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The game of craps uses two dice. This gives us 11 possible numbers (2 to 12) and 36 possible ways of rolling the dice.
- 2: 1-1 = 1/36
- 3: 1-2, 2-1 = 2/36 or 1/18
- 4: 1-3, 2-2, 3-1 = 3/36 or 1/12
- 5: 1-4, 2-3, 3-2, 4-1 = 4/36 or 1/9
- 6: 1-5, 2-4, 3-3, 4-2, 5-1 = 5/36
- 7: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1 = 6/36 or 1/6
- 8: 2-6, 3-5, 4-4, 5-3, 6-2 = 5/36
- 9: 3-6, 4-5, 5-4, 6-3 = 4/36 or 1/9
- 10: 4-6, 5-5, 6-4 = 3/36 or 1/12
- 11: 5-6, 6-5 = 2/36
- 12: 6-6 = 1/36
The chances that a 7 or 11 are rolled on the Come out roll are 8/36 or 2/9.
The chances that craps will be rolled on the Come out roll are 4/36 = 1/9.
The chances that a specific Point number comes before a seven are as follows:
- Point 4 = three chances for a 4, verses six chances for a 7 = 3:6 or 1:2
- Point 5 = four chances for a 5 verses six chances for a 7 = 4:6 or 2:3
- Point 6 = five chances for a 6 verses six chances for a 7 = 5:6
- Point 8 = five chances for a 8 verses six chances for a 7 = 5:6
- Point 9 = four chances for a 9 verses six chances for a 7 = 4:6 or 2:3
- Point 10 = three chances for a 10, verses six chances for a 7 = 3:6 or 1:2
Odds of 2-Stage Bets
2-stage bets are bets on the Pass, Donít Pass, Come and Donít Come.
Odds of winning the Pass Line bet (whole hand, not just Come Out roll) = 1.02869:1. It gets paid at Evens. The house edge is 1.41%. The exact same odds apply for winning a Come Box bet.
Odds of winning the Donít Pass bet (whole hand) = 1.02845:1. It gets paid at Evens. House edge is 1.36%. The exact same odds apply for winning a Donít Come bet.
The Odds on Pass Line, Donít Pass, Come, and Donít Come all pay true odds. In other words there is no house edge. The more Odds you take the more it will reduce the overall house edge down from 1.41% or 1.36% on the overall 2-stages.
See the list below:
- Single Odds on the Pass Line Bet leads to the overall Pass bet having a house edge of 0.848%.
- 2X odds leads to an overall Pass line edge of 0.606%.
- 3X odds leads to an overall Pass line edge of 0.471%.
- 3X-4X-5X (common structure) leads to 0.374%.
- 5X leads to 0.326%.
- 10X leads to 0.184%.
- 100X leads to 0.021%.
- Single Odds on the Donít Pass bet leads to the overall Donít Pass bet having a house edge of 0.682%
- 2X odds leads to an overall Donít Pass edge of 0.455%.
- 3X odds leads to an overall Donít Pass edge of 0.341%.
- 3X-4X-5X odds leads to an overall Donít Pass edge of 0.273%.
- 5X leads to 0.227%.
- 10X leads to 0.124%.
- 100X leads to 0.014%.
As you can see, taking the maximum Odds available at the table turns an already good Pass/Donít Pass bet into an excellent one.
Odds of Specific Number Bets
2 or 12 Ė These numbers are a 1/36 chance or 35:1 written as a ratio. Whereas the standard payout for bets on these numbers is only 30:1. A house edge of 13.89%.
3 or 11 Ė These are a 2/36 chance or 17:1 written as a ratio. Whereas the standard payout for bets on these numbers is only 15:1. A house edge of 11.11%
Field Bet (numbers 2,3,4,9,10,11,12) gets an even money payout, but the house edge really depends on the bonus payouts offered by the casino. If they offer Double on the 2 and 12, then the house edge is 5.56%, if they offer Double on the 2 and Triple on the 12 then the house edge is 2.78%.
Big 6,8 Ė This gets paid at evens, and the house edge is a whopping 9.09%
Place 6 or 8 Ė This gets paid at 7:6, not that much worse than itís true odds of 6:5 (ie six chances of a 7 to five chance of a 6), and it has a much lower house edge of just 1.52%. As you can see avoid the Big 6,8 bet in the corner but instead make Place bets on the specific Box numbers of 6 and/or 8.
Place 4 or 10 Ė This gets paid at 9:5, with true odds of 2:1 (six chances for the 7 to three chances for the 10). House edge is 6.67%
Place 9 or 5 Ė This gets paid at 7:5 with true odds of 3:2 (six chances for the 7 to four chances for the 9). House edge is 4.0%
In summary, the best Place numbers to bet are 6 and 8. Betting them both is generally a good idea because then you know you are more likely to win than lose (10:6).
If we prefer a slight variation of Place numbers, namely Buying numbers, then the house edge is generally 4.76% on all buy bets. This can be reduced if the casino/table has a rule of the commission only being paid on wins only. This can reduce it down to 1.67%. If we take the standard set up of 4.76% we can see that it is better to Buy the 4 or 10, but to Place the 5,6,8, or 9.
Hardway 6 or 8 Ė normally pays 9 to 1, with 10 to 1 being the true odds. Remember hardway bets stay on until a seven is rolled or the easy way is rolled. The house edge is a sizeable 9.09%.
Hardway 4 or 10 Ė normally pays 7 to 1, with 8 to 1 being the true odds. The house edge is a gigantic 11.11%.
On the dark side betting against the numbers we can Lay 6 or 8 for a 4% house edge, the 5 or 9 for a 3.23% house edge, and lay the 4 or the 10 for a 2.44% house edge. These all assumes the usual convention of paying 5% on the potential win.