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.
Win Probability
49.29%
Overall resolution
Win Amount
$10
1:1 payout
House Edge
1.41%
Expected Value
-$0
Per bet
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 | 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 |
EV = (Win Probability × Win) - (Lose Probability × Bet) = -$0 per bet
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.
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%.
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.
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.
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).
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%.
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.
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.
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.
Quick-start with common scenarios
Win Probability
49.29%
Overall resolution
Win Amount
$10
1:1 payout
House Edge
1.41%
Expected Value
-$0
Per bet