Expected Value in Gambling: The Number Behind Every Bet

Expected value, often shortened to EV, is the average amount a bet would win or lose per play if it were repeated an enormous number of times. You find it by multiplying every possible result by its probability and adding the products together. For almost every casino game and most sportsbook prices, the expected value of a bet is negative, and that negative number is the house edge or bookmaker's margin written in money.

EV will not tell you what happens tonight. It tells you what a bet costs on average, which is the most useful single figure for anyone treating gambling as paid entertainment.

The formula

For a bet with two outcomes, win or lose:

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

Games with more outcomes just add more terms: each result multiplied by its probability. If the answer is zero, the bet is fair. If it is negative, the bet costs money on average; if positive, it pays.

Three worked examples

A single number at roulette

A straight-up bet on one number at a single-zero wheel pays 35 to 1, and the ball can land in 37 pockets. For a $10 stake:

• Win: 1/37 chance of +$350
• Lose: 36/37 chance of −$10

EV = (350 − 360) ÷ 37 ≈ −$0.27 per $10 bet, a cost of about 2.7%. On a double-zero wheel the same bet pays the same 35 to 1 across 38 pockets, and the cost rises to about 5.3%.

A sports bet at −110

A typical point spread or total is priced at −110 on both sides: risk $110 to win $100. Suppose the game really is a coin flip.

• Win: 0.5 chance of +$100
• Lose: 0.5 chance of −$110

EV = 50 − 55 = −$5 per $110 risked, about −4.5%. To break even, a bettor would need to win 110 ÷ 210 of the time, roughly 52.4%. The gap between 50% and that figure is the margin, explained in more detail in how point spreads and their prices work.

A slot with a published RTP

Slots hide their individual probabilities, but many publish a return-to-player figure. RTP is expected value turned into a percentage. A game listed at 96% returns, in theory, $96 for every $100 wagered over a very long run, so the EV is −$4 per $100 staked. Over a few hundred spins the actual result can land far above or below that.

Bet	Expected result per $100 staked
Single number, single-zero roulette	about −$2.70
Single number, double-zero roulette	about −$5.26
Sports bet at −110, true 50/50 game	about −$4.55
Slot with 96% RTP	−$4.00 (theoretical)
Coin flip with a friend at even money	$0.00

Expected value versus variance

EV is the centre; variance is the spread around it. Two games can share the same expected value while behaving very differently. A low-volatility slot pays small amounts often and drifts steadily toward its average. A high-volatility slot can go a long while without paying and then return a large win. Both cost the same on average; the ride is different.

In a single evening, variance usually dominates. A winning night says almost nothing about whether a bet had positive EV, and a losing night says almost nothing about whether it was a poor choice. That is why judging a bet by its result alone is misleading: the decision and the outcome are two different things.

Why staking systems cannot change it

The expected value of a session is the sum of the expected values of its bets. Each bet's EV equals its stake multiplied by the edge. Raising stakes after losses, as the progressions in popular betting systems do, only increases the total staked and so increases the expected cost. No ordering of negative-EV bets adds up to a positive number.

Using EV as a budget tool

The practical use of EV for most people is estimating what an evening will cost on average:

1. Estimate how much you will wager in total, not just how much you bring. Three hundred spins at $1 means $300 wagered, even if you start with $50.
2. Multiply by the edge. At a 96% RTP, $300 wagered has an expected cost of about $12.
3. Compare that with what you are happy to pay for the entertainment, then set a hard cap above it to cover a bad run.

This is the same thinking behind splitting a budget into session units in bankroll architecture. Faster play, bigger stakes and longer sessions all increase the amount wagered, and with it the expected cost.

Questions people ask

Is there such a thing as a positive-EV bet?

In principle, a bet is positive EV when the true chance of winning is higher than the price implies. In practice, nobody knows the true chance of a sports result precisely, and casino games are built with a fixed edge. Claims of guaranteed positive-EV betting deserve a great deal of scepticism.

Is a negative-EV bet a bad bet?

Not necessarily. A cinema ticket has negative expected value too. The question is whether the price is one you are comfortable paying for the time spent.

Gambling is for adults and only where the law permits it; pay for it the way you would pay for a concert ticket, from spare money, and stop when that amount is spent.