Craps Pass Line Calculator
Calculate the complete odds, probabilities, and expected value for the Pass Line bet - the most popular bet in craps. Understand come-out roll odds and point probabilities.
Formula:P(Win) = P(Come-out Win) + Σ P(Point) × P(Make Point)
Win Probability
49.29%
Overall resolution
Win Amount
$10
1:1 payout
House Edge
1.41%
Expected Value
-$0
Per bet
Pass Line Bet
$
Come-Out Roll Analysis
22.2%
Win (7 or 11)
8 ways
11.1%
Lose (2, 3, 12)
4 ways
66.7%
Point Set
24 ways
| Roll | Ways | Probability | Result |
|---|---|---|---|
| 7 | 6 | 16.67% | WIN |
| 11 | 2 | 5.56% | WIN |
| 2 | 1 | 2.78% | LOSE |
| 3 | 2 | 5.56% | LOSE |
| 12 | 1 | 2.78% | LOSE |
| 4, 10 | 6 | 16.67% | Point |
| 5, 9 | 8 | 22.22% | Point |
| 6, 8 | 10 | 27.78% | Point |
Point Resolution Probabilities
| Point | Ways to Make | Ways to Lose (7) | Win Probability | True Odds |
|---|---|---|---|---|
| 4 | 3 | 6 | 33.33% | 2:1 |
| 5 | 4 | 6 | 40.00% | 3:2 |
| 6 | 5 | 6 | 45.45% | 6:5 |
| 8 | 5 | 6 | 45.45% | 6:5 |
| 9 | 4 | 6 | 40.00% | 3:2 |
| 10 | 3 | 6 | 33.33% | 2:1 |
Overall Pass Line Resolution
Win: 49.29%Lose: 50.71%House Edge: 1.41%
Expected Value Analysis
Bet Amount$10
Win Amount$10
Total Return on Win$20
Win Probability49.29%
Lose Probability50.71%
House Edge1.41%
Expected Value-$0
EV = (Win Probability × Win) - (Lose Probability × Bet) = -$0 per bet
Quick Answer
The Pass Line wins 49.29% of all resolutions with a 1.41% house edge. On the come-out roll, you win on 7 or 11 (22.2% chance) and lose on 2, 3, or 12 (11.1% chance). Any other roll establishes a point, which you must roll again before a 7 to win.
Key Facts
- Come-out: Win on 7 or 11 (8 ways, 22.2%), Lose on 2/3/12 (4 ways, 11.1%)
- Point established on 4, 5, 6, 8, 9, or 10 (24 ways, 66.7%)
- Overall Pass Line win rate: 49.29% | House edge: 1.41%
- Point 6/8: 45.45% chance to make | Point 4/10: 33.33% chance
- $10 Pass Line bet returns $20 on win (1:1 payout)
- Always take maximum odds behind Pass Line for lowest combined edge
Understanding the Pass Line Bet
The Pass Line is the fundamental bet in craps and one of the best bets in any casino game. It works in two phases: the come-out roll and the point phase. Understanding both phases is essential to appreciating why the house edge is only 1.41%.
Come-Out Roll
On the first roll (come-out), you're at a significant advantage: 8 ways to win instantly versus 4 ways to lose. However, 24 ways establish a point, shifting the odds.
Point Phase
Once a point is established, the math changes. Now you're racing against the 7, which can be rolled 6 ways. Points 6 and 8 are most favorable, while 4 and 10 are hardest to make.
Frequently Asked Questions
How does the Pass Line bet work?
On the come-out roll, Pass Line wins on 7 or 11 and loses on 2, 3, or 12. Any other number (4, 5, 6, 8, 9, 10) becomes the "point." You then win if the point rolls before a 7, or lose if 7 rolls first. Pass Line pays 1:1 ($10 wins $10).
What are the come-out roll probabilities?
Win on 7 (6/36 = 16.67%) or 11 (2/36 = 5.56%) = 22.22% total. Lose on 2 (1/36 = 2.78%), 3 (2/36 = 5.56%), or 12 (1/36 = 2.78%) = 11.11% total. Establish point = 66.67%.
What is the best point to establish?
Point 6 or 8 are best with 45.45% chance of making the point. Point 5/9 have 40% chance. Point 4/10 have only 33.33% chance. However, you cannot choose your point - it is determined by the come-out roll.
Should I always bet Pass Line?
Pass Line is one of the best bets in the casino at 1.41% edge. Don't Pass is slightly better at 1.36% but means betting against the shooter. For social play and good odds, Pass Line with maximum odds is the recommended strategy.
Can I remove my Pass Line bet?
No. Once a point is established, you cannot remove or reduce your Pass Line bet. This is because the odds shift in your favor after surviving the come-out roll. However, you can remove odds bets at any time.
Try These Examples
Quick-start with common scenarios
How this works
Calculations follow the published mathematics of the game — combinatorics for cards, probability theory for dice, and expected-value accounting for wagers. Results are verified against independent references (primarily Wizard of Odds). No calculation here is an opinion or recommendation; it is arithmetic applied to the rules of the game.
What this tool can’t do
When to consult a professional
This tool computes probability and expected value. It is not a betting system and cannot predict the outcome of any individual wager. If gambling is causing problems for you or someone you know, call the National Problem Gambling Helpline at 1-800-GAMBLER.
Sources
- [1]Wizard of Odds — Michael Shackleford, ASAIndustrywizardofodds.comAccessed Apr 21, 2026
Actuary; widely cited casino-game probability reference. Used for house-edge and EV verification.
- [2]National Council on Problem GamblingOfficial sourcencpgambling.orgAccessed Apr 21, 2026
Responsible-gambling guidance and 1-800-GAMBLER helpline.
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Win Probability
49.29%
Overall resolution
Win Amount
$10
1:1 payout
House Edge
1.41%
Expected Value
-$0
Per bet