What is the house edge in blackjack: the sum, worked in pounds

What is the house edge?

The house edge in blackjack is the operator’s share of each £1 you stake, averaged over a very large number of hands, and under the most generous common rule set it is about 0.28% with basic strategy. Stake £10 a hand and the expected cost is roughly 3p per hand.

Change one rule, a blackjack paying 6 to 5 instead of 3 to 2, and the working below adds 1.36% to that figure. The sum is on the board; every input is cited.

Wizard of Odds, the reference the rest of this page checks against, defines house edge as ‘the ratio of the average loss to the initial bet’ (read 21 September 2026).

The Gambling Commission describes the same idea from the other side, as return to player: ‘an average achieved over a significant number of game plays and not each time the gaming machine is played’ (read 21 September 2026). Edge is what the operator keeps; RTP is what comes back; for a fixed-rule game they add up to 100%.

Blackjack is the awkward case because the edge depends on what you do. The published figure assumes basic strategy, and the Wizard’s page states its numbers ‘are based on optimal or near-optimal player strategy’. Play differently and the edge is higher.

It cannot be lower.

Step 1 — write down the inputs

Inputs: a £10 stake; a rule set; a probability of each outcome under that rule set; a payout for each. Assumptions: the shoe is shuffled so that each hand is independent of the last, which is what RTS 7A’s ‘acceptably random’ requirement is for (read 21 September 2026).

And the player follows basic strategy, because that is the only version of ‘you’ the published figure describes.

The formula, once in symbols and once in words. EV = (p_win × win) − (p_lose × stake). Expected value equals the chance of winning times what you win, minus the chance of losing times what you stake.

The house edge is minus that expected value, divided by the stake.

For most games the sum is short because there are two or three outcomes with fixed probabilities. Blackjack has thousands of outcomes, so nobody works it by hand; the 0.28% comes from a full enumeration that Wizard of Odds publishes. What can be worked by hand is what each rule change adds, and that is Step 2.

Explain how house edge is calculated for blackjack variations.

Step 2 — put the £10 through the formula, one rule at a time. Take the 3 to 2 blackjack payout and change it to 6 to 5. The only hands affected are the ones where you hold a blackjack and the dealer does not.

On each of those you now receive £12 on a £10 stake instead of £15: a loss of £3, or 0.3 of the stake.

How often does that hand come up? With eight decks there are 416 cards, 32 aces and 128 ten-value cards. The chance of a two-card blackjack is 2 × (32/416) × (128/415) = 0.04745, about one hand in 21.

Given you hold one, the dealer’s chance of also holding one is 2 × (31/414) × (127/413) = 0.04605. So the chance of an unmatched player blackjack is 0.04745 × (1 − 0.04605) = 0.04527.

So what is the house edge in blackjack at 6 to 5?

Cost of the rule: 0.3 × 0.04527 = 0.01358, or 1.36% of every stake. Added to the 0.28% base, a 6 to 5 table with otherwise liberal rules carries about 1.64%. Pay even money on blackjack instead and the loss per affected hand is 0.5 of the stake: 0.5 × 0.04527 = 2.26%, for a total near 2.54%.

Try it with £10: the 6 to 5 rule alone costs 13.6p per hand in expectation, five times the whole edge of the liberal table.

How does the house edge vary between different types of blackjack?

It varies with the rule sheet, not the branding. The same arithmetic applies to any rule: find the hands it changes, find how often they occur, multiply by what the change costs, and add. The table below lists the rule sets we could compute or cite, with the working for each.

Where a figure is copied from Wizard of Odds rather than derived here, the table says so.

The lowest figure in the table is the liberal Vegas Strip set at 0.28%, and it carries a condition: basic strategy on every hand. The largest single jump is the payout on blackjack itself.

Deck count, dealer soft-17 rule and doubling limits each move the figure by fractions of a point; the 6 to 5 payout moves it by 1.36 points on its own.

The number that matters to your £10 is the one for the table you are actually at. A game’s help page states its rules; the working above turns those rules into pence per hand.

What does a 0.5% house edge mean?

It means that, averaged over a very large number of hands, the operator keeps half a penny of every pound staked. Try it with £10: the expected cost is 5p per hand. Over 100 hands it is £5.

Over 1,000 hands it is £50.

It does not mean you lose 5p on any given hand. On a single hand you lose £10, win £10, win £15 on a blackjack, or push. The 5p is the average of all of those, weighted by how often each happens.

The Commission’s RTP guide makes the same point for machines: for a machine showing 85% RTP, ‘you should not expect to win an average of 85 pence for every £1 you stake during a playing session’ (read 21 September 2026).

The long run is longer than your evening. Step 3 shows how much longer.

Step 3 — what the spread looks like over 100 hands

Take the simplest model first: 100 even-money bets at £10, each won with probability p. For an edge of 1.64%, p = (1 − 0.0164) / 2 = 0.4918. NIST gives the binomial mean as np and the standard deviation as √(np(1 − p)) (read 21 September 2026).

Mean wins: 49.18. Standard deviation of wins: √(100 × 0.4918 × 0.5082) = 5.0.

Each win moved from the mean is worth £20 (a £10 loss becomes a £10 win), so one standard deviation is 5.0 × £20 = £100 around an expected loss of £16.40. Real blackjack is wider than even money because of doubles, splits and the 3 to 2 payout; Wizard of Odds gives its standard deviation as 1.15 per unit staked.

With that figure: 1.15 × £10 × √100 = £115.

So the picture after 100 hands is an average of −£16.40 with a spread of about £115 either side. A £100 win and a £130 loss are both ordinary evenings. The edge is real and it is small; the spread is real and it is large; over 100 hands the spread wins the argument every time.

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.

Are there online casinos that publicly display their game’s house edge?

Usually the figure is published the other way round, as RTP. The Commission’s guide states that gaming machines ‘must make information available about their category, %RTP and whether they are compensated or random’ (read 21 September 2026); for a fixed-rule game, house edge is 100% minus that figure.

Online game help pages tend to carry an RTP line, and blackjack pages tend to carry a rule sheet instead, because the edge depends on your decisions.

We did not survey operators for this page and name none. What the working above gives you is the conversion: take the rule sheet from the game’s help page, find the payout on blackjack, and you have the largest term in the sum without waiting for anyone to publish it.

Reel & Story covers RTP as a slot concept; this page stops at the arithmetic.

Are there specific online casinos known for favourable house edge rules in video poker?

We do not name or rank operators, and video poker is outside this page’s table. The method is the same, though: the edge on a video poker game is set by its pay table, and the same formula, probability of each hand times its payout, summed, gives the return.

Two machines with the same name and different pay tables have different edges.

Wizard of Odds publishes those enumerations game by game; we cite the site rather than recompute it. If you want the number, read the pay table off the game’s help page and match it to the published table for that pay schedule.

Which casino game has the lowest house edge?

Of the rule sets on the board, blackjack under liberal Vegas Strip rules at 0.28% (Wizard of Odds, read 21 September 2026), with the condition that basic strategy is followed on every hand. Baccarat’s banker bet, at 1.06%, is the lowest figure that does not depend on the player’s decisions. Roulette on a single-zero wheel is 2.70% whatever you do.

Lowest is not good. A 0.28% edge on £10 a hand is still a cost of £2.80 per hundred hands in expectation, with a spread of about £115 around it. Understanding the sum makes the cost clearer; it does not make it smaller, and choosing not to play is the only rule set with an edge of zero.

A worked example in pounds

Inputs: £10 a hand, 100 hands, a table that pays 6 to 5 on blackjack with otherwise liberal rules. Assumptions: independent hands, basic strategy. Output: edge 1.64%, so expected cost £16.40; one standard deviation £115.

Now the same £10 for 100 hands at 3 to 2: expected cost £2.80, spread still £115. The rule change cost £13.60 in expectation over the session. The spread did not change, because the payout on a blackjack barely moves the variance; it moves the average.

That is the whole lesson in one line: rules move the average by pounds; chance moves the session by hundreds of pounds.

What this sum does not tell you

It does not tell you how to play a hand; Twenty-One Notes owns the rules and the basic-strategy decisions, and this page only assumes them. It does not tell you the edge on a table whose rules you have not read; the 0.28% is one rule set, and yours may differ on every line.

It does not tell you what will happen tonight. The average is exact and the session is one draw from around it.

Nothing in the working changes the next hand: RTS 7B guidance says random numbers ‘may not be discarded due to adaptive behaviour’ (read 21 September 2026), so the shoe does not owe you anything and does not remember you.

Questions answered

Six questions in the wording readers use, each answered in one sentence first and then from the working.

Sources

Sources checked 21 September 2026. Wizard of Odds, House Edge of Casino Games Compared (retrieved 21 September 2026): definitions, blackjack 0.28% and standard deviation 1.15 under liberal Vegas Strip rules, baccarat and roulette figures. Gambling Commission, Return to player: how much gaming machines payout (retrieved 21 September 2026).

Gambling Commission, RTS 7 – Generation of random outcomes (retrieved 21 September 2026). NIST/SEMATECH e-Handbook of Statistical Methods, Binomial Distribution (retrieved 21 September 2026). All rule-change arithmetic on this page is ours, from the card counts stated in the working.