Expected value (EV) is the average net result of a wager when the same decision is repeated under the same rules. A negative EV means the rules cost the player money on average over many trials. It does not predict the next spin, hand, or session.
The EV Formula
For a simple wager, multiply each possible net result by its probability and add the results. In symbols: EV = (probability of outcome 1 × net result 1) + (probability of outcome 2 × net result 2) + the same calculation for every other outcome.
Use net profit in the calculation. If a $10 wager wins $10, the net result is +$10. If it loses, the net result is -$10. The returned stake is not profit, so it should not be counted as an extra win.
| Question | What to record | Why it matters |
|---|---|---|
| What can happen? | Every win, loss, push, or side-bet result. | Missing outcomes can distort the average. |
| How likely is each result? | The probability under the exact rules. | A large payout may be rare. |
| What is the net result? | Profit or loss after commission and altered payouts. | Returned stake is not profit. |
| Which version applies? | Wheel, paytable, commission, deck, or rule variant. | A different version can change EV. |
What A $10 Roulette Bet Costs On Average
For a single-number bet on a single-zero European wheel, one number wins with probability 1/37 and the other 36 numbers lose. A $10 straight-up bet commonly pays 35:1, so the net result is +$350 on the winning number and -$10 otherwise.
EV = (1/37 × $350) + (36/37 × -$10) = -$0.2703, approximately. The long-run cost is therefore about 2.70% of the amount staked under those assumptions. This is an example of the calculation, not a forecast for one spin.
On a double-zero wheel, the extra zero changes the probability while the displayed payout is usually the same. The exact wheel matters more than the name of the bet. Check whether the table has one zero, two zeros, or a special rule before comparing numbers.
Expected Value And House Edge
House edge is the casino’s average advantage as a percentage of the amount wagered. For a $10 stake with a 2.70% house edge, the corresponding expected loss is $0.27 per wager when the rules and assumptions match the calculation. A player can win in the short term; EV describes the average across repeated trials.
RTP expresses the average amount returned under a defined game model, while EV expresses the net result of a particular decision. A slot’s advertised RTP is not a promise for one session, and it may not cover every bonus feature or side bet.
How To Compare Two Bets
- Write down the exact payout and commission for each bet.
- Use the same stake when comparing the results.
- Include side-bet cost separately instead of hiding it inside the main wager.
- Check whether a bonus changes the eligible games, payout, maximum stake, or wagering calculation.
- Prefer the lower house edge only as a cost comparison, not as a claim that the bet is safe or likely to win.
A Worked Comparison
Suppose a player compares two $10 bets. Bet A has a 2% house edge and Bet B has a 5% house edge. Under the same repeated-stake assumption, their expected losses are $0.20 and $0.50 per $10 wager respectively. The difference is $0.30 per wager on average, not a guarantee that Bet A wins the next round.
If the player adds a side bet, calculate it as a new wager. A high payout can raise the possible return while making the combined EV worse. Keep the main bet, side bet, commission, and returned stake on separate lines in the session record.
Common EV Mistakes
- Treating a recent winning streak as proof that EV changed.
- Using a payout from one table with probabilities from another.
- Calling returned stake a profit.
- Ignoring commission, reduced Banker payouts, or excluded bonus games.
- Assuming a high RTP removes short-term volatility or bankroll risk.
Use EV Before Money Is At Risk
Read the rule and paytable before depositing or placing a wager. If the probability, payout, or commission cannot be confirmed, the calculation is incomplete. That uncertainty is a reason to pause, not a reason to assume the most favourable number.
Related Guides
- Casino Odds By Game
- Baccarat Percentages
- Roulette Percentages
- Casino Strategy And Odds
- Casino Session Plan
Frequently Asked Questions
No. EV is a long-run average under stated rules. It cannot identify the next winning number, hand, spin, or session.
It means the wager produces a negative average net result for the player when repeated under the same assumptions. A single result can still be a win.
No. It is a comparison of average cost, not a guarantee. The result of a particular session remains uncertain.
Payouts, commissions, wheel type, deck composition, and special exceptions change the probabilities or net results used in the calculation.
