True Odds and the Odds Bet
Almost every bet in a casino pays you a little less than it should. That gap is the house edge, and it's everywhere — with one famous exception. The craps "free-odds" bet pays you exactly what the math says it's worth: no edge at all. To see why that's remarkable, you first have to separate two ideas that sound the same.
True odds vs payout odds
True odds describe how likely something really is. If an event happens once for every two times it doesn't, its true odds are 2-to-1 against. Payout odds describe what the casino actually pays when you win. In a perfectly fair game, the two match. In a real casino, the payout odds are set slightly worse than the true odds, and that sliver is the house's profit.
Take a single number in double-zero roulette: the true odds are 37-to-1 against, but it pays only 35-to-1. You're being shorted on every win. That shortfall, repeated, is the entire business model.
The free-odds bet
Craps does something almost no other game does. After a point is established on the Pass line, you're allowed to place an additional bet "behind the line" — the odds bet — and that extra wager is paid at true odds. No shaving, no shortfall. Its house edge is exactly zero.
The true odds depend on which point was set, because each point number has a different chance of repeating before a 7:
| Point | Ways to make it | True odds (vs 7) | Odds bet pays |
|---|---|---|---|
| 4 or 10 | 3 | 2 to 1 | 2 to 1 |
| 5 or 9 | 4 | 3 to 2 | 3 to 2 |
| 6 or 8 | 5 | 6 to 5 | 6 to 5 |
A worked example: point of 4
Say the point is 4. There are 3 ways to roll a 4 and 6 ways to roll a 7, so the true odds are 6-to-3, which simplifies to 2-to-1 against. You'll make the 4 once for every two times you seven out.
Now put $10 of odds behind the line. Over three "typical" decisions you'd expect to win once and lose twice:
- Two losses: −$10 − $10 = −$20
- One win at 2-to-1: +$20 = +$20
- Net over three decisions: $0
It breaks even in the long run. That's what "zero house edge" means in practice — the odds bet is neither helping nor hurting your expected value on its own. Compare that to the same $10 on almost any other bet, which would bleed a few percent.
Important nuance: the odds bet is a fair bet, not a winning one. It doesn't make money over time — it simply doesn't lose money to an edge. The Pass line bet it sits behind still carries its ~1.41% edge.
Why casinos cap it
If the odds bet is free, why not bet a fortune on it? Because casinos won't let you. Tables cap odds at some multiple of your line bet — "2x odds," "3x-4x-5x," sometimes more. The cap exists precisely because the casino makes nothing on this portion; they only allow it as an inducement to make the line bet, which does carry an edge. An uncapped odds bet would let you pour money through a zero-edge bet attached to a tiny edged one.
Lowering your blended edge
Here's the practical payoff. Because the odds portion is free, adding it dilutes the edge on your total action. Bet $10 on the Pass line alone and you face ~1.41%. Add $20 of odds and you're now risking $30, but the casino's edge still only applies to the original $10 — so your blended edge on the full $30 drops to roughly 0.5%. Pile on more odds and it falls further. You can't erase the edge, but the odds bet is the one legitimate lever that shrinks it.
On Riskr you can experiment with line bets and odds using fake chips — watch the blended edge shrink as you back the point, with nothing real on the line but leaderboard bragging rights.