It’s all great when you are winning, but losing is another story. Almost all of the wagers on a roulette table have the same expected value. It is the main reason why we say that calculating the potential value in roulette is simple.
Another point is that roulette is not complicated. For example, players can make a single bet, the wheel spins, and you get a payout if you win.
The good news is that if you are familiar with real money roulette, you can immediately get started with calculations. We recommend that you know what the game is all about before taking this step.
As you explore our roulette expected value guide, you’ll learn how to calculate probabilities across different roulette variants. We’ll also share practical roulette tips to help you assess the best roulette bets for your goals and understand the risks before placing a wager.
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Expected Value in Roulette
Calculating expected value in roulette is straightforward when you understand the probabilities, payouts, and potential losses associated with each wager. A roulette calculator can help you estimate the expected return of a bet using its probability of winning and payout.
Understanding roulette odds and payouts is also useful when comparing different wagers. These calculations can help you assess the risks involved, although they cannot predict individual outcomes.
For example, imagine Player A and Player B agree to flip a fair coin. Player A wagers $10, while Player B pays $11 if Player A wins. Player A has a 50% chance of winning $11 and a 50% chance of losing $10.
The expected value for Player A is:
(11 \times 0.5) – (10 \times 0.5) = \$0.50
This means Player A has a positive expected value of $0.50 per flip, on average, under these terms. The result comes from the potential $11 win weighted by its 50% probability, minus the potential $10 loss weighted by its 50% probability.
| Outcome | Calculation | Result |
|---|---|---|
| Win (50% chance) | $11 × 0.5 | +$5.50 |
| Lose (50% chance) | −$10 × 0.5 | −$5.00 |
| Expected value | $5.50 − $5.00 | +$0.50 |
Formula: Expected value = (Win × Win Probability) − (Loss × Loss Probability)
This means Player A has an average expected profit of $0.50 per flip over many flips, assuming the stated payouts and probabilities remain the same.
How to Calculate Expected Value in Roulette
The formula is:
EV=(Pwin×Win Amount)+(Ploss×Loss Amount)EV=(Pwin×Win Amount)+(Ploss×Loss Amount)
Where:
PlossPloss = Probability of losing
PwinPwin = Probability of winning
European Roulette Expected Value
When it comes to European roulette, nearly all wagers have the same house edge. Let’s explain what we mean. For example, players bet on one digit. If this bet wins, it will pay out 35-1.
Nonetheless, there is just a single winning result out of the possible 37. The odds of winning on one spin are 1/37 or 2.70%. While the chances of losing on any spin are 36/37 or 97.30.
This is how the calculations look: (35 x 027) – (1 x 973)946 – 973 = 0.027.
It can be expressed as a percentage value of 2.7%. We rounded off the figures above. The casino gets its advantage from the zero. This possible value is the same on every wager.
Why EV Matters in Roulette
- Avoid bad bets: American Roulette has a higher house edge (5.26%) due to the double zero.
- Helps manage expectations: Know that the house always has an edge.
- Compare bet types: All standard bets have the same EV, but different risk/reward profiles.
American Roulette Expected Value
The possible value is, to some degree, more for the casino in US roulette. This is because although the payouts are the same, there is an extra digit on the wheel (00). At times, this intimidates players. For example, the payout is identical,l which is 35-2, but the chances of winning are lower.
The main reason is that there is one winner out of 38 digits. On the other hand, players will lose 37 times out of 38. It might look small, but it has a huge impact on the expected value.
The calculation: (35 x 0263) – (1×9737). 921-947 =-0.053. The edge of the casino is 5.3%. The possible value is higher than this; we rounded off the figure. The house edge is closer to 5.26%.
This is the same as 2/38. See, it is nearly double the house edge of the European game. So, European roulette is a better option compared to the American.
Other Roulette Guides:
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- Flash Roulette
- How to play online Roulette
- Online Roulette FAQ
- Online Roulette Cheats
- Roulette Simulator
- American Roulette vs European Roulette
- Roulette Wheel
- New Roulette Games
- Can Roulette be Beaten?
- How to make money in Roulette
- Is Roulette all Luck?
- High Stakes Roulette
- Real Money Roulette Apps
- Best Roulette Lessons
- Strategy for Roulette
