The odds bet in craps pays exactly its true probability — zero house edge, the only standard casino wager priced fairly. It exists only attached to a pass/don't-pass (or come/don't-come) bet, and casinos cap how much of it you can take. This page derives the math and shows what the cap structure means for your total cost.
How it works
After a point is set, place additional chips "behind" your pass line bet. The odds bet wins and loses with the line bet, but pays true odds:
| Point | Repeat-vs-7 odds | Odds bet pays |
|---|---|---|
| 4 or 10 | 2:1 against | 2:1 |
| 5 or 9 | 3:2 against | 3:2 |
| 6 or 8 | 6:5 against | 6:5 |
If you want the math: a point of 4 repeats via 3 dice combinations against 6 ways to roll a 7 — exactly 2:1 against, exactly what it pays. Expected value: zero. The same check works for every point.
Why casinos allow a fair bet
Because you cannot place it alone. The odds bet only exists glued to a line bet that carries 1.41% (pass) or 1.36% (don't pass). The casino earns its edge on the line; the odds portion adds volume at cost-neutral pricing — and caps (3x, 3-4-5x, 5x, occasionally 10x+ the line bet) limit how far you can dilute the package.
The dilution table
| Odds taken | Combined house edge (pass + odds, of total wagered) |
|---|---|
| No odds | 1.41% |
| 1x | 0.85% |
| 2x | 0.61% |
| 3-4-5x | 0.37% |
| 5x | 0.33% |
| 10x | 0.18% |
The practical instruction: bet the table-minimum pass line and put your real stake in the odds. A $5 line + $25 odds wagers the same $30 as a $30 line bet, at roughly a fifth of the edge.
Laying odds (don't pass)
Don't-pass bettors lay odds instead — betting more to win less, at the same zero edge (the 7 is favoured once a point exists). Lay 6:5 against points of 4/10, 3:2 against 5/9, 5:6 against 6/8. Combined don't-pass + lay edges run marginally below the pass equivalents (1.36% line edge diluting the same way).
Bankroll note
Zero edge is not zero variance: max odds raise swing sharply — a 3-4-5x player wagers 4–6 units per point cycle. Unit-size from the total exposure per round, not the line bet. The pillar's framework applies: the odds bet makes craps cheap, not gentle.