Craps Dice Combinations: Odds, Probabilities, and What the Numbers Mean
Jake WilfredHere’s a number that should change how you think about craps: 16.67%. That’s the probability of rolling a 7 on any given throw. One out of every six rolls, on average, produces the number that ends most shooters’ turns.
Every bet on the craps table, every strategy guide ever written, every payout the casino offers, flows from one source: the 36 possible dice combinations created when two six-sided cubes hit the felt. Understand those combinations, and you understand why certain bets are smart and others are traps.
This guide covers every possible craps dice combination, the real probabilities behind each number, the critical difference between true odds and casino odds, and how the house edge is calculated from these numbers. If you’ve ever wondered why the pass line bet pays even money or why the field bet includes a double payout on 2, the answer lives in the math below.
- Two dice create exactly 36 possible combinations, producing totals from 2 through 12
- The number 7 can be rolled 6 ways out of 36, making it the most probable outcome at 16.67%
- The numbers 2 and 12 can each be rolled only 1 way, making them the rarest at 2.78%
- True odds reflect actual probability; casino odds are what the house pays, and the gap between them is the house edge
- Understanding “to” odds vs. “for” odds prevents confusion about payouts and expected returns
- Every craps bet’s house edge can be calculated from these 36 combinations once you know the casino’s payout structure
All 36 Dice Combinations in Craps
Two standard dice, each with six faces. That gives us 6 x 6 = 36 possible outcomes on every single roll. Not 11 (the range of totals from 2 to 12), but 36 distinct combinations, because rolling a 3+4 and rolling a 4+3 are different events even though both total 7.
This distinction is critical. It’s why a 7 is six times more likely than a 2. Both are valid totals, but the 7 has six paths to get there while the 2 has only one.
| Total | Possible Combinations | Number of Ways | Probability |
|---|---|---|---|
| 2 | 1+1 | 1 | 2.78% |
| 3 | 1+2, 2+1 | 2 | 5.56% |
| 4 | 1+3, 2+2, 3+1 | 3 | 8.33% |
| 5 | 1+4, 2+3, 3+2, 4+1 | 4 | 11.11% |
| 6 | 1+5, 2+4, 3+3, 4+2, 5+1 | 5 | 13.89% |
| 7 | 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 | 6 | 16.67% |
| 8 | 2+6, 3+5, 4+4, 5+3, 6+2 | 5 | 13.89% |
| 9 | 3+6, 4+5, 5+4, 6+3 | 4 | 11.11% |
| 10 | 4+6, 5+5, 6+4 | 3 | 8.33% |
| 11 | 5+6, 6+5 | 2 | 5.56% |
| 12 | 6+6 | 1 | 2.78% |
Notice the symmetry. The distribution forms a perfect bell curve centered on 7. Numbers equidistant from 7 (like 6 and 8, or 4 and 10) have identical probabilities. This symmetry is baked into the physics of two identical cubes, and it’s why the entire game of craps is structured the way it is.
Memorize three numbers: 7 has 6 ways, 6 and 8 have 5 ways each, and everything cascades from there. With those anchored in your mind, you can quickly assess any bet’s likelihood without consulting a chart. This knowledge directly informs which bets qualify as the best craps bets.
Why the Number 7 Dominates Craps
Seven isn’t just the most common roll. It’s the gravitational center around which the entire game orbits.
On the come-out roll, a 7 is your best friend if you’re on the pass line. It’s an instant win. After the point is established, that same 7 becomes your worst enemy. It ends the shooter’s turn and wipes out pass line bets, odds, place bets, and come bets in one fell swoop.
This dual personality explains why craps has such dramatic swings in energy. The entire table can go from euphoria to devastation on a single roll, and six times out of 36, that roll is a 7.
Say the point is 4. There are 3 ways to roll a 4 and 6 ways to roll a 7. That means the odds against making the point are 6:3, or 2:1. This is exactly why the true odds payout on a 4 is 2:1. The casino doesn’t add a markup on the free odds bet; it pays what the math dictates. Now compare that to a point of 6: 5 ways to roll a 6 vs. 6 ways to roll a 7, giving odds of 6:5. A point of 6 is much easier to make than a point of 4, and the payouts reflect this.
Understanding seven’s dominance also explains why experienced players gravitate toward bets on 6 and 8. With 5 ways to roll each, they’re the closest any number gets to rivaling the 7. A place bet on 6 or 8 has a house edge of just 1.52%, making it one of the better wagers on the layout.
True Odds vs. Casino Odds: Where the House Gets Its Edge
This is the concept that separates informed players from everyone else. True odds reflect the actual mathematical probability of an event. Casino odds are what the house pays you when that event happens. The gap between those two numbers is the house edge.
True odds are straightforward. If there are 6 ways to roll a 7 and 3 ways to roll a 4, the true odds of rolling a 4 before a 7 are 2:1. That means for every $1 you risk, the fair payout should be $2.
Casino odds are adjusted so the house makes money. For most bets, the casino pays slightly less than true odds. A place bet on 4 pays 9:5 instead of the true odds of 2:1 (which would be 10:5). That difference, $1 per $5 bet, is the casino’s profit margin.
| Number | Ways to Roll | True Odds (vs. 7) | Pass Line Odds Payout | Place Bet Payout |
|---|---|---|---|---|
| 4 | 3 | 2:1 | 2:1 | 9:5 |
| 5 | 4 | 3:2 | 3:2 | 7:5 |
| 6 | 5 | 6:5 | 6:5 | 7:6 |
| 8 | 5 | 6:5 | 6:5 | 7:6 |
| 9 | 4 | 3:2 | 3:2 | 7:5 |
| 10 | 3 | 2:1 | 2:1 | 9:5 |
Notice something? The pass line odds bet pays exactly true odds. No markup. No house edge. That’s why the free odds bet is the single best wager in any casino. The place bet payouts, by contrast, are slightly worse than true odds. That’s where the house earns its money on place bets.
For the full payout structure across every craps wager, check out our craps payout chart and odds page.
The free odds bet is the only wager in any casino game with a 0% house edge. But you can only place it after making a pass line, don’t pass, come, or don’t come bet. Think of the base bet as the “price of admission” to access the odds bet. Maximize your odds whenever the table allows, whether that’s 1x, 2x, 3-4-5x, or even 100x at some craps online casinos.
Understanding “To” Odds vs. “For” Odds
This is a subtle distinction that trips up a lot of players, and some casinos use the confusion to their advantage.
“To” odds tell you what you win on top of your original bet. If a bet pays 4 to 1, you risk $1 and get back $5 total: your original $1 plus $4 in winnings.
“For” odds include your original bet in the payout. If a bet pays 5 for 1, you get $5 total, but that includes the $1 you wagered. Your actual profit is only $4.
Here’s the trap: “4 to 1” and “5 for 1” are the same payout. But “5 for 1” sounds better because the number is bigger. Some casinos, particularly on proposition bets in the center of the layout, will display “for” odds to make the payouts look more attractive.
You see a bet labeled “30 for 1” on the any craps section. A player next to you sees “30 to 1” at a different casino. Are these the same? No. “30 for 1” means you get $30 total (your $1 back plus $29 profit). “30 to 1” means you get $31 total ($1 back plus $30 profit). That’s a $1 difference per bet, which compounds over hundreds of rolls. Always check whether the layout says “to” or “for.”
When comparing craps payouts across different casinos, always convert everything to “to” odds so you’re comparing apples to apples. If a payout is listed as “for,” subtract one from the first number to get the “to” equivalent. 5 for 1 = 4 to 1. 10 for 1 = 9 to 1. Simple conversion that prevents expensive mistakes.
How the House Edge Is Calculated From Dice Combinations
The house edge on any craps bet can be derived directly from the 36 dice combinations and the payout the casino offers. Let’s walk through the math for two common bets so the concept clicks.
Pass Line Bet House Edge
The pass line wins on the come-out with a 7 or 11 (8 ways out of 36: six for 7, two for 11). It loses on the come-out with a 2, 3, or 12 (4 ways: one for 2, two for 3, one for 12). The remaining 24 outcomes establish a point, and the pass line then wins or loses based on whether the point or a 7 comes first.
When you calculate the combined probability of winning across all scenarios, the pass line wins 49.29% of the time. It pays even money (1:1). The expected return per $1 bet is $0.9859, meaning the casino keeps $0.0141 per dollar wagered on average. That’s the 1.41% house edge.
Any Seven Bet House Edge
The any seven bet is simpler. There are 6 ways to roll a 7 out of 36 combinations (16.67% chance of winning). The bet pays 4:1.
If you bet $1 on any seven for 36 hypothetical rolls, you’d expect to win 6 times ($4 profit each = $24 gained) and lose 30 times ($1 each = $30 lost). Net result: -$6 over $36 wagered. That’s a 16.67% house edge, one of the worst bets on the table.
| Bet | Win Probability | Casino Payout | House Edge |
|---|---|---|---|
| Pass Line | 49.29% | 1:1 | 1.41% |
| Don’t Pass | 47.93% (win), 2.78% (push) | 1:1 | 1.36% |
| Free Odds | Varies by point | True odds | 0% |
| Place 6 or 8 | 45.45% | 7:6 | 1.52% |
| Place 5 or 9 | 40% | 7:5 | 4.00% |
| Place 4 or 10 | 33.33% | 9:5 | 6.67% |
| Field (2 pays double, 12 pays double) | 44.44% | Various | 5.56% |
| Field (2 pays double, 12 pays triple) | 44.44% | Various | 2.78% |
| Any Seven | 16.67% | 4:1 | 16.67% |
| Any Craps | 11.11% | 7:1 | 11.11% |
| Hard 6 or Hard 8 | 9.09% | 9:1 | 9.09% |
| Hard 4 or Hard 10 | 11.11% | 7:1 | 11.11% |
The pattern is clear. Bets with probabilities close to even money (like the pass line) have small house edges. Bets with long-shot probabilities and flashy payouts (like any seven or hardways) have enormous house edges. The casino gives you a payout that looks generous but is mathematically less than what the true odds justify.
Calculating Your Expected Loss
Once you know the house edge, figuring out your expected loss over a session becomes simple multiplication.
Expected Loss = Total Amount Wagered x House Edge
This doesn’t mean you’ll lose exactly that amount. It’s the mathematical average over thousands of bets. In a single session, you might win big or lose more than expected. Variance is real. But over time, the math converges.
You play craps for 2 hours. You average 60 rolls per hour and bet $10 on each. That’s 120 bets totaling $1,200 in action. On the pass line (1.41% edge), your expected loss is $1,200 x 0.0141 = $16.92. On the any seven bet (16.67% edge), your expected loss on the same action would be $1,200 x 0.1667 = $200.04. Same time at the table. Same dollar amount wagered. Twelve times the expected loss just from choosing a different bet.
This is why bankroll management matters so much. Players who stick to low-edge bets like the pass line, don’t pass, and free odds can play for hours with modest bankrolls. Players loading up on proposition bets burn through their money at a rate that makes the session short and painful.
Expected loss calculations assume you’re making the same bet repeatedly. In practice, most craps players mix bet types throughout a session. Your actual expected loss is the weighted average of all the bets you make. Stick to the best craps bets to keep that weighted average as low as possible.
A Quick Word on Dice Control
You may have heard that dice setting can influence which combinations appear. The idea is that by arranging the dice in a specific orientation and throwing with a consistent delivery, you can reduce the frequency of certain outcomes (usually the 7).
The theory has a dedicated following and some published authors backing it. The reality is that no controlled experiment has proven that dice control consistently works against the randomizing effect of the rubber pyramid back wall.
What’s not debatable is this: the 36 combinations and their probabilities are built into the physics of two balanced cubes. Unless someone can prove they’ve altered those physics through throwing technique, the math in this guide remains the foundation of every intelligent craps decision.
For a full breakdown of the techniques and the debate surrounding them, read our dedicated dice setting and dice sliding vs. dice control guides.
The Dice Math Doesn’t Lie
Every craps strategy, every betting system, every piece of advice you’ll ever read about this game flows from 36 dice combinations on a table. That’s it. Two cubes, six faces each, 36 possibilities.
Players who understand these combinations make better bets. They know why 6 and 8 are the smartest place numbers. They know why the pass line is a solid starting wager. They know why the any seven bet is a money pit dressed in a flashy payout. And they know that the free odds bet is the single best deal the casino will ever offer them.
You don’t need to be a mathematician to play craps well. You just need to respect what the dice are telling you. And now, you can.
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Craps Dice Combinations FAQs
There are exactly 36 possible combinations when rolling two six-sided dice. These produce totals ranging from 2 (only one combination: 1+1) to 12 (only one combination: 6+6), with 7 being the most common total at 6 possible combinations.
Seven is the most common number, with 6 out of 36 possible combinations producing it (16.67% probability). This is exactly why 7 plays such a central role in craps: it’s a natural winner on the come-out roll and the round-ending seven-out after a point is established.
The true odds against making a 6 or 8 are 6:5. There are 5 ways to roll a 6 (or 8) and 6 ways to roll a 7. That means you’ll make the point about 45.45% of the time. The free odds bet behind a pass line pays this exact ratio with zero house edge.
“To” odds state your profit on top of your original bet (4 to 1 means $4 profit on a $1 bet). “For” odds include your original bet in the total return (5 for 1 means $5 total back, including your $1 wager). The actual profit is the same in both examples ($4), but “for” odds use a bigger number that can be misleading. Always check which format your casino uses.
Because it pays true odds with a 0% house edge. The casino makes no profit on this bet. It’s the only wager in any casino game where the payout exactly matches the mathematical probability. You can only place it after a pass line, don’t pass, come, or don’t come bet. Our free odds bet guide explains the full mechanics.
Six ways: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. This makes 7 the most probable outcome on any roll, which is why the game’s structure revolves around it. Understanding this single fact helps explain nearly every payout and house edge on the craps table layout.
