Expected value (EV) explained

What is expected value?

Expected value (EV) is what a bet is worth on average: the amount you’d win or lose per bet if you could make the same bet thousands of times. You calculate it by multiplying each possible result by its probability and adding the results together:

EV = (probability of winning × amount won) − (probability of losing × amount lost)

Say a friend offers you $12 if a fair coin lands heads, and you pay $10 if it lands tails. Your EV is 0.5 × $12 − 0.5 × $10 = +$1 per flip. You’ll lose plenty of individual flips, but over hundreds of them you’d expect to be about $1 ahead per flip.

EV is the single most useful idea for comparing gambling and trading products, because it shows the built-in cost of each one. It’s also why we rate casinos on bonus value after wagering and prediction markets on fees in our rankings of the best online casinos in the US and the best US prediction markets.

EV at the casino: the house edge

Every casino game has a house edge: the casino’s average profit on each bet, as a percentage of the bet. Your EV as a player is the same number with a minus sign. The flip side is the return to player (RTP), which Michigan’s gaming rules define as “the expected percentage of bets or wagers that a specific game will return to the player in the long run”. RTP = 100% − house edge.

Single-zero roulette shows how it works. A single-number bet pays 35 to 1, and there are 37 pockets:

EV per $1 = (1/37 × $35) − (36/37 × $1) = −$0.027, a house edge of 2.70%.

Here is the EV of common games per $100 wagered, using house edges published by the Wizard of Odds:

Two things catch people out. First, the house edge applies to every dollar you wager, not the money you deposit: play a $100 balance through a 96% slot ten times and you’ve wagered $1,000, for an expected loss of $40. Second, rules matter: a blackjack table that pays 6:5 instead of 3:2 costs you about 1.39% more. Our guide to RTP and house edge covers game rules and state payout minimums in detail.

EV at the sportsbook: the vig

A sportsbook builds its margin, the vig, into the odds. At -110 on both sides of a game, each side implies a 52.38% chance (110 ÷ 210), which adds up to 104.76%. That overround is the book’s cut: it works out to a hold of about 4.5% of all the money wagered.

If the game is truly a coin flip, a $110 bet at -110 has an EV of 0.5 × $100 − 0.5 × $110 = −$5, about −4.5% of your stake. To break even at -110 you have to win 52.38% of your bets.

A bet only becomes +EV when your probability beats the implied probability. At +150 the implied chance is 40%. If you believe the true chance is 45%, the EV of a $100 bet is 0.45 × $150 − 0.55 × $100 = +$12.50.

To estimate the “true” probability, many bettors remove the vig from a sharp two-way line:

1. Convert both prices to implied probabilities: -150 is 60.00% and +130 is 43.48%.
2. Add them up: 103.48%.
3. Divide each by the total: 60.00 ÷ 103.48 = 57.98% and 43.48 ÷ 103.48 = 42.02%.

Those no-vig probabilities are the benchmark to compare other prices against. Our odds calculator converts between odds formats, and the EV calculator removes the vig and calculates your edge for you.

EV on a prediction market: price, probability and fees

A prediction market contract pays $1 if the event happens and $0 if it doesn’t, so its price is the market’s probability. Your EV per contract is simply:

EV = your probability − price − fee

On Kalshi, a taker buying at 50¢ pays a fee of 1.75¢ per contract. So you break even only if the true chance is above 51.75%. If you think it’s 55%, your EV is 55¢ − 51.75¢ = +3.25¢ per contract, or $3.25 on 100 contracts that cost you $51.75, a 6.3% expected return.

Fees change the break-even point with the price. At 90¢, Kalshi’s taker fee is 0.63¢, so you need better than a 90.63% chance. Most maker orders on Kalshi, limit orders that wait in the order book, pay no fee at all, so for them the break-even is the price itself.

Two cautions. A price is a crowd estimate, not a fact, and the CFTC warned platforms in August 2026 that dressing up contract prices as sportsbook odds can mislead. And you can sell a contract before it settles, so EV also helps you decide whether to hold or take a profit. Our guides to prediction market fees and reading prices as odds go deeper.

The EV of a casino bonus

Bonuses are the one place where a casino can hand you positive EV, because the bonus money can be worth more than the expected loss on the wagering it requires. A simple rule of thumb:

Bonus EV ≈ bonus − (required wagering × house edge)

A $100 bonus with a 15x requirement means $1,500 of wagering. At a 4% house edge you’d expect to lose $60, so the bonus is worth about +$40. If the requirement also applies to your deposit, or the games you play count only partly toward it, the EV can turn negative. Our casino bonus guide walks through the details.

Positive EV isn’t a sure thing

EV is a long-run average, and the short run can look very different. The +150 bet above, with a 45% chance of winning, still loses more often than it wins. You need many bets for results to drift toward the expected value, and a losing streak can wipe out your budget before they do.

That’s why bet sizing matters as much as finding value. A common approach is the Kelly criterion, which sizes a bet as a share of your bankroll:

Kelly stake = (b × p − q) ÷ b

Here b is the net odds (decimal odds minus 1), p your probability of winning and q = 1 − p. For the +150 bet at 45%: (1.5 × 0.45 − 0.55) ÷ 1.5 = 8.3% of your bankroll. Because probability estimates are rarely exact, many bettors stake a fraction of that, such as half. If your estimate is wrong, a “+EV” bet is really a −EV one, so treat any edge you calculate with caution.

Taxes change the math

EV is normally calculated before tax, but all gambling winnings are taxable in the US. From 2026, if you itemize, you can deduct only 90% of your gambling losses, capped at your winnings, so even a break-even year can leave you with a tax bill. Our guide to gambling and prediction market taxes explains the rules.

How SafeBet.ai uses expected value

Our AI sports picks are built around the same idea: every pick comes with the odds range in which it still has value, so you can check the price at your sportsbook or on a prediction market before you place it. Whatever you play, set a budget first and use the limits your casino or platform offers; our responsible gambling guide has more.

The bottom line

Expected value tells you what a bet costs, or earns, on average. Casino games and standard sportsbook bets are negative-EV by design, while prediction markets and bonuses can be positive-EV if the numbers line up. To compare the licensed options on the costs that drive EV, see our rankings of the best online casinos in the US and the top US prediction markets.