Craps
Under the stated rules, Pass has 1.41% house edge per initial line wager. Don’t Pass, with 12 pushing, has 1.36% when pushes stay in that denominator. Eligible true-odds portions have 0.00% edge, but adding them does not remove the base wager’s expected dollar loss. Place, field and proposition bets need their exact payouts and settlement conditions; they do not share one percentage.
Guide text revised . Sources and assumptions are linked below.
How the game works
Come-out and point
One player, the shooter, rolls the dice. A line wager starts with a come-out roll. Read Pass and Don’t Pass separately:
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| Come-out total | Pass | Don’t Pass, with 12 barred |
|---|---|---|
| 7 or 11 | Wins at 1:1 net | Loses |
| 2 or 3 | Loses | Wins at 1:1 net |
| 12 | Loses | Push: stake returned, no net gain |
| 4, 5, 6, 8, 9 or 10 | That total becomes the point | That total becomes the point |
After a point is set, the relevant line wager continues until the point or 7 appears. Point first: Pass wins and Don’t Pass loses. 7 first: Pass loses and Don’t Pass wins. Other totals do not resolve those line wagers. A new line wager starts a new come-out cycle after settlement.
A seven-out means a 7 during the point phase. It is different from a come-out 7, which wins a Pass wager. Other bets on the table can settle on different rolls, so the result for Pass is not the result for every chip.
Count the dice outcomes
There are 36 equally likely ordered pairs: the first die and second die each have six possible faces. Totals are not equally likely.
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| Total | Ways to make that total | Probability on one stated fair roll |
|---|---|---|
| 2 or 12 | 1 for each total | 1/36 for each |
| 3 or 11 | 2 for each total | 2/36 for each |
| 4 or 10 | 3 for each total | 3/36 for each |
| 5 or 9 | 4 for each total | 4/36 for each |
| 6 or 8 | 5 for each total | 5/36 for each |
| 7 | 6 | 6/36, or 16.67% |
The six ways to make 7 make it the most likely single total in this model. That probability describes the dice; whether 7 wins or loses a wager comes from the game rules.
Reference: craps rules, payout examples and wager denominators.
Bet types
Line and Come wagers
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| Bet | Settlement | House edge under the stated rules |
|---|---|---|
| Pass | Starts on a come-out; wins on 7/11, loses on 2/3/12, otherwise point before 7 wins. | 1.41% per initial wager |
| Don’t Pass | Starts on a come-out; wins on 2/3, pushes on 12, loses on 7/11, otherwise 7 before point wins. | 1.36%, including push wagers |
| Come | Starts during a point phase; its next roll acts as its own come-out and can establish a separate Come point. | 1.41% with the same rules |
| Don’t Come | Uses its own Don’t Come start and point, with 12 pushing in this example. | 1.36%, including push wagers |
A Come point can differ from the table’s main point. Check which bets are working during a later come-out roll and which can be removed or reduced. A line wager’s contract rules should not be assumed to match a place wager’s rules.
True odds behind an eligible wager
After the relevant point is established, the game may allow an additional odds wager. Taking odds behind Pass/Come wins if its point appears before 7. Laying odds behind Don’t Pass/Don’t Come wins if 7 appears first.
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| Point | Taking odds: net win per unit staked | Laying odds: net win per unit staked |
|---|---|---|
| 4 or 10 | 2:1 | 1:2 |
| 5 or 9 | 3:2 | 2:3 |
| 6 or 8 | 6:5 | 5:6 |
These fractions give 0.00% house edge on the odds portion when paid exactly under the stated model. They do not make that portion a guaranteed win or remove the required base wager. Check permitted amounts, payout precision and whether a quoted multiple limits the stake or the possible win. The same advertised multiple need not mean equal amounts risked when taking and laying odds.
Place bets
A place wager backs its named total before 7 while it is working. The following figures assume it stays active until one of those resolving outcomes and receives the exact stated net payout.
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| Place number | Net payout | House edge per wager carried to resolution |
|---|---|---|
| 6 or 8 | 7:6 | 1.52% |
| 5 or 9 | 7:5 | 4.00% |
| 4 or 10 | 9:5 | 6.67% |
This denominator is a wager carried to a win or loss, not a newly counted stake on every neutral roll. Buy and lay bets can instead use a commission; check how much is charged and when. Do not give those wagers the place-bet percentage merely because the number is the same.
Field: a one-roll wager
In the stated field game, 2, 3, 4, 9, 10, 11 and 12 win on the next roll; 5, 6, 7 and 8 lose. The ordinary winning totals pay 1:1 net. The special payouts on both 2 and 12 change the edge:
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| Net payout on 2 | Net payout on 12 | House edge |
|---|---|---|
| 2:1 | 2:1 | 5.56% |
| 2:1 | 3:1 | 2.78% |
Swapping which of 2 and 12 receives the triple payout leaves that calculation unchanged because each has one dice combination. As a mathematical counterexample, a field paying 3:1 on both would have 0.00% edge under these same rules. That is not a claim that a particular table currently offers it, and it shows why true odds should not be described as the only possible zero-edge casino wager.
Proposition and hardway wagers
Read whether a wager lasts one roll or remains active until particular outcomes settle it. These are exact examples rather than a universal range for every bet in the center of a layout.
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| Wager | Resolving event and net payout | House edge |
|---|---|---|
| Any 7 | Next roll is 7; pays 4:1 | 16.67% |
| Any craps | Next roll is 2, 3 or 12; pays 7:1 | 11.11% |
| 11 / Yo | Next roll is 11; pays 15:1 | 11.11% |
| 2 or 12, selected separately | Next roll is the chosen total; pays 30:1 | 13.89% |
| Hard 6 or Hard 8 | The chosen total appears as doubles before an easy version of it or 7; pays 9:1 | 9.09% |
| Hard 4 or Hard 10 | The chosen total appears as doubles before an easy version of it or 7; pays 7:1 | 11.11% |
Hardways here stay working until a win or loss; unrelated totals postpone settlement. A hard 8 is two 4s, while an easy 8 is any other dice pair totaling 8. Side bets, hop bets, promotional payouts and other variants need separate calculations.
The math
Probability is not the same as payout
For a bet that remains active until a win or loss, let p be its probability of winning on a roll and q its probability of losing on a roll. Neutral rolls postpone the outcome. Its eventual winning probability is p / (p + q) under the unchanged independent-roll model.
For a place 6 paying 7:6, five dice pairs win and six pairs make a losing 7. The eventual win probability is 5/11. Expected net return per unit staked is (5/11 × 7/6) − 6/11 = −1/66, giving 1.52% house edge.
For Any 7 at 4:1, six outcomes win four units and 30 lose one. The one-roll expected net return is (6 × 4 − 30) / 36 = −1/6, giving 16.67%. That wager’s payout is essential to the result; the probability of 7 alone does not determine its expected return.
Include the line wager’s whole cycle
Pass can resolve on the come-out or continue through a point. Weighting each branch by its dice combinations gives expected net loss of 7/495 of the initial stake, or 1.41%.
Don’t Pass with 12 barred gives 3/220, or 1.36%, per initial wager including the come-out-12 pushes. Excluding those wagers would change the denominator and the percentage. The figure is not a separate charge taken from each roll, and a push is not a loss.
See the published probability derivations; the examples here are independently checked from the 36 dice pairs and stated settlement rules.
Why true odds have zero edge
For point 4, three pairs make 4 and six make 7. Taking odds wins with probability 3/9 and pays 2:1 net, giving (3/9 × 2) − 6/9 = 0. Laying odds reverses the winning condition and pays 1:2, giving (6/9 × 1/2) − 3/9 = 0 per unit risked.
The corresponding 5/9 and 6/8 payouts work the same way with four and five point combinations. This is an expectation under exact payouts; either side can still lose the full odds stake.
Adding odds changes the denominator
Consider an unchanged one-unit Pass wager. Suppose exactly m extra units are added as true odds whenever any point is established, with the same m for every point. The chance of establishing a point is 24/36, or 2/3. In this model:
- Expected net loss per original line wager remains 7/495 units because the added odds have zero expected net loss.
- Average total amount newly staked per original line wager is 1 + 2m/3 units.
- Combined edge is (7/495) / (1 + 2m/3), expressed as a percentage.
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| Added odds amount after any point | Average total stake per original one-unit line wager | Combined percentage |
|---|---|---|
| None | 1 unit | 1.41% |
| 1 unit | 5/3 units | 0.85% |
| 2 units | 7/3 units | 0.61% |
| 5 units | 13/3 units | 0.33% |
| 10 units | 23/3 units | 0.18% |
This is average total action across complete line cycles; the odds stake is not placed on come-outs that resolve immediately. It assumes the same exact multiple on every point, no rounding or fees, and unchanged base stakes and number of cycles. It is not a 3–4–5 schedule or a laying-odds schedule.
The smaller percentage comes from a larger average total stake, while expected loss on the unchanged base remains the same. More money is exposed on point cycles and the distribution of possible results changes. A table maximum is a limit, not a target to spend.
Spending and results
For a fixed $100 of initial Pass wagers in this model, expected net loss is about $1.41. Initial Don’t Pass wagers with 12 pushing instead have about $1.36 expected net loss per $100. Neither is a guaranteed session cost. Adding other wagers changes total action and can add further expected loss; repeating unresolved rolls does not itself place a new line stake.
Compare definitions in the game comparison.
Tips for informed play
- Identify the wager’s phase. A come-out 7 and a point-phase 7 have different effects on Pass. Track separate Come points carefully.
- Read the exact payouts. Field payouts on both 2 and 12 matter; a bet’s name or layout position is not a return calculation.
- Keep the stake denominator visible. Per line cycle, per resolved wager, per roll and per total amount staked are different comparisons.
- Treat zero edge as an expectation. True odds can lose, require the eligible base wager and expose additional money.
- Set time and spending limits before play. Table energy, an available odds multiple or previous losses need not determine the next amount you risk.
Sources and scope
- Shackleford: craps rules, payouts and wager denominators. Published rule examples and mathematical tables, including field payout variants and the distinction between taking and laying odds.
- Shackleford: derivation of craps probabilities and expected returns. Original mathematical analysis used to cross-check the stated line, place, hardway and odds examples.
Checked September 5, 2026. Calculations independently enumerate the stated dice pairs and settlement rules. They assume exact payouts, unchanged fair-roll probabilities and the specified working/settlement conditions; they do not certify a particular table, dice-control claim, product availability, pace or session outcome.
Key terms
- Shooter
- The player rolling the dice.
- Come-out roll
- The first roll of a line-wager cycle.
- Point
- The established 4, 5, 6, 8, 9 or 10 tracked against 7 for that wager.
- Seven-out
- A 7 rolled after the relevant point is set; it loses Pass.
- Natural
- Here, a come-out 7 or 11 that wins Pass.
- Craps total
- A come-out 2, 3 or 12 that loses Pass under these rules.
- Push
- Return of a wager without net win or loss.
- Bar 12
- Here, the rule making Don’t Pass/Don’t Come push on an opening 12.
- Taking odds
- An eligible added wager backing the point before 7 at the stated true payout.
- Laying odds
- An eligible added wager backing 7 before the point at the stated true payout.
- Working
- Active for settlement on the relevant roll.
- Place bet
- A named total before 7, at its specified payout while working.
- Field
- The specified one-roll group of totals, with special payouts on 2 and 12.
- Hardway
- A chosen total as doubles before the easy form or 7.
- Net payout
- Winnings excluding the returned stake; distinguish this from a total-return amount.
- Resolution
- The event that settles the wager as a win, loss or push.
- Total action
- All new stakes placed, counted according to the stated model rather than counting held chips again each roll.
Common myths
What people believe, and what probability tells us.
Myth
Seven is always bad
The reality
Come-out 7 wins Pass; 7 after a point loses it.
Myth
Zero edge means the wager cannot lose
The reality
A true-odds wager can lose its full stake despite zero expected net loss.
Myth
Adding odds erases the base bet’s expected loss
The reality
The unchanged base retains its expected loss; added odds change total exposure and the combined denominator.
Myth
Every field bet has the same edge
The reality
The special net payouts on both 2 and 12 determine the calculation.
Myth
Every bet in the center lasts one roll
The reality
The stated hardways remain active until specified resolving events.
Myth
A streak makes the next roll due
The reality
Under the stated independent fair-dice model, earlier results do not change the next-roll probabilities.
Knowledge check
Pick an answer to reveal the explanation. Nothing is scored or saved.
Part of the Playbook Brand system, the open, public-domain core for player education. You can copy and adapt it under CC0.