Probability
Dice Expected Value Calculator
Use the exact fair-dice sum distribution to separate win probability, loss probability, expected value per play, horizon expectation, and break-even payout.
Expected dice total per play-
Equally likely outcomes-
Ways at or below one less than threshold-
Probability total meets threshold-
Probability total misses threshold-
Expected net value per play-
Expected net value across planned plays-
Net win payout required for zero expectation-
Decision view
Dice probability and payoff balance
Dice probability and payoff balanceExact win and loss probabilities combine with payout and stake to produce expected value and break-even payout.
Exact scenario comparisonWinning total threshold changes while all other entered assumptions remain constant.
| Winning total threshold | Expected dice total per play | Equally likely outcomes | Ways at or below one less than threshold | Probability total meets threshold | Probability total misses threshold | Expected net value per play | Expected net value across planned plays | Net win payout required for zero expectation |
|---|
How to use Dice Expected Value Calculator
- Define payout as net profit on a win.
- Define stake as the net loss on a miss.
- Evaluate expected value and risk separately.
Calculator guide
Understanding Dice Expected Value Calculator
A dice wager can have a frequent win and still lose money if payout is too small relative to the stake.
Calculation method
How the calculation works
Use the exact fair-dice sum distribution to calculate threshold probability, expected net value per play, horizon expectation, and the break-even win payout. Count equally likely dice outcomes at or above the entered threshold, weight payout and loss by exact probabilities, and solve the zero-EV payout.
Probability economics
Separate chance from payoff
A fair comparison needs both the event probability and the money attached to each outcome.
Worked situations
Practical examples
- Expected value is probability-weighted profit minus probability-weighted loss.
- One hundred plays multiply EV but do not guarantee that result.
- A break-even payout produces zero long-run expectation under the model.
Better inputs
Useful tips
- Confirm dice are fair and independent.
- Distinguish gross return from net payout.
- Set loss limits independently of EV.
Before relying on the result
Limitations and common mistakes
- Session outcomes, bankroll risk, taxes, limits, utility, dependence, and biased dice are excluded.
- Expected value is a long-run average.
- The calculator does not encourage gambling.
Reference
Key terms
- Win threshold
- Minimum dice total counted as a win.
- Expected value
- Probability-weighted average net result.
- Break-even payout
- Net win profit that makes EV zero.
- Outcome space
- All equally likely ordered dice results.
Important note
Calculated directly from the entered values using the displayed formula and rounding settings.
Frequently asked questions
Are dice sums equally likely?
No.
Does positive EV mean the next play wins?
No.
Is payout entered before returning the stake?
It should be entered as net win profit.
Does the page simulate dice?
No.