What is casino house edge and how does it work?

What is casino house edge and how does it work, in pounds?

Casino house edge is the share of each £1 staked that the operator expects to keep, on average, over a great many bets. How it works is simple: it is the gap between what a bet would need to pay to be fair and what it actually pays. It does not decide any single bet.

Take £10 on red at a single-zero roulette wheel. On an unbiased wheel, red has a chance of 18 in 37 and losing has a chance of 19 in 37. This does not prescribe the results of 37 spins. Assume a win pays 1 to 1 and zero loses the full stake: the winning profit is £10.

The formula is EV = (p_win × win) − (p_lose × stake). In words, you weight the win by how often it comes, then take away the stake weighted by how often it goes. Here that is (18/37 × £10) − (19/37 × £10), an average loss of 27p a spin.

That 27p is 2.70% of the £10, and it is the house edge on this bet. The Gambling Commission calls the house edge ‘a measure of the percentage that a casino would expect to keep, on average, from each hand or spin’.

We checked that wording on 24 September 2026; Figure 1 sets the same sum out in a chalk box. The displayed 27p and 2.70% are rounded.

Sources: Gambling Commission: return to player — how much gaming machines pay out; Massachusetts Gaming Commission: roulette rules, 8 October 2020, section 2.

What the house edge is actually measuring

House edge is the expected net loss divided by a stated stake base. Check the denominator: it can be the initial wager rather than every amount later added to the round.

Wizard of Odds, a reference site built specifically around this arithmetic, states it plainly: house edge figures are calculated against the initial bet, and they assume optimal or near-optimal strategy where a game allows a choice of play.

A quoted 0.6% edge means an average loss of about six pence for every £10 wagered, taken over enough bets for the average to show itself.

That last clause matters more than the percentage itself. A house edge is a long-run average, not a per-spin outcome. For a bet whose possible net results are +£10 and −£10, neither result is −6p. The 6p is the probability-weighted average across possible results, not a promised deduction from each bet.

Everything else in this article follows from taking that sentence seriously.

Sources: Wizard of Odds: house edge.

House edge and RTP: use the same stake base

Return to player, or RTP, measures expected prizes as a share of stakes. The Gambling Commission's public guide stresses that it is an average across many plays, not a promise about one session.

That guide discusses physical gaming machines, including compensated machines. Its examples of 10,000 or 100,000 plays are not a calculation method for every online game, and are not a target a reader should try to reach.

For the same game, rules, strategy and stake base, expected net loss equals stakes minus expected gross prizes. House edge and theoretical RTP therefore add to 100%. Bonus features do not break that accounting identity.

What can break a comparison is using different denominators or scopes. An edge stated against an initial ante cannot be compared directly with a return measured against the ante plus later wagers. A base-game RTP also differs from a figure that includes a jackpot contribution and prize.

RTS 3 expressly discusses house edge and RTP for remote games. RTS 9 allows a combined game-and-jackpot RTP or separate components, and asks for the appropriate RTP when a customer is ineligible for the jackpot.

Even a complete RTP does not reveal the chance of one particular feature. Many different outcome distributions can have the same average. Keep the quantity and the game conditions attached to the percentage.

Sources: Gambling Commission: return to player — how much gaming machines pay out; Wizard of Odds: house edge; Gambling Commission: RTS 3, rules and likelihood of winning; Gambling Commission: RTS 9, progressive jackpot systems.

Where the gap comes from: true odds against paid odds

Every house edge in this article reduces to the same comparison: what a bet would need to pay to be exactly fair, against what it actually pays. Single-zero roulette has 37 pockets, so a bet on one number has a true probability of 1 in 37.

A fair payout on a £1 bet would return £37 in total (£36 profit plus the stake back): odds of 36 to 1. The wheel instead pays 35 to 1, which returns £36. The difference between the fair payout and the paid payout, spread across all 37 possible outcomes, is the house edge: 1⁄37, or 2.70%.

Double-zero roulette repeats the same logic with 38 pockets instead of 37. The wheel still pays 35 to 1 on a single number, so the gap widens to 2⁄38, or 5.26%. That is almost double, from one extra losing pocket and no change to the payout.

The general method is to multiply every net payout by its probability and add the results. Counting pockets works here because this model assumes equally likely pockets. Other games need their own probability weights, not just an outcome count.

Section 2 of the Massachusetts roulette rules supplies a public example of 35-to-1 straight payouts and 1-to-1 red payouts. It is a US rule source, not a rule imposed on every British online game. Zero refunds or other payout changes need a new calculation.

Sources: Massachusetts Gaming Commission: roulette rules, 8 October 2020, section 2.

A comparison table, worked from published rule sets

This is a selection from Wizard of Odds' published table, read on 24 September 2026. It illustrates how published reference figures depend on a wager, rule variant and denominator. It is not a UK casino comparison or a claim that every current product uses these rules.

The reference publishes its own calculations and carries casino promotions; it is not a regulator. We checked the listed figures against its table. The roulette figures can also be reproduced from the stated pocket counts and payouts; the other reference calculations have not been independently reproduced here.

Sources: Wizard of Odds: house edge.

Variance: the spread nobody puts on the payout table

A house edge tells you the expected result of a bet. It does not describe how widely the possible cash results spread around that average.

Variance measures squared deviations from the mean, weighted by their probabilities. Its square root is the standard deviation, which uses the same units as the result. It is not a maximum loss or a guaranteed interval.

A binomial distribution counts successes in a fixed number of independent trials with the same success probability. NIST gives its mean as np and standard deviation as √(np(1 − p)). Here n is the number of trials and p is the success probability.

The win count for repeated single-number roulette bets fits that model under our assumptions. Unequal winning and losing payouts do not stop the count being binomial; they change its conversion into money. A £1 straight bet has net outcomes +£35 and −£1.

With K wins in n spins, its net result is 36K − n pounds. The cash standard deviation is therefore 36√(np(1 − p)). For one spin with p = 1/37 this is about £5.84, compared with about £1 for a £1 red bet.

Both have the same rounded 2.70% edge under these rules. Their payouts explain the very different spread. A game with several prize sizes needs its full payout distribution, not just a win count.

Sources: NIST Engineering Statistics Handbook: binomial distribution; Massachusetts Gaming Commission: roulette rules, 8 October 2020, section 2.

Why the swings swamp the edge early on

Put a number on that spread and the short-session behaviour of a house edge becomes far less mysterious. For n independent £1 bets with the same rules and probability distribution, expected loss is n multiplied by the edge. The finish after n bets is fixed in advance; the model assumes enough notional funds to complete them.

The standard deviation of the total result, by contrast, grows with the square root of n, multiplied by the per-bet standard deviation.

Take a single-zero even-money outside bet: edge 2.70%, per-bet standard deviation almost exactly 1 unit of stake (a bet that returns +1 or −1 has very little room for a wider spread). At 10 bets, expected loss is 0.27 units against a standard deviation of about 3.16 — the swing around the average is roughly twelve times the average itself.

For the chart and calculator we round the edge to 2.70% and the per-bet standard deviation to 1.

At 100 bets, expected loss is 2.7 against a standard deviation of 10: the swing has shrunk to about 3.7 times the average. In this rounded model, only past about 1,372 bets does expected loss overtake the standard deviation, and at 10,000 bets expected loss (270 units) is nearly three times the standard deviation (100 units).

Figure 3, after the comparison table, plots exactly this. The cost climbs ten times for every tenfold rise in bets, but the swing only about 3.2 times, so the cost overtakes it.

Sources: NIST Engineering Statistics Handbook: binomial distribution; Massachusetts Gaming Commission: roulette rules, 8 October 2020, section 2.

What a short run can and cannot tell you

The practical reading is not that the edge is unreal — it is that a result measured in dozens or low hundreds of bets is dominated by variance, not by the edge that produced it.

A result can sit well above or below its expectation in this model. A single result alone does not establish that the probabilities changed; its likelihood still depends on how far it lies from the mean.

The spread is the part that hurts, and it is the part the average hides. If a session has gone further than you meant it to, GamCare's helpline is 0808 8020 133.

The Gambling Commission lists 0808 8020 133 for England and Scotland and 0808 2819 265 for Wales. Use the linked support page to check the available route for your location.

Sources: NIST Engineering Statistics Handbook: binomial distribution; GamCare: talk to us now; Gambling Commission: self-exclusion and support contacts.

Try it: the edge-versus-swing calculator

The calculator puts your own numbers through the two formulas above. The average cost of a run is the number of bets × the edge × the stake. The swing around it is the square root of the number of bets × the per-bet spread × the stake.

Try it with £10. At a 2.70% edge, 100 even-money bets of £10 have an average cost of £27. The standard deviation of the result is about £100, roughly 3.7 times the cost.

Now set the spread to 5.84 for a single-number bet. The average cost stays at £27. The standard deviation grows to about £584.

These are rounded teaching inputs, not fitted measurements of a live game. A standard deviation is a measure of spread, not a probability of winning, a loss limit or an affordability calculation.

Sources: NIST Engineering Statistics Handbook: binomial distribution; Massachusetts Gaming Commission: roulette rules, 8 October 2020, section 2.

Independence: when a streak changes nothing

The repeated-bet calculations here assume independent trials with the same probability distribution. Under that assumption, knowing the last result does not alter the next result's probabilities.

For remote games regulated in Great Britain, RTS 7A requires acceptably random results and prohibits compensated behaviour. Its guidance discusses unpredictable outputs and avoiding repeated or synchronised RNG streams. Statistical analysis is one stated way to demonstrate randomness.

That standard does not make every game's successive wagers independent. RTS 7 expressly allows described features with different rules. RTS 3 also addresses multi-state games, including collected tokens and bonus rounds. Their current state can matter.

If a roulette model uses independent spins and unchanged payouts, a run of ten losses does not alter the eleventh spin's probability. It also does not change that model's house edge.

A technical requirement is not evidence that a particular product complies. Check the game rules before using independence, and do not treat a visible losing run as informative without specifying the question and model.

Our separate note on "at least one" explains the difference between a sequence probability set before play and a claim that a result is now owed.

Sources: Gambling Commission: RTS7, generation of random outcomes; Gambling Commission: RTS 3, rules and likelihood of winning.

What this model does not cover

This article derives expected loss from probabilities and payouts, then models repeated identical independent bets. It does not assume every casino product meets those repeated-bet conditions.

It does not calculate the house edge, feature probability or paytable of any specific commercial slot, live table or jackpot product; those figures are set by each provider's own rule set and are not recoverable from the general formulas here.

It also does not model bonus terms, wagering requirements, stake changes mid-session or account-level behaviour, and it makes no claim about what any individual player will experience, win or lose. Our separate note on why an average is not a session forecast covers that distinction in more depth. A stopping rule, changing stake or depleted balance needs a different model.

For the game-specific application of this same maths, Wheel Theory carries the full roulette probability derivations. Reel & Story covers slot RTP and volatility in depth, and Jackpot Anatomy explains progressive and fixed jackpot mechanics. Each applies the general ideas on this page to its own territory rather than re-deriving them.

If you are trying to work out whether you are spending more time or money than you intended, that is a different question from the maths here. Play in Balance explains limits and their limitations as a support topic rather than a probability question.

Sources: NIST Engineering Statistics Handbook: binomial distribution; Gambling Commission: RTS 3, rules and likelihood of winning; Gambling Commission: RTS 9, progressive jackpot systems; Gambling Commission: self-exclusion and support contacts.