Craps expected-value guide · Reviewed August 18, 2026
House edge is the average expected loss divided by the initial amount wagered. It does not predict one session. It gives you a common scale for comparing bets with different probabilities and payouts.
The useful formula
Expected value = Σ (probability of each outcome × net result of that outcome).
House edge = −expected value ÷ initial wager.
Interactive craps math
Craps bet calculator
Choose a common wager and stake to see the standard net win, stake treatment, correct chip multiple and modeled expected loss.
Only the profit is paid while this wager stays working. The combined total includes your stake only if you also take the wager down after the win.
Your $6 wager is a clean multiple for the standard 7-to-6 payout.
Wins when the selected 6 or 8 appears before 7. Standard payout: 7 to 6.
Educational estimate only. Actual tables can use different rules, limits, commissions or chip-rounding procedures. Buy bets, Lay bets and variable Field paytables are intentionally excluded.
House edge, hold and expected loss are different
- House edge is the mathematical average loss per initial wager under stated rules.
- Expected loss is amount wagered × house edge, extended across the number of decisions or cycles.
- Casino hold is an accounting result based on chips bought versus redeemed over a period; it is not the same as a bet’s house edge.
- Chance of winning is not enough by itself. A bet can win often and still be expensive if losses or payouts are structured badly.
Four steps for any craps wager
- List every mutually exclusive way the wager can end.
- Assign each outcome its probability.
- Use net win or loss, not a gross return that includes the original chip.
- Add probability × net result, then divide the expected loss by the initial wager.
Worked example: Place 6
A Place 6 is decided only when 6 or 7 rolls. Five combinations win and six lose. A proper $6 wager wins $7.
| Outcome | Conditional probability | Net result | Weighted result |
|---|---|---|---|
| 6 rolls first | 5/11 | +$7 | +$35/11 |
| 7 rolls first | 6/11 | −$6 | −$36/11 |
| Total | 1 | — | −$1/11 = −$0.0909 |
The expected loss is $0.0909 per $6 decision. Divide $0.0909 by $6: the house edge is 1.515%, normally rounded to 1.52%.
Same event, worse payout: Big 6
Big 6 also wins when 6 appears before 7, but a $6 bet normally wins only $6. The outcome probabilities are identical; only the payout changes.
| Bet | $6 win | Expected loss per decision | House edge |
|---|---|---|---|
| Place 6 | $7 | $0.0909 | 1.52% |
| Big 6 | $6 | $0.5455 | 9.09% |
This comparison preserves the original lesson’s strongest point: two bets can depend on the same dice event while carrying very different costs. See the full Big 6/8 comparison.
Worked example: Any 7
Any 7 wins on six combinations and loses on 30. At a standard 4-to-1 net payout for a $1 wager:
| Outcome | Probability | Net result | Weighted result |
|---|---|---|---|
| Seven | 6/36 | +$4 | +$24/36 |
| Anything else | 30/36 | −$1 | −$30/36 |
| Total | 1 | — | −$6/36 = −$0.1667 |
Expected value is −$0.1667 per $1. The house edge is therefore 16.67%. “Seven is the easiest total” is true, but does not rescue an underpaid proposition.
Worked example: two Field paytables
The Field has 16 winning combinations and 20 losing combinations. Fourteen winning combinations are the ordinary 3, 4, 9, 10, and 11 results; 2 and 12 create the bonus variation.
| Paytable | Expected result across 36 $1 bets | House edge |
|---|---|---|
| 2 and 12 both pay 2:1 | 14 + 2 + 2 − 20 = −$2 | 5.56% |
| 2 pays 2:1; 12 pays 3:1 | 14 + 2 + 3 − 20 = −$1 | 2.78% |
This is why a house-edge number is incomplete without the rule that produced it. Read the Field guide before assuming a layout’s price.
Worked hedge: $10 Pass plus $1 Any Craps
A “craps check” changes what happens on a come-out 2, 3, or 12, but it does not make the package free. Per completed Pass Line cycle:
- $10 Pass Line expected loss: $10 × 1.414% = about $0.1414.
- $1 Any Craps expected loss: $1 × 11.111% = about $0.1111.
- Combined expected loss: about $0.2525 per cycle.
- Combined initial action: $11; package edge relative to that initial action is about 2.30%.
On a come-out craps number, the $10 Pass loses and a standard 7-to-1 Any Craps win earns $7, leaving the package down $3. The side bet softens that particular result while increasing the package’s average expected cost.
What taking or laying Odds does
An Odds wager pays the true point-versus-seven ratio, so its own expected value is zero before chip rounding or a nonstandard rule. Adding Odds therefore leaves the flat bet’s expected dollar loss unchanged while increasing total money at risk.
If $20 Odds is added whenever a $10 Pass bet establishes a point, the maximum point-stage exposure is $30. But Odds is placed only on the two-thirds of initial cycles that establish a point, so average action per initial cycle is $10 + (2/3 × $20) = about $23.33. The flat bet’s expected loss remains about $0.1414 per initial cycle, which is about 0.606% of that average combined action. The larger wager can still produce much larger session swings.
Expected loss over time
A planning estimate is:
Average wager × decisions per hour × hours played × house edge
Suppose you average $18 on Place 6, see 30 decisions per hour, and play two hours. Total modeled action is $1,080. At 1.515%, expected loss is about $16.36. Actual results can finish far above or below that figure; the estimate describes the long-run center, not a session invoice.
Commissions and chip rounding
Buy and Lay bets add a commission, often called vigorish. The effective edge depends on whether the commission is charged when the wager is made, only on a win, or after a specific threshold—and whether the casino rounds to available chip units. Use the actual dollars paid, not a slogan such as “5% vig.”
For a $25 Buy 4 that wins $50, a $1 commission on wins is not the same economic price as collecting $1 before every decision. If a table charges $2 because of rounding, the practical edge changes again. State the commission timing and rounding assumption beside every calculation.
Why progressions do not change expectation
Suppose a wager loses an average of 1.5 cents per dollar. Betting $5, then $10, then $20 after losses changes the dollars exposed to each independent decision. It does not change the 1.5-cent expected cost per dollar. The progression’s expected loss is the sum of each possible wager amount multiplied by the same underlying edge.
A progression may change the chance of finishing a short session with a small profit, but it usually purchases that pattern with rarer, larger losses. Measure total action and worst-case exposure, not only the percentage of sessions reported as winners.
Common calculation mistakes
- Using “for 1” gross return as if it were net winnings.
- Counting rolls that do not resolve a standing wager as new wager decisions.
- Comparing only win probability while ignoring the payout.
- Using total combined action to advertise a low edge without disclosing the added dollars at risk.
- Assuming a system changes expected value merely because it redistributes wins and losses.
- Ignoring commissions, chip rounding, maximum payouts, and table-specific Field rules.
Frequently asked questions
Can a betting system reverse the house edge?
No ordinary progression changes the probabilities or payouts of its component wagers. It can change volatility, bet size, and the pattern of session results.
Does a 1% edge mean I lose $1 from every $100 session?
No. It means an average expected loss of $1 per $100 of qualifying action across repeated play. One session can win or lose much more.
Does making more bets raise every bet’s edge?
No. Each wager keeps its own edge. More positive-edge-for-the-house action usually raises total expected dollar loss.
Can practice lower the mathematical edge?
Practice cannot change a posted payout, but it can prevent wrong multiples, accidental bets, misread rules, and expensive choices.
Source and calculation notes
- Massachusetts Gaming Commission: Craps and Mini-Craps rules and payouts
- Craps Math: the 36 dice outcomes and conditional point probabilities
- All expected-value examples above were independently recomputed from stated probabilities and net payouts.
What happens to come bets when the passline point wins?
For details on Come bets, including details about your question, please refer to our article on Come bets. The sample Come-bet scenario in that article helps make it easy to understand. Here’s a summary