Expected Value of a Game Calculator
🎮 Expected Value of a Game Calculator
Compare win odds, payout, fees, and sample size to see the long-run value of any game setup.
Jump to the benchmark table and use this expected value of a game calculator to compare risk, payout, and long-run edge in one pass.
Use this calculator to measure a game's average return per play, then scale it by the number of plays so you can tell whether a setup is worth repeating.
📍 Presets
⚙ Game Inputs
How many times you expect to play the game or repeat the bet.
This is the stake, buy-in, or cost you pay each time.
Chance of the outcome that pays your main win profit.
Use the net profit for a win after the stake is settled.
This covers ties, refunds, or partial-return outcomes.
Use a negative value for a reduced refund or a fee-heavy push.
Add rakeback, loyalty credit, or a fixed side bonus here.
Extra percentage taken from the entry cost on every play.
EV per play
0.00
average net value each play
Neutral until the numbers move
EV over sample
0.00
total expected gain or loss
Based on the play count
Break-even win rate
0.0%
win chance needed to reach zero EV
Pushes and bonuses are included
ROI per play
0.0%
expected return versus cost
A quick edge check
📊 EV Breakdown
| Branch | Probability | Net value | Contribution |
|---|
🎯 Component Grid
1.00
Entry cost
Before fees
50.0%
Win chance
Primary driver
0.0%
Push chance
Secondary branch
0.00
Bonus value
Applied each play
📐 Reference Tables
| Game type | Main input | EV focus | Note |
|---|---|---|---|
| Pure win-loss game | Win chance + profit | Break-even rate | Only one success branch matters most |
| Push-heavy game | Push chance + refund | Refund value | Small pushes can rescue weak edges |
| Bonus-backed game | Rebate per play | Net floor | Every play gets a little support |
| Fee-heavy game | Rake percentage | Cost drag | House fees can erase a mild edge |
| Win profit | Push profit | Entry cost | Break-even win rate |
|---|---|---|---|
| 1.0 units | 0 units | 1.0 unit | 50.0% |
| 1.2 units | 0 units | 1.0 unit | 41.7% |
| 1.0 units | 0.2 units | 1.0 unit | 48.0% |
| 1.0 units | 0 units | 1.0 unit | 45.0% with 0.05 rebate |
| EV result | ROI | Read | Note |
|---|---|---|---|
| Positive EV | Above 0% | Good long run | The setup pays you back over time |
| Zero EV | 0.0% | Fair game | You are breaking even on average |
| Small negative EV | Below 0% | Thin drag | Minor fees or shortfalls matter here |
| Strong negative EV | Far below 0% | Bad price | The game is expensive to repeat |
💡 Practical Tips
Start with the cost line
If the entry cost plus fee already swamps the expected win profit, the game needs a bigger payout or a higher hit rate to stay viable.
Do not ignore pushes
Pushes can quietly raise EV when they refund value, or drag it down when they still cost you something.
Use this expected value of a game calculator to compare win odds, payout, and fees so you can see whether a game is fair, thin, or clearly -EV before you commit time or chips.
Expected value is an mathematical concept that determines whether a game or game setup will be profitable. Many people look at the wins and losses of each individual play into a game, but that dont reflect the true value of the games. One calculates the expected value of a game by taking the value of each possible outcome of that game and multiply by the probability of that outcome occurring.
If the expected value of a game is positive, the game will be profitable if played over many games. However, if the expected value is negative, the game will result in the loss of money when played over many games. Pushes in a game are the outcomes in which a player receive their original stake back into the game.
What Is Expected Value in Games
Players often overlook these pushes as they are not a win for the player. However, pushes has the ability to increase the expected value of a game. Games that contain more pushes will return money to players, preventing them from losing money at the same rate as they would in a game without pushes.
Fees are the cost that a player must pay to play a game. These fees will decrease the expected value of the game. Although the fees may be small when a player initiates the game, the cost will eventually become significant in relation to how many times a player plays the game.
Additionally, these fees will also reduce the profit that a player make from winning the game. For this reason, a player must ensure that the profit that is made from winning the game is more than the cost of the fees that are placed into the player. A player can use the break-even win rate for a game to calculate the percentage of wins that a player must have in order for the expected value of the game to equal zero.
This rate accounts for the wins, losses, and pushes that can happen within a game. For instance, if a game pays players one-to-one when they win, and there are no pushes, then the break-even win rate will be fifty percent. However, if there are pushes in the game, the break-even win rate can be more lower than fifty percent.
By calculating the break-even win rate, a player can compare the win rate that they will achieve to the win rate that is required to ensure that they make even money playing the game. The variance in the rate at which a player wins a game determines the fluctuations in the player’s results. Even if the expected value of a game is positive, the variance can cause a player to lose money over a long period of time.
Because of the variance in a games results, a player may have to play many games in order for the expected value to become apparent to the player. A small sample size of the number of games that are played will not provide the same results as a large number of games is played. In order to understand the true expected value of a game, a player must play a large number of games.
Some of the most common mistakes that a player can make when calculating the expected value of a game is to calculate the expected value incorrectly. Many players do not account for the fees that is placed on them when they play a game. Additionally, they may calculate the gross profit from winning the game as the net profit when they calculate the expected value of the game.
If they do not subtract the fees from the win that is calculated, they will calculate an expected value that is more higher than the actual expected value. Finally, players may also ignore the possible pushes that can occur within a game, even though players must include these pushes in the calculation of the expected value of a game. The return on investment (ROI) that a player makes in relation to the games that they play will indicate to the player whether a game is profitable or not.
If the ROI for a player is above zero, then the expected value for the games that they play is positive, which means that they will profit over time from playing these games. However, if the ROI is below zero, it means that the expected value for the player will be a loss over time. In order to ensure that they are playing games that profit them, a player should of use the expected value calculation to identify games with a positive ROI.
