Craps Odds and House Edge, Explained
After reading this you can compute the exact win probability and house edge for every common craps bet, and see how a free odds bet on the pass line lowers your average cost.
What the numbers mean and one quick example
Craps looks chaotic, but every bet reduces to counting the 36 equally likely outcomes of two dice. Take the Any seven bet. Of the 36 combinations, six of them total seven, so the win probability is 6/36 = 0.1667. The casino pays 4 to 1 on a win. Fair odds would be 5 to 1, because you lose 30 times for every 6 wins. That gap is the whole story of the house edge.
The expected value of a one unit bet is the payout times the win chance minus the stake times the loss chance:
So Any seven costs you about 16.67 cents per dollar wagered. That is one of the worst bets on the table. By contrast, the pass line costs about 1.41 cents per dollar. Same table, ten times the difference.
When this matters and when it does not
Use these figures to choose bets and to size a bankroll. The house edge tells you the average loss per dollar of action, so it drives the long-run cost of a session. If you know your total wagered amount, multiply by the edge to estimate expected loss.
The edge does not tell you what happens tonight. Over a few hours variance dominates. A pass line bettor with a 1.41 percent edge can easily walk away up or down several hundred dollars. The edge only asserts itself over thousands of decisions. Treat it as the price of entertainment, not a prediction of one visit.
Two edge conventions exist. "Per bet resolved" divides expected loss by the amount staked once. "Per roll" divides by the number of dice rolls, which matters for multi-roll bets like Place bets. This guide reports per resolved bet unless noted, because that is what you actually put at risk.
The general formula
Every craps bet has three inputs: the probability of winning p, the probability of losing q = 1 - p (ignoring pushes), and the payout b stated as "b to 1". The house edge on the amount at risk is:
Here b is the net win per unit staked, p is the win probability, and q is the loss probability. If a bet can push (the Field pushes on some rolls, the pass line never does), the pushes contribute zero and are simply excluded from both p and q when you measure edge per resolved bet.
The pass line needs a little more work because it resolves over several rolls. On the come-out roll you win on 7 or 11 (8 of 36) and lose on 2, 3, or 12 (4 of 36). Any other number sets the point, and you then win only by rolling that point again before a 7. Summing across all points gives a win probability of 244/495 = 0.4929 and a loss probability of 251/495 = 0.5071. With even money payout (b = 1):
House edges of the common bets
The table gathers the exact figures. Payouts are net "to 1". Place bets are shown at standard Las Vegas payouts.
| Bet | Win prob | Payout (to 1) | House edge |
|---|---|---|---|
| Pass line | 0.4929 | 1 | 1.41% |
| Don't pass (bar 12) | 0.4793 | 1 | 1.36% |
| Field (2 and 12 double) | 0.4444 | 1 or 2 | 5.56% |
| Place 6 or 8 | 0.4545 | 1.167 | 1.52% |
| Place 5 or 9 | 0.4000 | 1.4 | 4.00% |
| Place 4 or 10 | 0.3333 | 1.8 | 6.67% |
| Hardway 6 or 8 | 0.0909 | 9 | 9.09% |
| Hardway 4 or 10 | 0.1111 | 7 | 11.11% |
| Any seven | 0.1667 | 4 | 16.67% |
| Any craps | 0.1111 | 7 | 11.11% |
| Yo (eleven) | 0.05556 | 15 | 11.11% |
Read the pattern. The line bets sit near 1.4 percent. Place 6 or 8 is close behind at 1.52 percent. Everything toward the center of the layout gets steadily worse, and the one-roll proposition bets are the most expensive on the table.
How free odds change the picture
Once a point is set, you may back your pass line bet with a free odds wager. It pays true odds, so its own house edge is exactly zero. It cannot change the 1.41 percent edge on the flat bet, but it adds fair action, which dilutes the overall edge on your total money at risk.
Odds on the point pay: 6 to 5 on 6 or 8, 3 to 2 on 5 or 9, and 2 to 1 on 4 or 10. Combine the fixed loss of 7/495 from the flat bet with a zero-edge odds bet of multiple m, then divide by the larger total wager. The blended edge falls fast:
| Odds multiple | Combined edge |
|---|---|
| 0x | 1.414% |
| 1x | 0.848% |
| 2x | 0.606% |
| 3x | 0.471% |
| 5x | 0.326% |
| 10x | 0.184% |
Worked example: pass line, 3x odds, 10 dollar stake
This reproduces the demo: bet = pass, odds_mult = 3, stake = 10.
- Flat bet expected loss per resolved bet is
10 x 7/495 = 0.1414dollars. - The odds bet pays fair odds, so its expected value is exactly zero no matter the size.
- Average total wager depends on how often a point is set. A point is set on 24 of 36 come-out rolls, or 0.6667 of the time. When it is, you add up to 3x, so average odds action is roughly
10 x 3 x 0.6667 = 20dollars. - Average money at risk per resolved bet is about
10 + 20 = 30dollars, and the expected loss stays0.1414dollars. - Combined edge is
0.1414 / 30 = 0.00471, or 0.471 percent, matching the table.
Your expected loss in dollars did not change from the no-odds case. You simply moved more money at fair value, so the loss as a fraction of total action dropped by about two thirds.
Common mistakes
Do not read the combined edge as a better deal in dollars. Free odds lower the percentage, not your expected loss on the flat bet. If you also risk more total money, your variance grows. The odds bet is good because it is fair, not because it saves you cash.
Three errors show up repeatedly. First, confusing "to 1" with "for 1". A 15 to 1 payout returns 16 total; a 15 for 1 payout returns 15, a worse deal. Second, quoting the Place 6 or 8 edge as if it were per roll (0.46 percent) when comparing it to the pass line per resolved bet (1.41 percent); use the same convention on both sides. Third, believing that hedging a pass line with Any craps reduces cost. It does not. Adding a 11.11 percent edge bet to a 1.41 percent edge bet raises your blended cost, it never lowers it.
Related tools
To turn any of these edges into a session forecast, use the Expected Loss Calculator with your total wagered amount. For other games, the Roulette Odds page covers every roulette bet, and the Blackjack House Edge page derives the edge from your exact table rules. If you want to model the swing of a machine session rather than a table game, see the Slot Session Calculator.
Frequently asked questions
Is the pass line or don't pass the better bet?
Don't pass has a slightly lower edge, 1.36 percent against 1.41 percent, because the 12 pushes instead of losing. The difference is about 5 cents per 100 dollars wagered, so pick whichever you prefer to play.
Why is the edge on free odds zero?
Free odds pay the true mathematical odds of making the point. On a point of 4, you make it 3 times for every 6 sevens, and the bet pays 2 to 1, exactly matching. Fair payout means zero expected loss.
What is the single worst bet in craps?
Any seven, at a 16.67 percent house edge. You give up about 17 cents on every dollar, more than three times the field and over ten times the pass line.
Does taking maximum odds guarantee a win?
No. It lowers the percentage edge on total action but leaves the flat-bet expected loss unchanged and increases the size of your swings. Over one session you can still lose a large amount.
What does a 1.41 percent edge cost per hour?
At roughly 30 pass line decisions per hour and 10 dollars each, that is 300 dollars of action, so about 300 x 0.0141 = 4.24 dollars of expected loss per hour before odds bets.
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