10 = $25 on the five or nine, and $10 + 1.2 x $10 = $22 on the six or eight.
double Odds would add $20 to the flat $10, leaving $30 up for grabs; payoff for the $30 would be $10 + 2 x $20 = $50 on the four or 10, $10 + 1.5 x $20 = $40 on the five or nine, and $10 + 1.2 x $20 = $34 on the six or eight.
10X Odds would mean plunking down $100 behind the flat $10, escalating to $110 all told; payoff for the $110 would be $10 + 2 x $100 = $210 on the four or 10, $10 + 1.5 x $100 = $160 on the five or nine, and $10 + 1.2 x $120 = $130 on the six or eight.
Using these amounts at risk and payoffs, along with the probabilities of winning and losing on each number (respectively: 3/9 & 6/9 for four or 10, 4/10 & 6/10 for five or nine, and 5/11 & 6/11 for six or eight), edge during the point phase of the roll is as indicated in the accompanying table. The data show the improvement that can be achieved with increasing Odds multiples.
Edge for Pass and Come bets during the point phase of a roll for typical Odds multiplesOdds multiple
Point 0X 1X 2X 5X 10X 4 or 10 -33.33% -16.67% -11.11% -5.56% -3.03% 5 or 9 -20.00% -10.00% -6.67% -3.33% -1.82% 6 or 8 -9.09% -4.55% -3.03% -1.52% -0.83%
These house advantages, combined with the edge favoring the player during the come-out and allowing for the likelihood that one or another number will be the point, still leave the bosses in the catbird seat. But, when players take Odds, the overall edge against them is considerably lower the -1.42 percent on the flat bet alone. The data in the table also provide clues as to when craps buffs who are willing to sacrifice edge to have a choice of points rather than rely on the roll of the dice should consider Put rather than Place bets. All of which goes to show the wisdom of the words of that wondrous warbler, Sumner A Ingmark:
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