Expected Value (EV) in Gambling, Explained
Last reviewed: June 2026
The one-sentence definition: Expected value (EV) is the average amount a bet wins or loses per play if you made it many, many times. For essentially every casino bet, that number is negative — which is just another way of saying the house edge guarantees a long-run loss. EV is the single number that tells you what a bet is really worth.
If you understand EV, the rest of casino math falls into place: the house edge is simply EV expressed as a percentage. Here’s how to calculate it, with a worked example, and what it does — and doesn’t — tell you.
What is expected value?
Expected value is the probability-weighted average of every possible outcome. You take each thing that can happen, multiply its payoff by its probability, and add them all up:
EV = (outcome₁ × probability₁) + (outcome₂ × probability₂) + …
If EV is positive, the bet makes money on average (these barely exist in casinos). If it’s zero, it’s a “fair” bet (break-even long-run). If it’s negative, you lose on average — and nearly every casino bet lives here. That’s the mathematical meaning of house edge.
A worked example: roulette
Put $10 on a single number in American roulette. The wheel has 38 pockets (1–36 plus 0 and 00). One pocket wins and pays 35:1; the other 37 lose.
Per dollar bet, the EV is:
EV = (+35 × 1/38) + (−1 × 37/38) EV = (0.921) + (−0.974) = −0.053
So you lose about 5.3 cents per dollar, or roughly 53 cents on a $10 bet, on average. Expressed as a percentage, that −5.26% is the American roulette house edge. Switch to European (single-zero) roulette and the same math gives −2.70% — better, because there are 37 pockets instead of 38. Compare every game’s edge in House Edge by Game.
Notice the bet pays 35:1 but there are 38 outcomes. In a truly fair game it would pay 37:1. That two-pocket gap is where the casino’s profit lives.
EV scales with what you wager — not your deposit
A crucial, often-missed point: the percentage edge is fixed, but the dollar expected loss grows with total amount wagered.
| Total wagered | EV at −2.70% (European roulette) |
|---|---|
| $100 | −$2.70 |
| $1,000 | −$27 |
| $10,000 | −$270 |
This is why a small deposit can produce a large expected loss: if you re-bet your winnings over and over, your total wagered climbs far above your deposit, and EV is charged on every dollar that crosses the felt. It also explains why bonus wagering requirements are costly — see Wagering Requirements Explained.
EV vs. variance: why losing games still pay out sometimes
EV tells you the long-run average. It says nothing about any single session — that’s the job of variance. Variance is why a negative-EV game can still leave you up after an hour: short-run luck swings around the average. But the more you play, the more your results converge toward EV (the law of large numbers), and EV is negative.
This is the precise reason “betting systems” don’t work. Rearranging when you bet doesn’t change the EV of each bet, so the sum stays negative no matter the pattern. We bust that myth in The Gambler’s Fallacy & Betting Myths.
A second example: why “insurance” in blackjack is a bad bet
EV also explains specific in-game decisions. Take the blackjack insurance bet: when the dealer shows an Ace, you can bet up to half your wager that the dealer has a 10 underneath, paying 2:1.
In a single deck, of the 13 card ranks, 4 are tens (10, J, Q, K) and 9 are not. So roughly:
EV = (+2 × 4/13) + (−1 × 9/13) EV = (0.615) + (−0.692) = −0.077
That’s about a −7.7% EV — a worse bet than almost anything on the main game. The 2:1 payout sounds protective, but the true odds are about 2.25:1 against, so you’re underpaid. EV turns “feels safe” into a hard number: insurance is a money-loser, which is why correct basic strategy says never take it.
EV isn’t only for casinos
The same tool evaluates any uncertain choice — lottery tickets, extended warranties, even insurance products. You multiply each outcome by its probability and sum. Most consumer “gambles” (lottery tickets especially) are steeply negative-EV; you’re paying for the entertainment or peace of mind, not making a mathematically favorable bet. Recognizing negative EV is what lets you spend on those things deliberately rather than mistaking them for good deals.
How to use EV as a player
You can’t make casino games positive-EV, but you can lose less per dollar by choosing better-EV bets:
- Pick low-edge games and bets. Blackjack with good rules, baccarat Banker, and European over American roulette all have better (less negative) EV.
- Avoid the high-payout traps. The baccarat Tie and craps prop bets have deeply negative EV despite their flashy payouts.
- Treat the expected loss as the price of entertainment. Decide what that price is worth to you, and stop there.
Frequently asked
Is expected value the same as house edge? Effectively yes — the house edge is the negative EV of a bet expressed as a percentage of the amount wagered. A 2.70% house edge means an EV of −$0.027 per dollar.
Can a casino bet have positive expected value? Almost never in normal play. Rare exceptions involve advantage situations (e.g., card counting, certain promotions), not standard bets — and casinos actively counter them.
If EV is negative, how do people win? Short-term variance. Over a session, luck can put you ahead; over the long run, results trend toward the negative EV. Winning sometimes is normal and expected — it doesn’t make the bet profitable.
Sources & further reading
- Prof. Boston — Expected Value in Casino Gambling — the worked roulette EV calculation (accessed 2026-06-22)
- Casino-Games-Online — Expected Value — negative-EV and long-run framing (accessed 2026-06-22)
Educational explanation only. No real-money gambling happens on LearnTheOdds.
Responsible gambling: Play for entertainment, not income — the math favors the house over time. Set limits, never chase losses, and if it stops being fun, take a break. 21+. Need help? Call 1-800-MY-RESET (1800myreset.org).