Craps dice odds all come from one fact: two dice land in 36 equally likely ways. Six of those make 7, so a 7 shows 1 time in 6, while 2 and 12 show just 1 time in 36. From that grid you can work out the chance of any total, any point and any bet on the table.
Two dice make 36 equally likely combinations; 7 is the most common total (6 ways).
A point of 6 or 8 is made 5 times in 11; 5 or 9, 2 in 5; 4 or 10, 1 in 3.
The Pass Line wins 244 times in 495 decisions, about 49.3%.
A Pass Line decision takes about 3.4 rolls on average; a shooter's turn about 8.5.
Past rolls never change the odds of the next one.
Dice combinations
36
Chance of a 7
6 in 36 (1 in 6)
Chance of 2 or 12
1 in 36 each
Pass Line win chance
244 in 495 (49.29%)
Point set on come-out
24 in 36 (2 in 3)
Craps dice odds start with 36 combinations
Each die has six faces, and the two dice land independently, so there are 6 × 6 = 36 possible results. Treat the dice as two different colours: red 1 with blue 6 is a different result from red 6 with blue 1, even though both total 7. That's why some totals are far more common than others. The grid shows every one.
All 36 two-dice results (first die down, second die across)
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
Read the diagonals. 7 runs corner to corner six times; 6 and 8 appear five times each; 2 and 12 just once. Every probability on a craps table, from the Pass Line to the centre bets, is built by counting squares on this grid. Our dice probability guide covers the same method for three-dice games like sic bo.
Odds of rolling each total with two dice
Count the ways, divide by 36 and you have the probability of a total on any one roll. 'True odds against' compares losing ways with winning ways.
Probability of each total on one roll
Total
Ways
Probability
Percentage
True odds against
2
1
1/36
2.78%
35 to 1
3
2
2/36
5.56%
17 to 1
4
3
3/36
8.33%
11 to 1
5
4
4/36
11.11%
8 to 1
6
5
5/36
13.89%
6.2 to 1
7
6
6/36
16.67%
5 to 1
8
5
5/36
13.89%
6.2 to 1
9
4
4/36
11.11%
8 to 1
10
3
3/36
8.33%
11 to 1
11
2
2/36
5.56%
17 to 1
12
1
1/36
2.78%
35 to 1
The pattern is a pyramid: one more way for each step towards 7, then one fewer for each step past it. The probability basics page explains the counting method in general terms.
Why the 7 drives the craps odds
Because 7 is the most likely total, the game is built around it. On the come-out roll a 7 wins the Pass Line. After a point is set, a 7 ends the shooter's turn and settles most bets on the layout; that's the 'seven out' covered in what does seven out mean in craps?
Almost every multi-roll bet in craps is a race between its own number and the 7. Once you know a 7 has six ways, you can price any of them in seconds: just count the ways for the other number.
Odds of each point being rolled before a 7
When a point is set, only two kinds of roll matter: the point and the 7. Everything else is ignored. So the chance of making the point is its ways divided by its ways plus six.
Chance of rolling each number before a 7
Number
Ways to roll it
Ways to roll 7
Chance before a 7
True odds against
Odds bet pays
4 or 10
3
6
3/9 = 33.3%
2 to 1
2 to 1
5 or 9
4
6
4/10 = 40.0%
3 to 2
3 to 2
6 or 8
5
6
5/11 = 45.5%
6 to 5
6 to 5
The last two columns match because the odds bet is paid at exactly the true odds, which is why it carries no house edge. Place bets on the same numbers pay less than true odds: 9 to 5 on 4 or 10, 7 to 5 on 5 or 9 and 7 to 6 on 6 or 8. Our place bets guide shows what that gap costs.
Across all six points, weighted by how often each is set, a point is made 67 times in 165, about 40.6%. In other words, once a point is on, the 7 is favourite to arrive first.
Come-out roll odds
The first roll of a round, the come-out, splits into three outcomes for the Pass Line.
Come-out roll outcomes for the Pass Line
Outcome
Totals
Ways
Probability
Natural (Pass wins)
7 or 11
6 + 2 = 8
8/36 = 22.2%
Craps (Pass loses)
2, 3 or 12
1 + 2 + 1 = 4
4/36 = 11.1%
Point set
4, 5, 6, 8, 9 or 10
24
24/36 = 66.7%
So the Pass Line wins outright twice as often as it loses on the come-out, but two times in three the round moves on to a point, where the 7 has the upper hand. The how to play craps guide walks through the come-out roll in order.
Pass Line probability, step by step
Put the last two tables together and you get the Pass Line's overall chance of winning. For each point, multiply the chance of setting it by the chance of making it, then add the naturals.
Single-roll odds don't tell you how likely something is across a sequence. For that, work out the chance it doesn't happen on each roll and multiply. The chance of no 7 in one roll is 5/6, so the chance of at least one 7 in n rolls is 1 − (5/6)ⁿ.
Chance of at least one 7 in a run of rolls
Rolls
Calculation
Chance of at least one 7
1
1 − (5/6)
16.7%
2
1 − (5/6)²
30.6%
3
1 − (5/6)³
42.1%
4
1 − (5/6)⁴
51.8%
6
1 − (5/6)⁶
66.5%
10
1 − (5/6)¹⁰
83.8%
Two useful averages follow from the same maths. A Pass Line decision takes about 3.38 rolls (557 ÷ 165), and a shooter's turn lasts about 8.53 rolls before a seven-out. And 'once in 36' isn't a promise: the chance of seeing at least one 12 in 36 rolls is only about 63.7%.
These averages hide big swings. Some shooters seven-out on their second roll; a few roll for a long time. Neither tells you anything about the next shooter.
Craps dice odds against what the bets pay
Compare the true odds with the payouts and you can see the house edge on every bet. The bigger the gap, the more the bet costs.
'Hot dice keep rolling.' A long hand is ordinary variance. The next roll still has a 1 in 6 chance of a 7; see the hot hand fallacy.
'Online dice aren't real odds.' Gambling Commission technical standards require simulated dice to have the same probabilities as real dice, with each die independent of the other.
'Setting the dice changes the odds.' Online you don't throw anything: RNG decides virtual dice, and live dice are handled by the studio. The 36-way grid applies either way.
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Frequently asked questions
What are the odds of rolling a 7 in craps?
The chance is 1 in 6, or 16.67%, on any roll. Six of the 36 two-dice combinations total 7 (1-6, 2-5, 3-4 and their reverses), more than any other number. That makes 7 the pivot of the game: it wins the Pass Line on the come-out and ends the shooter's turn afterwards. See what does seven out mean in craps? and our craps hub for how the 7 settles bets.
What is the hardest number to roll in craps?
2 and 12 are the hardest totals, each made in just one way (1-1 or 6-6), so each has a 1 in 36 chance, about 2.78%, on any roll. 3 and 11 come next at 2 in 36. A one-roll bet on 2 or 12 usually pays 30 to 1 against true odds of 35 to 1, a 13.89% house edge. Our proposition bets page covers these bets, and dice probability explains the counting.
What are the odds of making a point in craps?
It depends on the point. A 6 or 8 is rolled before a 7 five times in 11 (45.5%), a 5 or 9 two times in 5 (40%), and a 4 or 10 one time in 3 (33.3%). Averaged across all points, a point is made about 40.6% of the time. The odds bet pays exactly these true odds, and the Pass Line guide explains what happens after the point is set.
What percentage of the time does the Pass Line win?
The Pass Line wins 244 out of every 495 decisions on average, which is 49.29%. About 22.2% comes from a 7 or 11 on the come-out roll and the rest from points that are made before a 7. Because it pays even money, losing 50.71% of the time gives a house edge of 1.41%. Our craps house edge page lists the edge on every bet, and the Pass Line guide explains the bet.
How many rolls does a craps round last?
A Pass Line decision takes about 3.38 rolls on average, and a shooter's full turn lasts about 8.53 rolls before a seven-out. These are averages from the dice probabilities; real hands vary a lot, from two rolls to dozens. That matters for budgeting, because multi-roll bets stay at risk across several rolls. Our cost per hour guide and craps strategy page show how to plan around it.
Are 6 and 8 rolled as often as 7?
No. 6 and 8 each have five combinations against six for 7, so each comes up 13.89% of the time compared with 16.67% for 7. A 7 is 20% more likely than any single 6 or 8. That one-combination gap is why bets on 6 or 8 before a 7 lose slightly more often than they win. See Big 6 and Big 8 and place bets for how the payouts compare.
Are online craps dice odds the same as real dice?
They should be at a UK-licensed casino. The Gambling Commission's technical standards say a game simulating dice must match the probabilities of the real device, with each simulated die independent. Live games use physical dice, so the 36-combination grid applies there too. What can differ is the paytable. Our RNG testing page explains how online games are checked, and live craps UK covers live tables.
Can you improve your odds by tracking past rolls?
No. Each roll of fair dice is independent, so a 7 has the same 1 in 6 chance whether the last ten rolls were all 7s or contained none. Online games also can't adjust results to balance out past outcomes under UK rules. Tracking rolls can be fun, but it gives no edge. Read about the gambler's fallacy and independent events.
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