Dice probability in craps
Count the dice combinations, and every chance and payout in craps follows from the count.
Thirty-six ways two dice can land
Each die has six faces, so two dice give six times six, or thirty-six, combinations. Each combination is equally likely.
Example: the total four comes up 3 ways – one and three, two and two, three and one. On a red die and a blue die, one-three and three-one are different rolls.
Dice probability chart
- Two or twelve – 1 way each
- Three or eleven – 2 ways each
- Four or ten – 3 ways each
- Five or nine – 4 ways each
- Six or eight – 5 ways each
- Seven – 6 ways
Probability of rolling a 7
Seven has 6 ways, the most of any total: one and six, two and five, three and four, four and three, five and two, six and one. Every face on the first die has exactly one partner on the second die that makes seven.
So the chance of a seven on any roll is 16.67%. Past rolls do not change it – see the gambler's fallacy.
Rolling the point before a seven
After a point is set, only two totals matter: the point wins, the seven loses. Compare the ways of the point with the 6 ways for seven.
- Point four or ten – 3 ways vs 6, fair odds 2 to 1
- Point five or nine – 4 ways vs 6, fair odds 3 to 2
- Point six or eight – 5 ways vs 6, fair odds 6 to 5
How the ways set every craps payout
Compare any payout with the fair odds from the ways count – the gap is the house edge.
The odds bet behind the pass line pays the fair odds exactly. A place bet on six pays 7 to 6 instead of 6 to 5, which gives a house edge of 1.52%.
The pass line wins 49.29% of the time at even money, so the house edge is 1.41%. Compare all bets on craps payouts or test them in the craps simulator.
Questions
What is the probability of rolling a 7 with two dice?
Seven can be rolled 6 ways out of thirty-six, so the chance is 16.67% on every roll. No other total has more ways.
How many combinations are there with two dice?
There are thirty-six combinations, because each of the six faces on one die can pair with each of the six faces on the other die.
What are the odds of rolling a 4 before a 7 in craps?
Four has 3 ways and seven has 6 ways, so the fair odds against making the four are 2 to 1. The odds bet pays exactly that.
Why is 6 or 8 easier to make than 4 or 10?
Six has 5 ways and four has only 3 ways, while seven always has 6 ways. More ways for the point means a better chance to roll it before a seven.
Can dice probability help me win at craps?
No. Knowing the odds shows which bets cost less, but every bet except the odds bet has a house edge, such as 1.41% on the pass line, and the house edge wins over time.