Expected value meaning

Expected value meaning with a simple example

Expected value is a probability-weighted average. List every outcome, multiply each by its chance of happening, and add the results. The answer is what one try is "worth" on average, even though no single try ever produces exactly that figure.

Take £1 on red at single-zero roulette. There are 18 red pockets out of 37. You win £1 with probability 18/37 and lose £1 with probability 19/37. The EV is (18/37 × £1) − (19/37 × £1) = −£1/37, or about −2.7p. That is the house edge seen as a pound figure. The Wizard of Odds roulette guide (opens in a new tab) sets out the same maths for every bet on the table.

Negative EV is normal for gambling. It means that, on average, playing costs money. That is the price of the entertainment, and it is why our casino bonus glossary always treats a bonus as something that offsets cost rather than creates profit.

Expected value of free spins

Free spins are the easiest offers to value. Their EV is the number of spins × the stake per spin × the game's RTP. If the winnings are paid as cash with no wagering, that is the whole calculation. If they carry wagering, subtract the expected cost of that wagering as well.

Most spin offers also need you to stake your own money first. That qualifying bet has its own small negative EV, which you should set against the spins. A £10 slots bet at 96% RTP has an EV of about −40p.

EV of the UK offers we list: worked figures

The table works through the five partner offers using 96% RTP (a 4% edge) unless the game is fixed. Figures are averages over very many players and assume every spin is used and every condition met; real results vary widely.

For the match bonuses, the simple figure leaves out real-world limits: you may lose the balance before finishing, the 7-day (Casumo) or 3-day (10bet) deadline may pass, and 10bet caps bonus winnings at £1,000. Our full expected value of a casino bonus guide includes those effects, and the wagering calculator runs your own numbers.

What expected value can't tell you

• Your actual result. 100 spins at 10p with an EV of £9.60 can easily return £1 or £40.
• The range of outcomes. That depends on volatility, not EV.
• What happens after the offer. Every stake beyond the bonus conditions has the usual negative EV, so continuing to play costs money on average.
• Whether it suits you. A positive average on a bonus doesn't make gambling a sensible way to spend money you need.

This is why the Advertising Standards Authority's guidance on free bets and bonuses (opens in a new tab) says an offer shouldn't be called free if you must risk your own money to qualify. A bonus doesn't change the long-run cost of play; it only offsets part of it.

How the 10x wagering cap changed bonus EV

Before 19 January 2026, high wagering often wiped out a bonus's EV. A £100 bonus at 35x meant £3,500 of play; at a 4% edge that cost about £140 on average, so the bonus had a negative EV before any other condition. The Gambling Commission's announcement that gambling promotions are to be safer and simpler (opens in a new tab) capped wagering at 10x the bonus. The same £100 now needs £1,000 of play, costing about £40 on average. Our 10x wagering cap page has the background, and is a casino bonus worth it? applies it to real decisions.

How to work out a bonus's expected value

1. Find the bonus amount or the spins × stake face value.
2. Read the wagering multiple and multiply by the bonus to get the total to wager.
3. Check the RTP of the games you'll use and work out the edge (100% − RTP).
4. Multiply total wagering by the edge to get the expected cost.
5. Subtract the cost from the bonus, then note any max win, expiry or max bet limits that lower it further.

For a worked walk-through of step 2, see how to calculate wagering requirements; for spins, free spins maths.

Expected value and our partners' spin offers

The no-wagering spin offers have the simplest EV because winnings are paid as cash. Coral gives 100 free spins at 10p after you deposit and bet £10 on slots (spins valid 7 days, accept within 48 hours); Ladbrokes gives 50 free spins a day for 10 days at 10p after a £10 slots spend, claimed by 23:59 each day; PlayOJO gives 80 spins on Big Bass Bonanza at 10p with a first deposit of £10 or more. Coral and Ladbrokes exclude PayPal, Skrill, Neteller, Paysafe and prepaid cards. All three are 18+ and for new customers only, and terms apply. Compare them on our no wagering bonus page.

18+. Gambling should be entertainment that costs money, not a way to make it. Decide a budget before you play: set a budget. Free, confidential help: National Gambling Helpline 0808 8020 133.