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Exact casino math
Craps
Reducer-style table state with exact roll frequencies and bet-resolution logic across line, odds, place, buy, and hardways.
Model come-out, point, and per-roll bet resolution before layering in more niche proposition bets.
Rules focusThe rule assumptions and model boundary this page uses for its calculations.
The table is a state machine: come-out rolls establish points, active bets travel, and every roll resolves against a known distribution.OutputsThe main numbers or result groups this page will produce after you run the analysis.
Roll distributionLine bet outcomesOdds payout logicNext-state preview
Rules
Craps as a state machine
Come-out rolls, points, traveling bets, and per-roll resolution are all deterministic once the table state is known.
The table is a state machine: come-out rolls establish points, active bets travel, and every roll resolves against a known distribution.
- Come-out rolls establish the point on 4, 5, 6, 8, 9, or 10.
- Pass and Come share the same underlying EV; Don't Pass and Don't Come mirror the opposite side.
- Persistent bets are modeled as bets racing their number against 7.
Analyzer
Preview a configured craps table
Build the table state first, choose the dice next, and keep the live preview above the reference table.
Line and come bets
Working bets
Current tablePoint 69 configured bet(s)
ScenarioPass line, Pass odds, Field, Come, Come on 8, Come odds on 8, Place 6, Buy 4, Hard 8Persistent bets default to off on the come-out.
Selected rollHard 85 ways, 13.89%
Dice rollPick both dice directly. Hardways only apply when the dice are doubles on 4, 6, 8, or 10.
Die one
Die two
Hard 84 + 4 = 8
Choose two dice to preview how the configured state resolves.
Reference
Core bet table
Keep the payout reference below the live preview so the configured table stays first.
| Bet | Payout | Win / push | EV / unit | House edge |
|---|---|---|---|---|
| Pass lineExact line-bet EV from the come-out roll through the point cycle. | 1:1 | 49.29% / 0.00% | -0.014u | 1.41% |
| Don't PassBars 12 on the come-out, which creates the small push probability. | 1:1 | 47.93% / 2.78% | -0.014u | 1.36% |
| ComeOnce a Come bet is made, its EV matches the Pass line from that new come-out cycle. | 1:1 | 49.29% / 0.00% | -0.014u | 1.41% |
| Don't ComeOnce a Don't Come bet is made, it mirrors Don't Pass math with the same bar-12 push. | 1:1 | 47.93% / 2.78% | -0.014u | 1.36% |
| Pass odds on 4 / 10True odds with zero house edge after the point is established. | 2:1 | 33.33% / 0.00% | 0.000u | 0.00% |
| Pass odds on 5 / 9True odds with zero house edge after the point is established. | 3:2 | 40.00% / 0.00% | +0.000u | -0.00% |
| Pass odds on 6 / 8True odds with zero house edge after the point is established. | 6:5 | 45.45% / 0.00% | 0.000u | 0.00% |
| Don't Pass odds on 4 / 10True odds with zero house edge when fading 4 or 10. | 1:2 | 66.67% / 0.00% | 0.000u | 0.00% |
| Don't Pass odds on 5 / 9True odds with zero house edge when fading 5 or 9. | 2:3 | 60.00% / 0.00% | -0.000u | 0.00% |
| Don't Pass odds on 6 / 8True odds with zero house edge when fading 6 or 8. | 5:6 | 54.55% / 0.00% | 0.000u | 0.00% |
| FieldOne-roll wager whose edge depends on the table's bonus schedule for 2 and 12. | 1:1, 2:1 on 2, 3:1 on 12 | 44.44% / 0.00% | -0.028u | 2.78% |
| Place 4 / 10Persistent bet that wins when 4 or 10 rolls before 7. | 9:5 | 33.33% / 0.00% | -0.067u | 6.67% |
| Place 5 / 9Persistent bet that wins when 5 or 9 rolls before 7. | 7:5 | 40.00% / 0.00% | -0.040u | 4.00% |
| Place 6 / 8The strongest standard place-bet family on the table. | 7:6 | 45.45% / 0.00% | -0.015u | 1.52% |
| Buy 4 / 10Assumes the commission is collected on wins, matching the reducer's current behavior. | True odds less vig | 33.33% / 0.00% | -0.017u | 1.67% |
| Buy 5 / 9Assumes the commission is collected on wins, matching the reducer's current behavior. | True odds less vig | 40.00% / 0.00% | -0.020u | 2.00% |
| Buy 6 / 8Assumes the commission is collected on wins, matching the reducer's current behavior. | True odds less vig | 45.45% / 0.00% | -0.023u | 2.27% |
| Hard 4 / 10Wins only on the hard combination before an easy total or 7 appears. | 7:1 | 11.11% / 0.00% | -0.111u | 11.11% |
| Hard 6 / 8Wins only on the hard combination before an easy total or 7 appears. | 9:1 | 9.09% / 0.00% | -0.091u | 9.09% |