Craps is one of the most exciting casino games, but it can also be one of the most confusing. With over 20 different bet types, understanding the mathematics behind each wager is crucial for making informed decisions. This section breaks down the key concepts you need to know.
Understanding Dice Combinations
Two six-sided dice produce 36 possible combinations. The number 7 is the most common outcome with 6 ways to roll it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), giving it a 16.67% probability. The numbers 2 and 12 are the rarest, each with only 1 combination (1+1 and 6+6) for a 2.78% probability. Numbers 6 and 8 each have 5 combinations (13.89%), while 5 and 9 have 4 each (11.11%), and 4 and 10 have 3 each (8.33%). This distribution of outcomes is the foundation of all craps odds calculations.
Benefits of Using a Craps Odds Calculator
Removes guesswork by showing exact probabilities and expected values for every bet type
Compare bets objectively to focus on those with the lowest house edge
Especially useful for new players learning which bets offer the best value at the craps table
Practical Applications
Plan your betting strategy before your next casino visit by comparing expected values
Understand the real cost of each wager at your typical stake level
Use phase breakdowns to see how the come-out roll and point resolution affect your odds
Common Mistakes to Avoid
Chasing losses with high house edge proposition bets — stick to low-edge bets even when on a losing streak
Believing in the "gambler's fallacy" — each roll is independent, and past results don't influence future outcomes
Ignoring the difference between Field 2x and Field 3x payouts — the 3x version has almost half the house edge (2.78% vs 5.56%)
Worked Examples
Example: $10 Pass Line Bet
With a $10 Pass Line bet, the probability of winning is 49.29% (244/495) and the payout is 1:1. The house edge is 1.41%, so your expected value is $10 × -0.0141 = -$0.14. This means on average, you lose about 14 cents per $10 bet. On the come-out roll, you have a 22.22% chance of winning immediately (rolling 7 or 11) and an 11.11% chance of losing (rolling 2, 3, or 12). The remaining 66.67% of the time, a point is established and your odds depend on which point number was rolled.
Example: $12 Place 6 Bet
A $12 Place 6 bet pays 7:6, meaning you win $14 for a $12 wager. The probability of winning is 45.45% (5/11) because there are 5 ways to roll a 6 and 6 ways to roll a 7. The house edge is just 1.52%, making it one of the best bets on the table after Pass/Don't Pass. Your expected value is $12 × -0.0152 = -$0.18. Place bets on 6 and 8 are popular among experienced players because they combine reasonable odds with a very low house edge.
Example: $10 Don't Pass Bet
A $10 Don't Pass bet has a 47.93% win probability and pays 1:1, with a house edge of only 1.36% — the lowest on the craps table. Your expected value is $10 × -0.0136 = -$0.14. On the come-out roll, you win on 2 or 3 (8.33% probability), lose on 7 or 11 (22.22%), and push on 12 (2.78%). The "bar 12" push is what prevents Don't Pass from being a player-advantage bet. Once a point is established, you have the statistical advantage because 7 is more likely than any individual point number.
The Don't Pass and Don't Come bets have the lowest house edge at 1.36%, making them the mathematically best bets in craps. The Pass Line and Come bets are close behind at 1.41%. While Don't bets are slightly better statistically, many players prefer Pass Line bets for the social aspect of betting with the shooter.
When you place a Don't Pass or Don't Come bet, rolling a 12 on the come-out roll results in a push (tie) rather than a win. This is called 'bar 12' and is what gives the casino its edge on these bets. Without barring the 12, Don't Pass would actually have a player advantage, so casinos use this rule to maintain their house edge of 1.36%.
Craps odds are based on the 36 possible combinations of two six-sided dice. For example, there are 6 ways to roll a 7 (giving it a 16.67% probability) but only 1 way to roll a 2 or 12 (2.78% each). Line bets involve multiple phases — the come-out roll determines if you win immediately, lose, or establish a point — making their overall probability a weighted average across all possible outcomes.
Odds bets (also called "free odds") are additional bets placed behind your Pass Line, Don't Pass, Come, or Don't Come bet after a point is established. They are unique in casino gambling because they pay at true odds with zero house edge. For example, odds on point 6 pay 6:5, and odds on point 4 pay 2:1. The maximum odds bet varies by casino (commonly 3x, 4x, 5x, or even 100x). Taking maximum odds is the mathematically optimal strategy because it reduces the overall house edge on your combined bet significantly.
Pass Line bets must be made before the come-out roll and cover the entire sequence (come-out + point resolution), giving a 49.29% overall win probability with a 1.41% house edge. Place bets can be made at any time on a specific number (4, 5, 6, 8, 9, or 10) and win if that number is rolled before a 7. Place 6 and Place 8 have the best odds at 1.52% house edge, while Place 4 and Place 10 have a higher 6.67% edge. The key advantage of Place bets is flexibility — you choose when to make them and can remove them at any time.
The casino's edge in craps comes from paying less than true odds on winning bets. For example, a true odds payout for Any 7 would be 5:1 (since there are 30 non-7 combinations and 6 that make 7), but the casino pays only 4:1. For line bets, the edge comes from the come-out roll asymmetry — on Pass Line, you win on 8 outcomes (7 or 11) but lose on only 4 (2, 3, or 12), yet the point resolution phase more than offsets this advantage. The "bar 12" rule on Don't Pass prevents that bet from having a player edge. The only zero-edge bet in craps is the odds bet, which is why experienced players maximize it.
