The Craps Coach

 

 

Craps Odds

All craps players need to know the odds of rolling the dice.  In order to fully understand how good your chances are at winning, it is essential for you to understand just how often each dice roll shows up on the table.  The reason the game is centered around the number 7 is simply because this number is rolled more than any other number.  You better believe the casino has calculated the odds for every single roll of the dice, and knows how and what their advantage over the player is for every bet.

Here's the math behind it. 

As you know, a die has six sides with six different values, and that two die are rolled every time.  A good guess would be that since there are six different numbers on two die's then there would be twelve different possible outcomes of the roll.  However, a closer look reveals there are thirty-six different possible outcomes of the dice roll. Since there are two die, the same number can be rolled in many different ways. Just like calculating the odds of playing a lottery, all different number combinations must be considered.

The way to go about calculating these various combinations is by starting at the low end of possible rolls.  The lowest number on the dice is one.  If both die were rolled as one's (snake eyes) the outcome would be 2.  This is one possible roll.  The next number up is a three.  To determine how many times this can be rolled, do some simple math.  There is only one equation that will produce this outcome: 2 + 1 = 3.   Therefore, there are two different possible outcomes:

Die One = 1, Die Two = 2  Or  Die One = 2, Die Two = 1

To further explain, let's use the number seven as a possible outcome.  Simple math reveals the sum of 7 can be produced in three ways: 1 + 6, 2 + 5 and 3 + 4.  Going one step further, to calculate the number of times these outcomes can be rolled, simply multiply the outcome by 2 (representing two die) and you have the value of six - There are six ways to roll the number 7 with two die.  The combinations are shown here:

Die One = 1, Die Two = 6  Or  Die One = 2, Die Two = 5 Or  Die One = 3, Die Two = 4

Die One = 6, Die Two = 1  Or  Die One = 5, Die Two = 2 Or  Die One = 4, Die Two = 3

If we were to do the same for each roll outcome, we would see that the possible ways of rolling a 6 are the same as rolling an 8.  Likewise, a 5 and 9 have equal chance of being rolled, as do a 4 and 10, 3 and 11 and 2 and 12.

Knowing this is important, for it will keep you in the know regarding what your payoffs may during any given wager.  Remember, just because your winning bet depends on your point being rolled before a seven, does not mean those odds are the same for every point.  Knowing this may just play a part if you have a choice of increasing your stake on a wager.  To calculate the percentage of you chances at rolling a certain number, divide the number of possible outcomes by the number of total dice outcomes (36).  For the number 7, this would show as 6/36 x 100% = 16.6%

Calculating craps odds and probability seems hard, but it's not as complicated as one might think. When calculating the probabilities of any gambling activity, the first thing one looks at is the number of potential outcomes. When rolling two six-sided dice, like you in a game of craps, there are 36 possible outcomes. (There are only 11 possible totals, 2 through 12, but there are 36 combinations that can result in those totals.)

There is only one way to roll a 2 (or a 12). Roll a 1 on each die (or a 6 on each die.) Since there are 36 possible combinations, and only 1 of those combinations can total 2, the probability of getting a 2 on a roll is 1 out of 36, or 35 to 1, as stated in odds terms. There are 2 ways to roll a 3 though - you can roll a 1 and a 2, or roll a 2 and a 1, so the probability of rolling a 3 is 2 out of 36. 2 out of 36 is the same as 1 out of 18, which stated in odds terms is 17 to 1.

Here's a chart outlining the possible combinations, how many ways each total can be rolled, and what the odds are for each total.

Total Number of Ways to Roll This Total Odds Combinations
2 1 35 to 1 1,1
3 2 17 to 1 1,2 + 2,1
4 3 11 to 1 1,3 + 3,1 + 2,2
5 4 8 to 1 1,4 + 4,1 + 2,3 + 3,2
6 5 6.2 to 1 1,5 + 5,1 + 2,4 + 4,2 + 3,3
7 6 5 to 1 1,6 + 6,1 +2,5 + 5,2 + 3,4 + 4,3
8 5 6.2 to 1 2,6 + 6,2 + 3,5 + 5,3 +4,4
9 4 8 to 1 3,6 + 6,3 + 4,5 +5,4
10 3 11 to 1 4,6 + 6,4 + 5,5
11 2 17 to 1 5,6 + 6,5
12 1 35 to 1 6,6

Calculating the Odds in Craps

The formula used to calculate the odds of rolling a specific total in craps is actually pretty simple. Divide 36 by the number of combinations that will make that total. Since there are 6 combinations which will total 7, the probability is 36 divide by 6, or 1 in 6 chance of rolling a 7.

Converting this to odds is easy to. Odds are always stated as the number of possibilities of something not happening versus the number of possibilities of something happening. For every roll of 7 there will be 5 rolls that aren't 7.

Craps Probabilities and the House Edge

The house edge is the difference between what the house pays out on a bet and it's true odds. For example, if a casino pays $30 for a $1 bet that someone will roll a 2, it's making a profit, because the true odds are 35 to 1. To be a break even bet, the casino would need to pay out $35 on that bet. (And return the $1 bet.) But if a casino had nothing but break even bets, it wouldn't make a profit. Without a profit, they'd have no reason to exist, and one wouldn't get to play craps.

It's good to understand how probabilities and odds are calculated because not all bets have as high a house edge as other bets. If one understands the math behind the odds, one can then choose the better bets, the ones with the lowest house edge. Choosing the bets with the lowest house edge is just good craps strategy.

 

Bet

House Edge %

Pass Line/Come

1.41

Don't Pass/Come

1.40

Pass Line/Come Bet 2X odds

.85

Don't Pass/Come 2X odds

.83

Place 6 and 8

1.52

Place 5 and 9

4.00

Place 4 and 10

6.67

Buy 6 or 8

4.76

Buy 5 or 9

4.76

Buy 4 or 10

4.76

Lay 6 or 8

4.00

Lay 5 or 9

3.23

Lay 4 or 10

2.44

Field Bet

5.56

Any Craps

11.11

Hardway 6 or 8

9.09

Hardway 4 or 10

11.11

Yo or 3

11.10

2 or 12

13.90

Any 7

16.70

 

TRUE ODDS

4

5

6

8

9

10

2 to 1

3 to 2

6 to 5

6 to 5

3 to 2

2 to 1

Pays 2 units for

Pays 3 units for

Pays 6 units for

Pays 6 units for

Pays 3 units for

Pays 2 units for

every 1 unit bet

every 2 units

every 5 units

every 5 units

every 2 units

every 1 unit bet

 

bet

bet

bet

bet

 

HOUSE ODDS FOR PLACE BETS

4

5

6

8

9

10

9 to 5

7 to 5

7 to 6

7 to 6

7 to 5

9 to 5

Pays 9 units for

Pays 7 units for

Pays 7 units for

Pays 7 units for

Pays 7 units for

Pays 9 units for

every 5 units

every 5 units

every 6 units

every 6 units

every 5 units

every 5 units

bet. Make bets

bet. Make bets

bet. Make bets

bet. Make bets

bet. Make bets

bet. Make bets

in multiples of

in multiples of

in multiples of

in multiples of

in multiples of

in multiples of

5.

5.

6.

6.

5.

5.