Expected value explained: the one number behind every bet, how to calculate it for any odds format, and why a positive number is not a promise

Guide · Updated October 26, 2026 · 18+ · Not legal, tax or financial advice · By BetG8 Editorial · Sports

Short answer: Expected value, or EV, is the average result of a bet per play if you could repeat it many times at the same price and the same true probability. For a single bet it is the probability of winning times the profit, minus the probability of losing times the stake. A $100 bet at −110 wins $90.91 or loses $100; if the outcome is a true coin flip, the EV is 0.5 × $90.91 − 0.5 × $100 = −$4.55, which is the sportsbook's margin seen from the bettor's side. The same bet needs a true probability above 52.38 percent to have positive EV. On a prediction market contract that pays $1, EV per contract is simply your probability minus the price minus the fee. A positive EV is only as good as the probability behind it, and even a correct one loses often in the short run. This guide is arithmetic, not a recommendation to bet or trade.

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Every discussion of whether a bet is good or bad comes down to expected value, whether or not it uses the name. The vig, implied probability, the Kelly criterion and closing-line comparisons are all ways of estimating or protecting it. The idea is old: probability theory grew out of seventeenth-century questions about how to divide the stakes of an unfinished game fairly, and the answer was to weight each possible outcome by its chance. This guide shows the formula, applies it to the price formats you will meet, works through one sportsbook bet and one exchange contract with fees, and explains why the number does not tell you what will happen next.

The formula

For any gamble with several possible outcomes, expected value is the sum, over all outcomes, of the probability of the outcome times what you gain or lose if it happens. A bet has two outcomes, so the general formula shrinks to one line:

EV = p × profit − (1 − p) × stake

Here p is the true probability that the bet wins, profit is what you collect on top of your stake when it wins, and stake is what you lose when it does not. A bet is called fair when its EV is zero: neither side has an advantage, and over many repetitions the money simply moves back and forth. Positive EV means the bettor is being paid more than the risk justifies; negative EV means the price favours the other side. The probability in the formula is the true one, which nobody observes directly. The price only gives you the market's estimate, and the whole difficulty of betting lies in the gap between the two.

The same formula in every odds format

The formula does not change between formats; only the way the profit is written does. With decimal odds d, a winning $1 returns d dollars including the stake, so EV per dollar staked is p × d − 1. American odds convert in two steps: a positive line such as +150 means $150 profit on $100, so the profit per dollar is 1.50; a negative line such as −120 means you stake $120 to win $100, so the profit per dollar is 100 ÷ 120 = 0.833. A prediction market contract bought at price c pays $1, so its EV per contract is p − c before fees. The table shows the −110 case, the standard price on both sides of a point spread, for a $100 stake.

True probability of winning	Win (× $90.91)	Loss (× $100)	EV per $100 bet	EV as share of stake
45%	$40.91	$55.00	−$14.09	−14.1%
50%	$45.45	$50.00	−$4.55	−4.5%
52.38%	$47.62	$47.62	$0.00	0.0%
55%	$50.00	$45.00	+$5.00	+5.0%
60%	$54.55	$40.00	+$14.55	+14.5%

The break-even row, 52.38 percent, is 110 ÷ 210, the probability implied by the price itself. That is the general rule: a bet has positive EV exactly when your probability is higher than the probability the price implies. At decimal odds of 2.50, the implied probability is 1 ÷ 2.50 = 40 percent; with a true chance of 45 percent the EV is 0.45 × 2.50 − 1 = +12.5 cents per dollar, and at 40 percent it is zero. Our implied probability guide covers the conversions in both directions.

A worked example on an exchange, fees included

Suppose a Yes contract is offered at 42 cents, you estimate the event's chance at 47 percent, and you buy 100 contracts at the market as a taker on Kalshi. The fee comes from Kalshi's published schedule: 0.07 × contracts × price × (1 − price), rounded up.

Step	Calculation	Result
Cost of 100 contracts	100 × $0.42	$42.00
Kalshi taker fee	0.07 × 100 × 0.42 × 0.58, rounded up	$1.71
Total outlay	$42.00 + $1.71	$43.71
Break-even probability	$43.71 ÷ $100 payout	43.71%
EV if your 47% is right	0.47 × $100 − $43.71	+$3.29 (7.5% of outlay)
EV if the true chance is 44%	0.44 × $100 − $43.71	+$0.29
EV if the true chance is 43%	0.43 × $100 − $43.71	−$0.71
Same order on a Polymarket sports market	fee 0.05 × 100 × 0.42 × 0.58 = $1.22	break-even 43.22%

Three points stand out. The price says 42 percent, but after the fee you need more than 43.7 percent to break even, so a trader who thinks the market is one point too low has no edge at all. The fee is fixed by the price, not by your view, so it takes the same bite whether your estimate is good or bad. And EV scales linearly: if your estimate is three points too high, about nine-tenths of the expected profit in this example disappears. You can run other prices and quantities through our prediction market fee calculator, which returns the break-even probability on both venues.

Why positive EV still loses

EV describes an average over many repetitions, not the result of the next bet. Each bet in the −110 table either wins $90.91 or loses $100, so the spread of results is wide compared with an edge of a few dollars. Take a bettor whose true chance is genuinely 55 percent at −110 and who places 100 bets of $100. The expected profit is $500. The standard deviation of the total is about $950, so the chance of being behind after 100 bets is roughly 30 percent. After 1,000 bets the expected profit is $5,000, the standard deviation about $3,000, and the chance of being behind falls to about 5 percent. That is the arithmetic of a real, sizeable edge that the bettor somehow knows to be real. Most estimates are less certain than that, and the cost of an overestimate is asymmetric: at a true 50 percent the same 1,000 bets lose $4,545 on average. Position sizing rules such as the Kelly criterion exist because EV alone says nothing about how much of a bankroll a bet deserves.

Where the house edge lives in EV terms

A sportsbook does not charge a fee; it sets prices whose implied probabilities add up to more than 100 percent. On a −110/−110 market they add up to 104.76 percent, and a bettor on either side of a true coin flip has an EV of −4.55 percent of stake, which is the margin our vig guide breaks down. Combining bets multiplies the effect. A two-leg parlay of −110 coin flips pays decimal odds of 3.64 and wins 25 percent of the time, an EV of −8.9 percent; three legs pay 6.96 at a 12.5 percent chance, an EV of −13.0 percent. Exchanges have no built-in margin on the price, but they charge a fee and the trader pays the bid-ask spread, so the starting EV of a trade at a fair price is negative there too, just by a different route. On any venue, a bet with no information edge has negative expected value by construction.

Common mistakes

Using the market's probability as your own. If p comes from the same price you are betting into, EV is zero before costs and negative after them. A positive EV calculation needs an independent estimate. Leaving out costs. The fee, the spread and, at a sportsbook, the vig all belong in the calculation; a one-point edge disappears under a 1.7-cent fee. Counting bonus money at face value. Promotional credits often carry wagering requirements that change the real payoff, so the EV has to be calculated on what can actually be withdrawn. Judging EV by results. A losing bet can have been positive EV and a winning one negative; with outcomes this noisy, a few dozen results say very little about the quality of the estimates behind them.

What this guide does not cover

This guide covers expected value for single bets and binary contracts. It does not cover how to build a probability estimate, the variance of correlated bets, closing-line value as an indirect measure of EV, or tax, which reduces the value of winnings in a way that depends on your situation. Fee figures are from Kalshi's fee schedule effective July 7, 2026 and Polymarket's fee documentation as of October 2026; both change, and some Kalshi series carry different multipliers. The variance figures are calculated with a normal approximation and assume independent bets at the same price and probability. Nothing here is legal, tax, financial or betting advice, and nothing here suggests that any particular bet has positive expected value.

Frequently asked questions

What is expected value in betting?

Expected value is the average amount a bet wins or loses per play if it could be repeated many times at the same price and probability. It is the probability of winning times the profit, minus the probability of losing times the stake. A $100 bet at -110 on a true 50 percent outcome has an expected value of minus $4.55.

How do you calculate expected value from decimal odds?

Per dollar staked, expected value equals the probability of winning times the decimal odds, minus 1. At decimal odds of 2.50 and a 45 percent chance, that is 0.45 times 2.50 minus 1, or plus 12.5 cents per dollar. At a 40 percent chance it is exactly zero.

How do fees affect expected value on Kalshi or Polymarket?

A contract pays $1 if the event happens, so expected value per contract is your probability minus the price minus the fee per contract. 100 contracts at 42 cents on Kalshi carry a taker fee of $1.71, which raises the break-even probability from 42 percent to 43.71 percent.

Does a positive expected value guarantee a profit?

No. Expected value is a long-run average and depends on the probability estimate being right. Even with a true 55 percent chance at -110, a run of 100 bets of $100 finishes behind roughly 30 percent of the time, and an overestimated probability turns a positive number negative.