Expected Value in Casino Games Explained
What expected value means
Expected value (EV) is the average outcome of a bet if it were repeated a very large number of times, expressed as a dollar figure rather than a percentage. It's the concept that turns an abstract house edge percentage into something concrete and comparable: instead of saying "this bet has a 2.70% house edge," EV lets you say "this specific $50 bet has an expected value of −$1.35," a number you can directly compare against a different bet size or a different game entirely.
EV is not a prediction of what will happen on your next bet — a single bet always resolves as a specific win or loss, never as a fractional average. It's a statement about the long-run average across many repetitions of that exact bet, which is why it's most useful as a comparison tool between different options rather than as a forecast of any individual outcome.
The formula
Expected value is calculated by multiplying each possible outcome by its probability, then summing those products:
EV = (Probability of winning × Amount won) − (Probability of losing × Amount lost)
Take a single-number bet on European roulette, wagering $10. The probability of winning is 1/37, paying 35-to-1 (a $350 win on top of getting the original $10 back, or equivalently a $350 profit). The probability of losing is 36/37, losing the $10 wagered. The calculation: (1/37 × $350) − (36/37 × $10) = $9.46 − $9.73 = −$0.27. The expected value of that $10 bet is −$0.27 — a small negative number that represents the average cost of making that exact bet repeatedly over a large number of spins. Divide −$0.27 by the $10 wagered and you get −2.70%, the same house edge figure that comes from calculating the game's payout structure directly. EV and house edge are two views of the same underlying math — the casino odds & house edge guide covers the relationship in full, and how casino odds work covers the true-odds-versus-payout-odds mechanic that generates the percentages plugged into this formula.
Worked examples across different games
Seeing EV calculated for a few different bets, at a consistent $20 wager, makes the comparison concrete:
| Bet | House Edge | EV on a $20 Bet |
|---|---|---|
| Craps — Pass line | 1.41% | −$0.28 |
| Blackjack — perfect basic strategy | ~0.5% | −$0.10 |
| Baccarat — Banker | ~1.06% | −$0.21 |
| European roulette — any bet | 2.70% | −$0.54 |
| American roulette — any bet | 5.26% | −$1.05 |
| Baccarat — Tie (8-to-1) | ~14.4% | −$2.88 |
The pattern to notice: EV scales directly with both house edge and bet size. Doubling your bet doubles your expected cost at a fixed house edge; choosing a bet with double the house edge at a fixed bet size does the same thing. This is why EV is a genuinely useful comparison tool — it lets you weigh "which bet" and "how much" on the same scale, rather than treating house edge and bet size as separate considerations.
Why every standard casino bet has negative EV
It follows directly from the definition of house edge that every standard casino bet has negative expected value for the player — a positive house edge (from the casino's side) is mathematically the same thing as a negative EV (from the player's side), just expressed from the opposite perspective. There's no legitimate standard casino wager with positive EV for the player; if one existed on a standard bet, it wouldn't remain available for long, since it would represent a guaranteed long-run loss for the casino offering it.
This doesn't mean every bet is equally bad — the size of that negative EV varies enormously, from close to zero (craps odds bets sit at exactly $0 EV, the one true exception) up to a significant chunk of the amount wagered (a Tie bet in baccarat, or a proposition bet in craps). Comparing EV across bets is the most direct way to see that variation clearly, which is the entire basis for casino games with the lowest house edge and casino games with the highest house edge.
The narrow exceptions
A small number of specific situations produce genuinely positive EV for a skilled player, and they're worth naming precisely because they're the exception that proves how rare this is. Certain full-pay video poker pay tables — most notably some Full Pay Deuces Wild variants — calculate to slightly above 100% RTP under perfect strategy, meaning a small positive EV, though realizing it requires memorized optimal play on every hand and access to the specific full-pay version, which isn't always available. Card counting in blackjack, when it works, shifts EV positive during specific favorable deck compositions by adjusting bet size in response to real, tracked information about remaining cards — a fundamentally different mechanism from a betting system reacting to past outcomes, since deck composition genuinely does change the odds of what's dealt next. Certain casino promotions and bonus structures can also carry positive EV if the value of the offer exceeds its wagering requirement's expected cost, though this depends entirely on the specific terms. All of these are covered in complete detail, including exactly how narrow and conditional they are, in can you beat the house?
EV over time: why the math compounds
Because EV scales with the number of bets placed, not just their size, the total expected cost of a session grows with every additional bet, even at a fixed house edge. Placing a $10 bet once at a 2% house edge has an EV of −$0.20; placing that same $10 bet 100 times has a total expected cost of −$20, not because the per-bet math changed, but because it was repeated 100 times. This is why pace of play — how many bets per hour a given game produces — has a real, multiplying effect on total expected cost independent of the house edge itself, a relationship covered in more depth in the casino odds & house edge guide and in the practical bankroll context of casino bet sizing explained.
EV vs. what actually happens in a single session
It's worth being direct about the gap between EV and any individual session's real outcome. EV describes an average across a very large number of repetitions; a single session, even a fairly long one, is nowhere close to that number of repetitions, which means actual results routinely land well above or below the EV figure. A player can have negative-EV bets all session and still finish up money, and a player can have the same negative-EV bets and finish down considerably more than the EV alone would suggest. Neither outcome contradicts the math — it's exactly what variance predicts. Variance in casino gambling explained covers this gap between long-run average and short-run outcome in full.
Frequently asked questions
What does "expected value" mean in gambling? The average outcome of a bet if it were repeated many times, expressed as a dollar figure. It's calculated from the probability and size of every possible outcome, and it's the dollar-figure version of a bet's house edge.
Is expected value the same as house edge? They describe the same underlying math — house edge is a percentage rate, EV is that rate applied to a specific bet size to produce a dollar figure. Divide a bet's EV by its size and you get the house edge (as a negative percentage from the player's side).
Does negative EV mean I'll definitely lose money? Not in any individual session — EV is a long-run average, and short-term results vary widely due to variance. Negative EV means that, averaged over a very large number of repetitions, the bet costs money; it says nothing certain about any single session.
Can any casino bet have positive expected value? Standard casino bets are designed with negative EV for the player. A small number of narrow exceptions exist — certain full-pay video poker under perfect strategy, blackjack card counting under specific conditions, and some positive-EV promotions — covered in can you beat the house?
How do I calculate the EV of a bet I'm considering? Multiply the probability of each outcome by its dollar result, then sum those products. For a simple win/lose bet: (probability of winning × amount won) − (probability of losing × amount lost).
Does bet size affect EV? Yes, directly and proportionally — doubling your bet size doubles your expected cost at a fixed house edge. This is different from house edge itself, which stays constant regardless of bet size.
