Expected value in craps is the average amount a bet is worth over the long run after probability and payout are combined. Most craps bets have negative expected value for the player. A bet can win tonight, hit often, or feel smart, while still being mathematically priced to lose over enough decisions.
Quick Facts
- Expected value combines chance of winning, chance of losing, payout, and stake.
- Negative EV means the player gives up value over time.
- House edge is negative player EV expressed as a percentage of the initial stake.
- Odds bets are the major exception because they are paid at true odds.
- EV does not predict one session.
- Total action matters: more resolved wagers means more expected loss.
- A low-edge bet with oversized stakes can still create ugly bankroll swings.
Plain Talk
Expected value is the “average truth” behind a bet.
Not the next roll. Not your last session. Not the loud guy who hit a horn bet. The average.
If a bet pays less than its true risk deserves, the difference becomes casino edge. That is the backbone of craps house edge and craps odds.
The Wizard of Odds craps appendix shows expected-return calculations for craps bets, the Wizard of Odds craps basics lists common house edges, and the Britannica overview of probability theory gives broader background on probability ideas behind EV.
How It Works
Expected value asks one question:
“If this exact bet were repeated many times, what is the average gain or loss per bet?”
The structure is simple:
| Piece | Meaning |
|---|---|
| Probability of win | How often the winning event occurs |
| Net win | How much profit the bet pays, not including returned stake |
| Probability of loss | How often the losing event occurs |
| Stake | Amount risked |
| EV | Long-run average result |
Easy One-Roll Example: Any Seven
Any Seven wins if the next roll is 7. There are six winning combinations out of 36 and thirty losing combinations.
A common payout is 4 to 1.
For a $1 bet:
| Outcome | Probability | Net Result |
|---|---|---|
| Roll 7 | 6/36 | +$4 |
| Roll anything else | 30/36 | -$1 |
The EV is negative because true odds would require a 5 to 1 payout, but the casino pays 4 to 1.
Multi-Roll Example: Place 6
A Place 6 wins if 6 appears before 7. Non-deciding rolls are ignored for that specific bet.
There are five ways to roll 6 and six ways to roll 7.
A $6 Place 6 usually wins $7. The payout is close to fair, but not exact. That small shortfall creates the house edge.
Craps Table Example
A player says, “I only bet small. It does not matter.”
They play for one hour:
| Bet Habit | Average Action | Approximate Edge | Expected Loss |
|---|---|---|---|
| Pass Line decisions | $100 total | 1.41% | $1.41 |
| Place 6/8 decisions | $240 total | 1.52% | $3.65 |
| Field bets | $150 total | 2.78% | $4.17 |
| Horn/props | $60 total | High, varies | Often far more expensive |
The individual bets feel small. The total action is not small.
That is why the expected loss calculator is more honest than memory. Players remember the buy-in and cash-out. The casino sees total resolved action.
From the Casino Side:
Casinos do not need every player to make bad decisions every roll. They need enough total action at positive house edge.
The game manager looks at drop, hold, average bet, roll speed, table occupancy, and rating accuracy. A low-edge Pass Line player can still generate theoretical win if they play long enough. A prop-bet player can generate high theoretical win quickly because the edge is larger and the bets resolve fast.
Comps also connect to expected value. A casino does not comp based on whether you were lucky. It estimates theoretical loss from average bet, time, game speed, and house edge.
Common Mistakes
- Thinking EV means what will happen in the next session.
- Counting returned stake as profit.
- Ignoring how many times a bet resolves per hour.
- Calling a bet “good” because it won recently.
- Comparing payout size without comparing probability.
- Forgetting that odds bets lower combined edge but increase variance.
- Treating low house edge as permission to bet too much.
Hard Truth
Expected value is the casino’s quiet employee. It works every roll, even when the player is celebrating.
FAQ
What does expected value mean in craps?
It means the average win or loss of a bet over many repeated decisions after probability and payout are combined.
Is craps expected value always negative?
For the player, most craps bets have negative EV. The odds portion of an odds bet is the major 0% edge exception.
Does negative EV mean I cannot win tonight?
No. You can win any short session. Negative EV describes the long-run average, not one result.
How is EV different from house edge?
EV is the amount or value lost on average. House edge expresses that loss as a percentage of the initial stake.
Why do proposition bets have bad EV?
They usually pay less than true odds and resolve quickly, so the casino edge hits often.
Can betting systems change EV?
No. Changing bet size after wins or losses does not change the underlying probability and payout of each bet.
Why does total action matter?
Expected loss is based on total money wagered and resolved, not just your buy-in.
Deeper Insight
Expected value is where craps myths go to die.
A system may change the shape of your results. It may produce more small wins and fewer large losses. It may feel controlled. But if every underlying bet is negative EV, the system is still negative EV.
A player who makes only Pass Line bets faces a smaller edge than a player who sprays proposition bets. But both are still in negative-expectation territory unless the comparison is limited to the true-odds portion of odds bets.
This is why “I was ahead for two hours” is not a math argument. Short-term variance can cover the house edge for a while. It can also punish a low-edge player quickly.
EV is not emotional. It does not care whether the shooter is friendly, the table is loud, or the dice hit the back wall cleanly.
Formula / Calculation
Expected Value = (Probability of Win × Net Win) - (Probability of Loss × Stake)
House Edge = -Player EV / Initial Stake
Expected Loss = Total Amount Wagered × House EdgeAny Seven example for $1 at 4 to 1:
EV = (6/36 × $4) - (30/36 × $1)
EV = $0.6667 - $0.8333
EV = -$0.1667
House Edge = $0.1667 / $1 = 16.67%Formula Explanation in Plain English
Multiply how often you win by what you win. Subtract how often you lose by what you risk. If the result is negative, the average bet favors the casino. The bigger your total action, the more that average has room to show up.
Related Reading
To see where EV begins, read craps probability basics and Why 7 Is the Most Important Number. To connect EV to player cost, use craps house edge and the expected loss calculator. For the practical warning, read why betting systems fail.