True odds describe the mathematically fair price of a craps outcome. Casino payouts describe what the table actually pays. The difference between those two numbers is one of the clearest ways to see where house edge comes from.
Craps is especially useful for learning this because the game places fair-odds wagers and short-paid wagers beside each other on the same layout. An odds wager behind a Pass or Come bet can pay at true odds, while a Place bet on the same point number pays less than true odds. The dice do not care which betting box the chips are in. The pricing rules do.
True odds come from combinations, not payout signs
Two fair dice produce 36 equally likely ordered combinations. The totals are not equally likely because some totals can be made in more ways than others.
| Total | Ways to roll | Probability |
|---|---|---|
| 2 | 1 | 1/36 |
| 3 | 2 | 2/36 |
| 4 | 3 | 3/36 |
| 5 | 4 | 4/36 |
| 6 | 5 | 5/36 |
| 7 | 6 | 6/36 |
| 8 | 5 | 5/36 |
| 9 | 4 | 4/36 |
| 10 | 3 | 3/36 |
| 11 | 2 | 2/36 |
| 12 | 1 | 1/36 |
Once a point is established, many craps calculations reduce to a race between the point and 7. The true payout is based on the ratio of losing combinations to winning combinations.
For a point of 6, there are five ways to roll 6 and six ways to roll 7. If the only relevant outcomes are 6 and 7, the fair net payout is 6:5. For point 5, the fair payout is 3:2. For point 4, it is 2:1.
That is the mathematical basis of the free-odds wager.
Fair price and casino price side by side
The easiest comparison is to put the true payout and common casino payout in the same row.
| Wager example | Winning outcomes vs losing outcomes | True net odds | Common paid odds | Pricing effect |
|---|---|---|---|---|
| Odds on 4 or 10 | 3 vs 6 | 2:1 | 2:1 | Fair price |
| Odds on 5 or 9 | 4 vs 6 | 3:2 | 3:2 | Fair price |
| Odds on 6 or 8 | 5 vs 6 | 6:5 | 6:5 | Fair price |
| Place 6 or 8 | 5 vs 6 | 6:5 | 7:6 | Short pay |
| Any Seven | 6 wins vs 30 losses | 5:1 | Often 4:1 | Large short pay |
| Any Craps | 4 wins vs 32 losses | 8:1 | Often 7:1 | Short pay |
Rules and proposition payouts can vary by casino and jurisdiction, so the layout or approved rules at the table control the actual wager. The analytical method stays the same: compare probability with payment.
Why the odds wager can have zero house edge
A true-odds wager has zero theoretical house edge because the payout exactly compensates for the probability disadvantage.
Take $10 odds on a point of 4. The point has three combinations and 7 has six. The point wins one-third of resolved 4-versus-7 races and loses two-thirds.
At a 2:1 payout:
EV = (1/3 × $20) − (2/3 × $10) = $0
That does not make the wager safe. The player can still lose the entire $10 immediately when 7 arrives first. Zero house edge means the long-run average price is fair, not that short-term variance disappears.
It is also important that the free-odds wager is normally attached to a Pass, Don’t Pass, Come, or Don’t Come wager. The base wager has its own house edge. Saying “craps has a zero-edge bet” is therefore incomplete if the player has to make a nonzero-edge contract bet to access it.
Read odds bet explained for the full structure.
Place 6 shows how a small payout change creates an edge
A Place 6 and an odds wager on 6 both care about the same basic contest: will 6 appear before 7? The difference is the price.
The true odds are 6:5. A common Place 6 payout is 7:6.
With an $18 Place 6:
- Five winning combinations produce a $21 profit.
- Six losing combinations lose $18.
Across 11 equally weighted resolved outcomes, the total result is:
5 × $21 − 6 × $18 = $105 − $108 = -$3
The average loss per resolved $18 wager is $3/11, or about $0.2727. Relative to the $18 stake, the house edge is about 1.52%.
Nothing about the dice changed. The entire edge came from the payout being shorter than the fair 6:5 price.
This is the cleanest reason to compare place bet house edge with the odds wager.
Any Seven demonstrates why a high hit rate can still be poor value
Seven is the most common total with two dice: six combinations out of 36. That makes “Any Seven” look attractive to players who focus only on how often 7 appears.
But the fair payout is determined by both wins and losses. Six combinations win and thirty lose, so fair net odds are 30:6, or 5:1.
If the table pays 4:1, the expected value of a $1 wager is:
EV = (6/36 × $4) − (30/36 × $1)
EV = $0.6667 − $0.8333 = -$0.1667
That corresponds to a house edge of about 16.67% on the initial wager.
The lesson is broader than craps: a bet can hit relatively often and still be expensive if the payout is too short. Conversely, a rare bet can be reasonably priced if the payout closely matches its probability.
Big payout numbers do not reveal value by themselves
Players are naturally drawn to signs such as 15:1, 30:1, or 150:1. A large numerator looks generous. It tells you nothing about value until you know how unlikely the event is.
Suppose an event has a true probability of 1 in 31. Its fair net payout is 30:1. If a casino pays 25:1, the bet is short-paid even though 25:1 looks large. If another event wins almost half the time and pays close to even money, it may be far better value despite a much smaller headline payout.
This is why proposition bet house edge is a more useful guide than ranking bets by the size of the payoff printed on the layout.
“For one” and “to one” language can cause confusion
Craps payouts are sometimes described in language that players interpret differently. A payout of “5 to 1” usually means $5 profit plus return of the $1 stake. Some table procedures, especially on certain proposition wagers or informal explanations, can create confusion about whether the quoted number includes the original stake.
The safe method is to ask what the net profit will be on a specific wager amount and read the table rules. Mathematically, house-edge calculations should use net win separately from return of the original stake.
That distinction matters in expected-value formulas:
EV = Probability of win × Net profit − Probability of loss × Amount lost
Do not count the returned stake as profit.
Don’t-side true odds reverse the ratio
On Don’t Pass or Don’t Come odds, the player is effectively betting on 7 before the point. The fair odds therefore reverse.
If the point is 4, the player has six ways to win with 7 and three ways to lose with 4. A fair wager can risk $2 to win $1, often described as laying 2:1.
For point 5 or 9, the fair relationship is laying 3:2. For point 6 or 8, it is laying 6:5.
This can feel unintuitive because the player risks more than the potential win. But fair pricing depends on probability. When your side is more likely to win, a fair payoff is smaller than the amount risked.
The craps odds page provides the probability foundation for both sides.
House edge and expected loss are related but not identical questions
House edge is a percentage price per unit of initial wager under a defined rule set. Expected loss translates that percentage into money over repeated action.
For a bet with a 4% house edge:
Expected loss = Total initial action × 4%
If a player makes $500 of that action over a session, theoretical loss is $20. If another player creates $5,000 of identical action, theoretical loss is $200.
That is why a “low-edge” bet can still cost significant money when the wager size or number of decisions is high. Read why low house edge can still lose for the exposure side of the issue.
Vig and commission are another way to create casino pricing
Not every craps edge appears as a short payout. Some wagers use a commission or vig. In those cases, the underlying payoff may be close to true odds but the fee changes expected value.
The correct comparison therefore includes all economic terms:
- probability of winning;
- net payout when winning;
- amount lost when losing;
- commission or vig;
- when the commission is charged;
- any special push or bar rules.
Two bets with the same point number can have different house edges because those details differ.
A practical method for evaluating any craps payout
When faced with a wager you do not recognize, use a five-step process:
1. Identify the exact winning and losing conditions. Do not rely on the bet’s nickname.
2. Count the relevant dice combinations. Use 36 equally likely ordered outcomes as the base when one roll resolves the wager, or conditional point-versus-7 combinations when appropriate.
3. Calculate the fair net payout. Losing combinations divided by winning combinations gives the true-odds price for a binary resolved event.
4. Read the actual casino payout. Include commission, push rules, and whether the quoted payoff is net profit.
5. Calculate expected value. The gap between fair price and paid price becomes the player’s long-run cost.
This method is more reliable than memorizing which bets experienced players call “good” or “bad.”
Why true odds are a powerful casino-math teaching tool
True odds strip away the mystery from house edge. The casino does not need the dice to behave differently for different bets. It can offer multiple prices on outcomes generated by the same dice.
A Place 6, odds on 6, and other 6-related wagers can all depend on the same physical total while producing different expected values because their payout rules differ. That is casino pricing in its simplest form.
The free-odds wager is unusual because the price is mathematically fair. The casino can offer it because it is embedded in a broader game with base wagers, other betting choices, table speed, and overall action.
For the complete picture, continue with craps house edge, craps odds, odds bet explained, and the craps odds calculator.