Expected Value (EV) for Gamblers
EV is the math behind “good” and “bad” bets. It tells you how much you expect to win or lose on average if you could repeat the same bet thousands of times.
What Is Expected Value?
Expected value (EV) is the average result per bet if you could play the same bet over and over under the same conditions. It combines:
- All the possible outcomes of a bet.
- How much you win or lose in each outcome.
- The probability of each outcome.
Basic EV Formula
EV = (win amount × probability of winning) + (loss amount × probability of losing)
For more than two outcomes, you just add extra terms.
EV is usually measured in money per bet. For example, an EV of -0.05 on a $1 bet means you lose 5 cents per bet on average.
Simple EV Example: Fair Coin Flip
Start with a clean, fair bet and then see what happens when the house tilts the math.
Fair 50/50 Bet
Suppose you bet $10 on a fair coin flip. If you win, you gain $10 profit; if you lose, you lose $10.
EV = (+$10 × 0.5) + (−$10 × 0.5)
EV = $5 − $5 = $0
Over many flips, you’d expect to break even (ignoring any fees).
EV & Typical Casino Games
Every casino game has a built-in house edge that creates negative EV for the player. Some games are “less bad” than others.
| Game / Bet | Approx. House Edge | Approx. EV on $10 Bet |
|---|---|---|
| Blackjack (basic strategy) | ~0.5% | −$0.05 per $10 |
| Banker bet in Baccarat | ~1.0–1.2% | −$0.10 to −$0.12 per $10 |
| European Roulette (single-zero) | 2.7% | −$0.27 per $10 |
| American Roulette (double-zero) | 5.26% | −$0.53 per $10 |
| Many slot machines | 4–10%+ (varies) | −$0.40 to −$1.00+ per $10 |
These are approximate and depend on rules and specific games, but the pattern is clear: some games drain your bankroll a lot faster than others.
For more detail, see House Edge by Game.
EV in Sports Betting
In casino games, the house edge is built into the rules. In sports betting, your EV depends on how your estimate of the true probability compares to the price the sportsbook offers.
Step 1 – Convert Odds to Implied Probability
Suppose a team is priced at -110. From the Odds Explained page:
Implied probability at -110 ≈ 52.4%
Step 2 – Have Your Own Estimate
Let’s say you believe, after research, that the team actually has a 55% chance to win.
It’s hard to consistently find positive-EV sports bets. Books have sophisticated models, and casual bettors overestimate their edge. Treat “I have an edge” as a bold claim that needs real evidence, not vibes.
Negative-EV Traps: Lotteries, Parlays & Side Bets
Some offers look exciting because of the payout size, but the EV is brutal. A few classic examples:
Lotteries & Huge Jackpots
Jackpots can pay millions, but the chance of winning is tiny. The EV per ticket is usually heavily negative – often worse than most casino games.
Longshot Parlays
Parlays multiply odds, but they also multiply the chance of losing. Books can inflate the margin on each leg, making the combined EV much worse than betting games individually.
Want to understand how parlays stack risk? Try the Parlay Estimator.
Where Positive EV Might Exist
For recreational players, gambling should still be treated as paid entertainment. But it’s useful to know where the math can tilt in your favour, at least temporarily.
- Promos & bonuses: Generous bonuses with low wagering and fair game contributions can be close to break-even or even slightly +EV if used carefully.
- Comps & cashback: If a game has a small house edge and you receive meaningful cashback or rewards, your “net EV” can move closer to zero.
- Skill games: In some poker and sports markets, skilled players can find positive-EV spots, especially against weaker competition.
None of this removes risk. Even positive-EV play requires strict bankroll management and emotional control.
Common EV Mistakes to Avoid
- Confusing EV with short-term results. You can win 10 negative-EV bets in a row or lose 10 positive-EV bets in a row; EV is about the long run.
- Ignoring EV because “it’s just for math people”. The basics are simple and protect your wallet as much as any “system”.
- Thinking entertainment value cancels negative EV. It can justify the cost, but the math still applies.
- Assuming you have an edge without data. Gut feelings and small sample results aren’t proof of positive EV.
If you find yourself increasing stakes to “chase” a perceived edge after losses, that’s usually emotion talking, not EV. Combine this page with our Tilt Control guide and Responsible Gambling resources.
Next Steps: Use EV Without Overcomplicating Things
You don’t need to calculate EV on every single spin or hand. Instead, use it as a mindset:
- Know which games have lower house edges (see House Edge by Game).
- Use the Odds & Parlay Calculators to understand price and probability.
- Stick to a written plan from Bankroll Management 101.
- Remember that gambling is paid entertainment, not a reliable way to make money.
The house will always have an edge overall – EV just helps you decide how much you want to pay for that entertainment and which games drain you the slowest.