Expected Value Gamble Calculator
The expected value of a gamble is the probability-weighted average of all possible outcomes. This calculator accepts up to five outcomes, each with a probability (in percent) and a net payoff. Positive payoffs represent winnings; negative payoffs represent costs or losses. The probabilities must sum to 100%. The calculator computes EV = sum of (probability times payoff) for all outcomes, showing you the average result per play over many repetitions. Game designers use this to balance rewards; gamblers use it to understand the long-run cost of play.
Enter probability (%) and net payoff for each outcome. Probabilities must sum to 100.
Expected value formula
EV = sum of (p(i) * v(i)) for all i
where p(i) is probability of outcome i and v(i) is its payoff
Probabilities must sum to 1 (100%). Each outcome contributes p(i) times v(i) to the expected value. A fair game has EV = 0; a house-edge game has EV less than 0 for the player.
Expected value in game design
- Slot machines, roulette, and most casino games have a negative EV for the player, typically between -1% and -10% per bet.
- Skill-based games with positive EV for skilled players (like poker) allow expert players to profit in the long run.
- In video game economies, EV analysis ensures loot boxes and crafting recipes feel rewarding without being exploitative.
- Card game design uses EV to balance strong cards, ensuring one strategy is not dominant over all alternatives.
Expected value: frequently asked questions
What is expected value in probability?
Expected value (EV) is the average outcome you would expect over many repetitions of the same gamble. It equals the sum of each possible outcome multiplied by its probability. A positive EV means you win on average; negative EV means you lose on average.
How do I enter the inputs correctly?
Enter each outcome's probability as a percentage (must sum to 100) and its net payoff (positive means you win that amount, negative means you pay). The calculator multiplies each probability by its payoff, sums the products, and shows the expected value per play.
What does a negative expected value mean for a game?
A negative EV means the player is expected to lose money on average over many plays. Casino games are designed with a negative EV for the player (house edge). Game designers use EV to calibrate reward systems and economy balance.
Does expected value tell me the outcome of a single play?
No. EV is a long-run average, not a prediction for any single event. On a single play you might win or lose any of the possible amounts. EV only becomes a reliable predictor after a large number of repeated plays (law of large numbers).
How is house edge related to expected value?
House edge is the negative of the player's expected value expressed as a percentage of the bet. For example, if EV per dollar bet is -0.05, the house edge is 5%. The calculator shows this when a bet amount is entered.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: itl.nist.gov/div898/handbook/.
- National Council of Teachers of Mathematics: nctm.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.