Craps Rules and Odds: A Complete Mathematical Guide to Dice Betting
Craps stands as one of the most thrilling and mathematically interesting games in any casino. The sound of dice rolling, players cheering, and chips stacking creates an atmosphere unlike any other table game. Yet beneath the excitement lies elegant probability theory that determines every outcome. Understanding these mathematics reveals why craps offers some of the best and worst bets simultaneously.
According to the American Gaming Association, craps remains a staple of casino floors worldwide, generating significant revenue while offering players house edges as low as 0% on certain wagers. This comprehensive guide covers everything from basic rules to advanced probability analysis, helping you understand why professional gamblers have long considered craps one of the most favorable games available.
The Mathematics of Two Dice
Before understanding craps strategy, you must understand dice probability. Two six-sided dice produce 36 possible combinations (6 x 6), but only 11 possible outcomes (totals 2 through 12). The distribution of these outcomes forms the mathematical foundation of the entire game.
Sample Roll
Total: 7
Complete Dice Probability Distribution
The number of ways to roll each total directly determines the probability and true odds:
| Total | Combinations | Probability | Odds Against |
|---|---|---|---|
| 2 | 1 (1-1) | 2.78% | 35:1 |
| 3 | 2 (1-2, 2-1) | 5.56% | 17:1 |
| 4 | 3 (1-3, 2-2, 3-1) | 8.33% | 11:1 |
| 5 | 4 (1-4, 2-3, 3-2, 4-1) | 11.11% | 8:1 |
| 6 | 5 (1-5, 2-4, 3-3, 4-2, 5-1) | 13.89% | 6.2:1 |
| 7 | 6 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) | 16.67% | 5:1 |
| 8 | 5 (2-6, 3-5, 4-4, 5-3, 6-2) | 13.89% | 6.2:1 |
| 9 | 4 (3-6, 4-5, 5-4, 6-3) | 11.11% | 8:1 |
| 10 | 3 (4-6, 5-5, 6-4) | 8.33% | 11:1 |
| 11 | 2 (5-6, 6-5) | 5.56% | 17:1 |
| 12 | 1 (6-6) | 2.78% | 35:1 |
Understanding the Basic Game Flow
Craps can appear intimidating due to its numerous betting options and fast pace. However, the core game follows a simple two-phase structure that any player can quickly understand.
Phase 1: The Come-Out Roll
Every craps round begins with the come-out roll, where a shooter (the player rolling the dice) establishes the initial outcome:
- Natural (7 or 11): Pass Line bets win immediately, Don't Pass bets lose
- Craps (2, 3, or 12): Pass Line bets lose immediately. Don't Pass wins on 2 or 3, pushes on 12 (bar the 12)
- Point (4, 5, 6, 8, 9, or 10): The rolled number becomes "the point" and the game moves to Phase 2
The point numbers - when rolled on come-out, game enters Phase 2
Phase 2: The Point Phase
Once a point is established, the shooter continues rolling until one of two outcomes occurs:
- Point is Made: The shooter rolls the point number again before a 7. Pass Line wins, Don't Pass loses.
- Seven-Out: The shooter rolls 7 before making the point. Pass Line loses, Don't Pass wins. The dice pass to the next shooter.
This fundamental structure creates the game's mathematical properties. According to research published in the Journal of Gambling Studies, the interplay between sevens and point numbers produces a house edge that has remained consistent across centuries of play.
The Core Bets: Pass Line and Don't Pass
These two fundamental wagers represent the heart of optimal craps play. Understanding their mathematics is essential before considering any other betting options.
Pass Line
Win on 7/11 come-out, lose on 2/3/12. After point, win if point rolls before 7.
The most popular bet in craps. Simple to understand and offers excellent odds. This is where optimal strategy begins. Combine with maximum odds for the best results.
Optimal ChoiceDon't Pass (Bar 12)
Win on 2/3 come-out, push on 12, lose on 7/11. After point, win if 7 rolls before point.
Slightly better odds than Pass Line. Called "wrong way" betting since you win when others lose. Mathematically superior but socially less popular at crowded tables.
Best OddsPass Line Mathematics
The Pass Line house edge calculation requires analyzing both phases of the game:
Pass Line Probability Analysis
Come-Out Phase:
P(Win on 7 or 11) = 8/36 = 22.22%
P(Lose on 2, 3, or 12) = 4/36 = 11.11%
Point Phase Probabilities (Win = Point Before 7):
Point 4 or 10: 3 ways to win, 6 ways to lose = 3/9 = 33.33%
Point 5 or 9: 4 ways to win, 6 ways to lose = 4/10 = 40.00%
Point 6 or 8: 5 ways to win, 6 ways to lose = 5/11 = 45.45%
Combined Win Probability: 49.29%
House Edge: 100% - 2(49.29%) = 1.41%
Don't Pass Mathematics
The Don't Pass bet offers slightly better odds due to the "bar 12" rule:
Don't Pass Probability Analysis
Come-Out Phase:
P(Win on 2 or 3) = 3/36 = 8.33%
P(Push on 12) = 1/36 = 2.78%
P(Lose on 7 or 11) = 8/36 = 22.22%
Point Phase (Win = 7 Before Point):
Point 4 or 10: 6/9 = 66.67%
Point 5 or 9: 6/10 = 60.00%
Point 6 or 8: 6/11 = 54.55%
House Edge: 1.36%
The Free Odds Bet: Zero House Edge
The Free Odds bet represents the most remarkable wager in any casino, offering true mathematical odds with zero house edge. No other standard casino bet provides this level of fairness. Understanding and maximizing this bet is the cornerstone of advanced craps strategy.
Why Free Odds Matters
After a point is established, you can place an additional "odds" bet behind your Pass or Don't Pass wager. This bet pays at true odds:
- Points 4 and 10: Pay 2:1 (true odds are 2:1)
- Points 5 and 9: Pay 3:2 (true odds are 3:2)
- Points 6 and 8: Pay 6:5 (true odds are 6:5)
Because payouts exactly match the mathematical probability, the casino has zero advantage on this portion of your bet.
Combined House Edge with Odds
While the Free Odds bet itself has no house edge, you must first make a Pass or Don't Pass bet. The combined house edge depends on how much odds you take. Research from the UNLV Center for Gaming Research confirms these calculations:
| Odds Multiple | Pass Line Combined Edge | Don't Pass Combined Edge |
|---|---|---|
| No Odds | 1.41% | 1.36% |
| 1x Odds | 0.85% | 0.68% |
| 2x Odds | 0.61% | 0.46% |
| 3x-4x-5x Odds | 0.37% | 0.27% |
| 5x Odds | 0.33% | 0.23% |
| 10x Odds | 0.18% | 0.12% |
| 100x Odds | 0.02% | 0.01% |
With 100x odds (offered at some casinos), the combined house edge drops to nearly zero, making craps essentially a fair game. However, such high odds require significant bankroll and expose you to substantial variance. Most casinos offer 3x-4x-5x odds as a reasonable middle ground.
Come and Don't Come Bets
Come and Don't Come bets work identically to Pass and Don't Pass, but can be made after a point is established. They effectively create a new, independent betting sequence.
Come Bet
Same as Pass Line, but made during point phase. Establishes its own point independent of the main game.
Allows multiple points to be in action simultaneously. You can take odds on Come bets just like Pass Line. Increases action but also variance.
Good ValueDon't Come
Same as Don't Pass, but made during point phase. Wins when 7 rolls before your Come point.
Mathematically identical to Don't Pass. Allows "wrong way" betting on multiple numbers. Lay odds available for zero house edge supplemental betting.
Good ValuePlace Bets: Convenient but Costly
Place bets allow you to bet directly on specific numbers (4, 5, 6, 8, 9, or 10) without going through the come-out process. While convenient, they come at a mathematical cost.
| Place Bet | True Odds | Casino Pays | House Edge |
|---|---|---|---|
| Place 6 or 8 | 6:5 | 7:6 | 1.52% |
| Place 5 or 9 | 3:2 | 7:5 | 4.00% |
| Place 4 or 10 | 2:1 | 9:5 | 6.67% |
| Buy 4 or 10 (with vig) | 2:1 | 2:1 (5% vig) | 4.76% |
The Place 6 and Place 8 bets offer reasonable value at 1.52% house edge, only slightly worse than Pass Line with no odds. However, Place 4/10 and Place 5/9 carry significantly higher edges. If you must bet on specific numbers, Place 6/8 are acceptable; for other numbers, use Come bets with odds instead.
Proposition Bets: The Worst Bets in Craps
The center of the craps table features colorful proposition bets with enticing payouts. These bets consistently rank among the worst wagers in any casino, similar to the Tie bet in baccarat which carries a 14.36% house edge.
| Proposition Bet | Typical Payout | House Edge | Recommendation |
|---|---|---|---|
| Any 7 | 4:1 | 16.67% | Never |
| Any Craps (2, 3, or 12) | 7:1 | 11.11% | Never |
| 2 or 12 (Snake Eyes/Boxcars) | 30:1 | 13.89% | Never |
| 3 or 11 | 15:1 | 11.11% | Never |
| Hard 6 or 8 | 9:1 | 9.09% | Never |
| Hard 4 or 10 | 7:1 | 11.11% | Never |
| Horn Bet | Various | 12.50% | Never |
| Hop Bets | 15:1 or 30:1 | 11.11-16.67% | Never |
Field Bet: Tempting but Flawed
The Field bet covers 2, 3, 4, 9, 10, 11, and 12 in a single wager. At first glance, betting on seven numbers seems advantageous. The mathematics reveal otherwise.
While Field covers seven numbers, the losing numbers (5, 6, 7, 8) appear in 20 out of 36 combinations (55.56%). The winning numbers appear only 16 times (44.44%). The bonus payouts on 2 and 12 don't fully compensate for this disadvantage.
Field (2x on 2 and 12)
Standard Field bet paying double on 2 and 12.
Poor value despite covering many numbers. The dominant frequency of 5, 6, 7, 8 ensures long-term losses.
AvoidField (3x on 12)
Enhanced Field paying triple on 12. Some casinos offer this variant.
Better than standard Field but still inferior to Pass Line with odds. Only acceptable if no better options exist.
MarginalOptimal Craps Strategy
Optimal craps strategy is remarkably simple once you understand the mathematics. Unlike games such as blackjack where complex basic strategy charts are required, craps optimal play can be summarized concisely.
Recommended Strategy
- Bet Pass Line or Don't Pass exclusively
- Take maximum odds your bankroll allows
- Consider Come/Don't Come for added action
- Place 6 and 8 are acceptable alternatives
- Set loss limits before playing
- Understand outcomes are purely random
What to Avoid
- Never make proposition bets
- Avoid Field bets (especially 2x version)
- Skip Place 4, 5, 9, and 10
- Don't chase losses with bigger bets
- Ignore "dice setting" superstitions
- Never bet what you can't afford to lose
Dice Control: Myth vs. Reality
Some players claim they can influence dice outcomes through precise throwing techniques. Scientific analysis, including studies from IEEE on random motion systems, consistently shows that casino dice (properly manufactured and handled) produce random outcomes regardless of throwing technique.
The physics of dice bouncing on a textured table, hitting rubber bumpers, and interacting with each other creates chaotic motion that overwhelms any initial throwing precision. While dice control practitioners may genuinely believe in their abilities, controlled studies have never demonstrated reproducible advantage.
Comparing Craps to Other Casino Games
Understanding where craps fits in the casino landscape helps informed game selection. As analyzed in our guide to how casino games work, house edge varies dramatically across different wagers.
| Game/Bet | House Edge | Skill Required |
|---|---|---|
| Craps (Don't Pass + 100x Odds) | 0.01% | None |
| Craps Free Odds | 0.00% | None |
| Blackjack (Basic Strategy) | 0.50% | Significant |
| Baccarat (Banker) | 1.06% | None |
| Craps (Pass/Don't Pass) | 1.36-1.41% | None |
| European Roulette | 2.70% | None |
| American Roulette | 5.26% | None |
| Craps (Any 7) | 16.67% | None |
Craps with maximum odds offers the lowest house edge of any game requiring no skill. For players who prefer straightforward betting without memorizing strategy charts, craps with full odds represents mathematically optimal casino play.
Online Craps Considerations
Online craps follows identical rules and mathematics to land-based versions. As explained in our article on how regulators test RNG systems, reputable online casinos use certified random number generators that produce mathematically fair outcomes.
Key Differences Online
- Speed: Online games proceed faster, increasing theoretical hourly loss at the same bet size
- Odds Limits: Online casinos may offer different odds multiples than land-based venues
- Social Element: The camaraderie of live craps is absent; online play is more solitary
- Minimum Bets: Online often offers lower minimums, allowing smaller bankroll play
Frequently Asked Questions
What is the house edge on the Pass Line bet in craps?
The Pass Line bet has a house edge of 1.41%, making it one of the best bets in the casino. When combined with maximum Free Odds, the combined house edge drops dramatically. With 10x odds, the combined edge is only 0.18%; with 100x odds, it approaches 0.02%.
What is the Free Odds bet in craps?
The Free Odds bet is a supplemental wager made after a point is established. It pays at true mathematical odds with zero house edge, making it the only bet in any casino with no house advantage. You can take odds on Pass Line/Come bets or lay odds on Don't Pass/Don't Come bets.
Should I bet on proposition bets in craps?
Never. Proposition bets like Any 7 (16.67% edge), Hard Ways (9-11% edge), and Horn bets (12.5% edge) are among the worst wagers in any casino. While their payouts appear attractive, the mathematics ensure long-term losses far exceeding the core bets.
Is craps a good game for beginners?
Yes, despite its intimidating appearance. The fundamental bets (Pass Line, Don't Pass) are simple and offer excellent odds. Start with these basic bets, learn to take odds, and ignore complex proposition bets. The fast pace becomes comfortable quickly with a little practice.
Can you control the dice in craps?
No. Despite claims from "dice setting" advocates, physics studies consistently show that casino dice produce random outcomes. The combination of table texture, rubber bumpers, and chaotic dice-on-dice collisions overwhelms any initial throwing precision. Controlled scientific studies have never demonstrated reproducible advantage.
Conclusion: The Mathematics of Craps
Craps combines exciting gameplay with some of the most favorable mathematics in the casino. The Pass/Don't Pass bets at 1.36-1.41% house edge provide excellent value, while the Free Odds bet offers the only zero-edge wager in standard casino gaming. Conversely, proposition bets represent some of the worst odds available anywhere.
Optimal craps strategy is simple: bet Pass Line or Don't Pass, take maximum odds your bankroll allows, and avoid everything in the center of the table. Unlike roulette where every bet carries the same edge, craps rewards informed players who stick to mathematically sound wagers.
The game's complexity lies in its numerous betting options, not its strategy. Once you understand that only a handful of bets offer acceptable odds, craps becomes one of the most straightforward and player-friendly games in the casino. The mathematics are immutable: the Free Odds bet pays true odds, and no amount of superstition or dice manipulation can change the probabilities embedded in two cubes, each with six sides.
Disclaimer: This article is for educational purposes only and does not constitute gambling advice. Craps is a negative expectation game; the house maintains a mathematical advantage on all bets except Free Odds. All gambling carries risk of financial loss. Never gamble with money you cannot afford to lose. If gambling is affecting your life negatively, please visit our responsible gambling resources for help.