Canonical: https://www.playbookrg.com/brand/content/games/craps/ Description: 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. > Static reading copy of the published page, including authored disclosures. Interactive controls, personalized state, and account data are not reproduced. Use the canonical page for interaction and citations, and the dedicated content feeds for complete resource inventories. Source terms still apply; this format does not extend the Brand CC0 license to other products or third-party material. # 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 September 5, 2026. Sources and assumptions are linked below. [Download guide text (.md)]() [Download quick reference (.md)]() House-edge example 1.41% Pass Per initial line wager, including pushes Don't Pass with 12 barred is 1.36%. True-odds portions have no house edge, but require an eligible line/come bet. Their zero edge does not remove the expected loss on that base bet. - [Shackleford: craps probability derivations]()Mathematical analysis [Compare all ten games →]() ![Craps house-edge examples distinguish line wagers, true odds and the field bet’s exact payouts]() From the Playbook Brand system · Free to copy and adapt · CC0 01 ## 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: Craps — How the game works — Come-out and point: Come-out total, Pass, Don’t Pass, with 12 barred | 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. Craps — How the game works — Count the dice outcomes: Total, Ways to make that total, Probability on one stated fair roll | 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](). 02 ## Bet types ### Line and Come wagers Craps — Bet types — Line and Come wagers: Bet, Settlement, House edge under the stated rules | 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. Craps — Bet types — True odds behind an eligible wager: Point, Taking odds: net win per unit staked, Laying odds: net win per unit staked | 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. Craps — Bet types — Place bets: Place number, Net payout, House edge per wager carried to resolution | 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: Craps — Bet types — Field: a one-roll wager: Net payout on 2, Net payout on 12, House edge | 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. Craps — Bet types — Proposition and hardway wagers: Wager, Resolving event and net payout, House edge | 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. 03 ## 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. Craps — The math — Adding odds changes the denominator: Added odds amount after any point, Average total stake per original one-unit line wager, Combined percentage | 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](). 04 ## Tips for informed play 1. **Identify the wager’s phase.** A come-out 7 and a point-phase 7 have different effects on Pass. Track separate Come points carefully. 2. **Read the exact payouts.** Field payouts on both 2 and 12 matter; a bet’s name or layout position is not a return calculation. 3. **Keep the stake denominator visible.** Per line cycle, per resolved wager, per roll and per total amount staked are different comparisons. 4. **Treat zero edge as an expectation.** True odds can lose, require the eligible base wager and expose additional money. 5. **Set time and spending limits before play.** Table energy, an available odds multiple or previous losses need not determine the next amount you risk. 05 ## 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. 06 ## 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. 07 ## 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. 08 ## Knowledge check Pick an answer to reveal the explanation. Nothing is scored or saved. 1. 01 What is the edge on the added true-odds portion, paid exactly under this guide’s model? A 1.41% on every odds wager B 1.36%, regardless of which side it backs C 0.00%, while the required base wager keeps its own expected loss D Zero chance of losing the stake 2. 02 On a come-out 7, what happens to Pass under the stated rules? A It loses, because every 7 is a seven-out B It wins at 1:1 net C The 7 becomes the point D It pushes in the same way as Don’t Pass on 12 3. 03 The field wins on 2, 3, 4, 9, 10, 11 or 12. Ordinary wins pay 1:1; both 2 and 12 pay 2:1 net. What is its house edge? A 2.78%, regardless of the special payouts B 5.56%, from (20 − 14 − 2 − 2) / 36 C 0.00%, because two totals pay double D The Pass line’s 1.41% 1. 1. What is the edge on the added true-odds portion, paid exactly under this guide’s model? 1. 1.41% on every odds wager 2. 1.36%, regardless of which side it backs 3. 0.00%, while the required base wager keeps its own expected loss 4. Zero chance of losing the stake **Answer: C.** The odds payouts balance their win and loss probabilities. This does not make each result a push or cancel the base wager’s expected loss. Adding more odds behind an unchanged base increases the amount exposed on point cycles. Own dice-pair and payout calculation, checked against the linked craps analyses. 2. 2. On a come-out 7, what happens to Pass under the stated rules? 1. It loses, because every 7 is a seven-out 2. It wins at 1:1 net 3. The 7 becomes the point 4. It pushes in the same way as Don’t Pass on 12 **Answer: B.** Come-out 7 and 11 are immediate Pass wins. Once a point has been set, a 7 before that point instead loses Pass. The wager’s phase matters; this is not a result for every other bet on the table. Stated line-wager rules, checked against the linked craps rules reference. 3. 3. The field wins on 2, 3, 4, 9, 10, 11 or 12. Ordinary wins pay 1:1; both 2 and 12 pay 2:1 net. What is its house edge? 1. 2.78%, regardless of the special payouts 2. 5.56%, from (20 − 14 − 2 − 2) / 36 3. 0.00%, because two totals pay double 4. The Pass line’s 1.41% **Answer: B.** There are 20 losing pairs, 14 ordinary one-unit winning pairs and two special pairs paying two units each. Expected loss is 2/36 of the stake, or 5.56%. Paying one special total 3:1 instead changes the edge to 2.78%. Own enumeration of the specified field outcomes and payouts; linked craps rules and analysis. Part of the [Playbook Brand system](), the open, public-domain core for player education. You can copy and adapt it under CC0. [← All game guides]() [Playbook Brand]()