Craps Odds and House Edge: Every Bet on the Table

A craps table offers the widest spread of house edges in a casino, from 1.36% on the don’t pass line to more than 16% on some centre-table propositions. The same roll of the dice settles all of them, so the difference is not in the game but in the payout table and the number of outcomes each bet covers. This page derives each figure from those two things, states the rules each figure depends on, and converts the edges into money per hour at a stated stake and roll rate.

The table and the dice

A craps table is a felt layout with a marked come area, a don’t come area, a pass line, a don’t pass line, and a centre section of proposition bets. Two six-sided dice are used. The 36 equally likely outcomes are the foundation of every calculation that follows. The distribution of totals is:

These probabilities are fixed by the dice. No past result changes them. The dice have no memory, and a table that has not seen a 7 for twenty minutes is no more likely to produce one on the next roll than a table that just produced three in a row.

The come-out roll and the point

The pass line bet is resolved in two stages. The first roll is the come-out. If the come-out is 7 or 11, the pass line wins even money. If it is 2, 3, or 12, it loses. Any other total becomes the point. The dealer places a puck on that number. The shooter then rolls until either the point repeats, in which case the pass line wins even money, or a 7 appears, in which case it loses.

The don’t pass bet is the reverse: it wins on a come-out of 2 or 3, pushes on 12, loses on 7 or 11, and wins even money if a 7 appears before the point repeats.

Deriving the pass line edge

The pass line edge is not a single probability but a weighted average over the possible points. The calculation proceeds in three steps.

Step 1: Come-out outcomes. On the come-out, 7 or 11 wins, 2, 3, or 12 loses, and any other total establishes a point. The probability of winning on the come-out is (6+2)/36 = 8/36. The probability of losing is (1+2+1)/36 = 4/36. The remaining 24/36 establishes a point.

Step 2: Point resolution. For each point, the probability of repeating the point before a 7 is the number of ways to make the point divided by the sum of ways to make the point and ways to make a 7. The ways to make a 7 are always 6.

Step 3: Combine. The probability of establishing each point is the number of ways to make that total divided by 36. The overall probability of winning after a point is established is the sum over points of P(point) times P(point before 7).

• Point 4: (3/36) * (3/9) = 9/324
• Point 5: (4/36) * (4/10) = 16/360
• Point 6: (5/36) * (5/11) = 25/396
• Point 8: (5/36) * (5/11) = 25/396
• Point 9: (4/36) * (4/10) = 16/360
• Point 10: (3/36) * (3/9) = 9/324

Converting to decimals and summing: 0.02778 + 0.04444 + 0.06313 + 0.06313 + 0.04444 + 0.02778 = 0.2707. So the probability of winning after a point is established is about 0.2707.

The total probability of winning the pass line is the come-out win plus the point win: 8/36 + 0.2707 = 0.2222 + 0.2707 = 0.4929. The probability of losing is 1 - 0.4929 = 0.5071. The house edge is the difference between the probability of losing and winning, since the payout is even money: 0.5071 - 0.4929 = 0.0142, or 1.42%. The commonly cited figure is 1.41%, which comes from carrying more decimal places through the calculation. The exact fraction is 7/495, which is 0.0141414… = 1.41%.

This figure depends on the pass line paying even money and on the come-out rules as stated. If a casino offers 3-4-5x odds, the pass line edge itself is unchanged; the odds bet is a separate wager with no edge.

Deriving the don’t pass edge

The don’t pass bet wins on a come-out of 2 or 3, pushes on 12, and loses on 7 or 11. If a point is established, it wins if a 7 appears before the point repeats.

The probability of winning on the come-out is (1+2)/36 = 3/36. The probability of losing is (6+2)/36 = 8/36. The probability of a push is 1/36. The remaining 24/36 establishes a point. For each point, the probability of a 7 before the point is 1 minus the probability of the point before a 7. So for point 4, P(7 before 4) = 6/9 = 0.6667, and so on.

The overall probability of winning after a point is established is the sum over points of P(point) * P(7 before point).

• Point 4: (3/36) * (6/9) = 18/324 = 0.05556
• Point 5: (4/36) * (6/10) = 24/360 = 0.06667
• Point 6: (5/36) * (6/11) = 30/396 = 0.07576
• Point 8: (5/36) * (6/11) = 30/396 = 0.07576
• Point 9: (4/36) * (6/10) = 24/360 = 0.06667
• Point 10: (3/36) * (6/9) = 18/324 = 0.05556

Sum: 0.05556 + 0.06667 + 0.07576 + 0.07576 + 0.06667 + 0.05556 = 0.39598.

Total probability of winning: 3/36 + 0.39598 = 0.08333 + 0.39598 = 0.47931. Probability of losing: 8/36 + (0.2707) = 0.2222 + 0.2707 = 0.4929. Wait, that’s not right. The probability of losing after a point is established is the probability of the point repeating before a 7, which is 0.2707. So total losing probability is 8/36 + 0.2707 = 0.4929. The push probability is 1/36 = 0.02778. Check: 0.47931 + 0.4929 + 0.02778 = 1.0000. Good.

The house edge on don’t pass is the difference between losing and winning probabilities, adjusted for the push: (0.4929 - 0.47931) / (1 - 0.02778) = 0.01359 / 0.97222 = 0.01398, or 1.40%. The commonly cited figure is 1.36%, which comes from a more precise calculation. The exact fraction is 3/220 = 0.013636… = 1.36%. The discrepancy arises because the push is excluded from the denominator. The correct edge is 1.36%.

This figure depends on the don’t pass bar being 12. Some tables bar 2 instead, which changes the edge slightly.

Free odds: the only zero-edge bet

After a point is established, a pass line bettor may place an additional wager behind the line, called odds. This bet is paid at true odds: 2:1 on points 4 or 10, 3:2 on 5 or 9, and 6:5 on 6 or 8. Because the payout matches the true probability, the expected value of the odds bet is zero. The house has no edge on it.

The odds bet does not change the house edge on the pass line itself. It dilutes the overall edge because a larger fraction of the total amount wagered is on a zero-edge bet. For example, if a player bets 10 on the pass line and 10 in odds, the total wager is 20. The expected loss is 1.41% of 10, which is 0.141. The overall edge is 0.141/20 = 0.705%. With 100 in odds, the overall edge is 0.141/110 = 0.128%. The pass line edge remains 1.41% on the flat bet.

This is the only bet in a casino that carries no house edge. It depends on the casino allowing odds and on the maximum odds multiple, which is typically 3-4-5x, meaning 3x on 4 and 10, 4x on 5 and 9, and 5x on 6 and 8.

Proposition bets: the loudest and the worst

The centre of the table offers bets on specific outcomes: any 7, any craps, the hardways, and the individual totals. These have high payouts and high house edges.

The house edge for any 7: the probability of winning is 6/36 = 0.1667. The payout is 4:1, so a 1 bet returns 5 on a win (4 profit plus stake). The expected value is (6/36)*4 - (30/36)*1 = 24/36 - 30/36 = -6/36 = -0.1667, or 16.67%.

For any craps: probability of winning is 4/36 = 0.1111. Payout 7:1. Expected value: (4/36)*7 - (32/36)*1 = 28/36 - 32/36 = -4/36 = -0.1111, or 11.11%.

For hard 8: probability of winning is 2/36 = 0.0556. Payout 9:1. Expected value: (2/36)*9 - (34/36)*1 = 18/36 - 34/36 = -16/36 = -0.4444, or 44.44%? That’s not right. Wait, hard 8 wins if the dice show 4-4 before any other combination that makes 8 or a 7. The probability of winning is not simply 2/36. The correct probability for hard 8 is 2/36? No, the hardway bet is resolved over multiple rolls. The probability of rolling a hard 8 before an easy 8 or a 7 is 2/(2+4+6) = 2/12 = 1/6 = 0.1667. The payout is 9:1, so expected value: (1/6)*9 - (5/6)*1 = 9/6 - 5/6 = 4/6 = 0.6667? That would be positive, which is impossible. Let’s recalculate: the hardway bet wins if the shooter rolls a 4-4 before rolling a 7 or any other combination that makes 8 (which are 2-6, 3-5, 5-3, 6-2). The ways to roll a hard 8 are 1 (4-4). The ways to roll an easy 8 are 4. The ways to roll a 7 are 6. So the probability of winning is 1/(1+4+6) = 1/11 = 0.0909. The payout is 9:1, so expected value: (1/11)*9 - (10/11)*1 = 9/11 - 10/11 = -1/11 = -0.0909, or 9.09%. That matches the table.

For hard 4 or 10: ways to roll hard 4 is 1 (2-2). Ways to roll easy 4 is 2 (1-3, 3-1). Ways to roll 7 is 6. Probability of winning: 1/(1+2+6) = 1/9 = 0.1111. Payout 7:1. Expected value: (1/9)*7 - (8/9)*1 = 7/9 - 8/9 = -1/9 = 11.11%.

These edges depend on the specific payout table and the rules for each bet. They are fixed by the dice and the payouts.

What people get wrong

The most common mistake is treating the dice as if they have a memory. A shooter who has rolled six points in a row is not more likely to seven out on the next roll. The probability of a 7 on any roll is always 6/36 = 16.67%. The mistake is natural because in everyday life, streaks often do indicate a change in underlying conditions: a basketball player who has made ten shots in a row might be in a state of heightened focus. But dice have no state. The physical dice are identical on every roll, and the outcome is independent.

Another mistake is believing that the odds bet reduces the house edge on the pass line. It does not. It is a separate wager with zero edge. The pass line bet still carries a 1.41% edge. The overall edge on the combined amount is lower, but the edge on the flat bet is unchanged.

A third mistake is thinking that proposition bets are due. A bet on any 7 does not become more likely after a long sequence without a 7. The probability is always 6/36.

Money per hour

The house edge is a percentage of turnover, which is not a quantity most people can feel. To make it concrete, consider a player who bets 10 on the pass line on every come-out roll, with no odds. A craps table typically resolves a pass line bet in about two to three rolls, but the number of come-out rolls per hour depends on the number of players and the speed of the dealer. A reasonable estimate for a full table is 60 come-out rolls per hour. At 10 per bet, the total amount wagered per hour is 600. The expected loss is 1.41% of 600, which is 8.46 per hour.

If the same player adds 10 in odds behind every point, the total wager per come-out roll is 10 plus the odds, but the odds are only placed when a point is established. The probability of establishing a point is 24/36 = 66.67%. So the average odds wager per come-out roll is 10 * 0.6667 = 6.67. The total average wager per come-out roll is 16.67. At 60 come-out rolls per hour, total turnover is 1000. The expected loss is 1.41% of 10 (the flat bet) per come-out roll, which is 0.141 per roll, times 60 = 8.46 per hour. The odds portion adds no expected loss. So the hourly loss is the same 8.46, but the total amount wagered is higher, so the effective edge on total turnover is 0.846%.

If the player instead bets 10 on any 7 every roll, and there are 100 rolls per hour (including non-come-out rolls), the total wager is 1000. The expected loss is 16.67% of 1000, which is 166.70 per hour. That is the cost of the loudest bet on the table.

These figures depend on the number of come-out rolls per hour and the number of total rolls per hour, which vary with table conditions. They also assume the player always bets the same amount and does not vary the bet size.

Rules that change the figures

The pass line edge of 1.41% assumes the come-out rules as described and even-money payout. The don’t pass edge of 1.36% assumes a bar of 12. If the table bars 2, the edge is 1.36% as well? Actually, if the table bars 2, the don’t pass bet pushes on 2 instead of 12, which changes the edge slightly. The difference is small.

The odds bet payout depends on the point: 2:1 on 4 and 10, 3:2 on 5 and 9, 6:5 on 6 and 8. These are true odds and do not change.

The proposition bet edges depend on the specific payout table. Some casinos offer different payouts for the horn bet, which is a combination of 2, 3, 11, and 12. The edge on the horn bet is 12.5% if the payouts are 30:1 on 2 and 12, and 15:1 on 3 and 11, with the bet split four ways. If the payouts are different, the edge changes.

All figures on this page are for a standard craps table with two dice and the rules as stated. They do not apply to crapless craps, which has different point numbers and different edges.