House edge and RTP: what the numbers mean for casino games
Expected value, RTP and the house edge worked out for roulette, a 15-slot wheel, dice, 9/6 Jacks or Better and blackjack, and what they mean per session.
Fact-checked 18 October 2026 · 5 sourcesThe house edge is the share of every bet a game keeps on average. RTP, return to player, is the share it pays back. They are one number seen from two sides: RTP = 1 − edge. This article works out the edge for several games from their rules, then shows what it means for a real session, where luck matters far more than the edge in the short run and far less in the long run.
Expected value in one line
The expected value of a bet is the average result if you could make it an enormous number of times: add up each outcome's probability times what it returns, then subtract the stake. Divided by the stake, that is RTP minus 1, which is minus the edge.
Take red on a single-zero roulette wheel. Eighteen of the 37 pockets win, and a win returns twice the stake (the stake plus an equal win). So 1 coin brings back 18/37 × 2 = 36/37 = 0.973 coins on average. RTP is 97.30% and the edge is 2.70%. The edge exists because the game pays slightly less than the true odds: the green zero loses for red and black alike, and nothing pays you for it.
Worked examples
Every figure below is computed from the game's rules, with the method in the second column.
| Game and bet | How it's computed | RTP | House edge | |---|---|--:|--:| | Single-zero roulette, red | 18/37 × 2 | 97.30% | 2.70% | | Single-zero roulette, one number | 1/37 × 36 | 97.30% | 2.70% | | Double-zero roulette, red | 18/38 × 2 | 94.74% | 5.26% | | Double-zero roulette, 0-00-1-2-3 | 5/38 × 7 | 92.11% | 7.89% | | 15-slot wheel, T or CT | 7/15 × 2 | 93.33% | 6.67% | | 15-slot wheel, bonus | 1/15 × 14 | 93.33% | 6.67% | | Dice at a 1% edge, any target | chance × 0.99 / chance | 99.00% | 1.00% | | 9/6 Jacks or Better, perfect play | every deal, hold and draw | 99.54% | 0.46% | | Blackjack, basic strategy (rules below) | exact infinite-deck model | 99.49% | 0.51% |
Roulette and the 15-slot wheel
On a single-zero wheel every standard bet carries the same 2.70%, because each pays as if the zero weren't there. A double zero raises that to 5.26%, and the American five-number bet on 0, 00, 1, 2 and 3 is worse still at 7.89%, the figures the Wizard of Odds lists too.
A CS2-style wheel has 15 slots: 7 T, 7 CT and 1 bonus. T and CT pay 2× on 7 slots in 15, and the bonus pays 14× on 1 slot in 15. Both work out to 14/15, so every bet costs the same 1/15, or 6.67%, on average. The bonus bet isn't a better or worse deal, just a much bumpier one. The CS2 roulette article goes through the wheel in detail.
Dice
A dice game that sets its multiplier to (1 − edge) / chance has the same RTP at every target. At a 1% edge a 49.5% chance pays 2×, a 10% chance pays 9.9× and a 1% chance pays 99×, and in each case chance × multiplier = 0.99. Moving the target changes how often you win and how much, never the average cost.
Video poker: 9/6 Jacks or Better
The 9/6 in the name is the pay for a full house (9 for 1) and a flush (6 for 1). The rest of the table: royal flush 800, straight flush 50, four of a kind 25, straight 4, three of a kind 3, two pair 2, and a pair of jacks or better 1.
The return with perfect play comes from going through all 2,598,960 possible deals, all 32 ways to hold cards in each, and every possible draw, keeping the best hold every time. A program doing exactly that for this article gives 99.5439%, an edge of 0.46%, and every hand count matches the Wizard of Odds table exactly (for example, 493,512,264 royal flushes out of 19,933,230,517,200 weighted outcomes). That figure assumes the best hold on every hand; each mistake costs a little.
Blackjack
Blackjack's edge depends on the rules and assumes basic strategy, the best decision for each hand against each dealer card. For an infinite deck where the dealer stands on soft 17, blackjack pays 3:2, doubling is allowed on any two cards and after splits, and pairs can be split up to three times (aces once, one card each), the Wizard of Odds gives a player expectation of −0.511734%. An exact model of those rules written for this article, with the dealer peeking for blackjack, gets the same −0.511734%. Allow only one split and the edge rises to about 0.57%. The blackjack basic strategy article covers the decisions themselves.
The edge applies to everything you wager
The edge is charged on every bet, so the expected cost grows with the total amount wagered, not with your deposit. Deposit 100 coins, bet 1 coin at a time on dice at a 1% edge, and after 1,000 bets you have wagered 1,000 coins. The expected loss is 1% of that, 10 coins, even though you never had more than about 100 at risk. Winnings that you bet again are wagered again, and they pay the edge again.
Variance: why one session looks nothing like the edge
The edge is an average. Your actual result spreads around it, and that spread (the standard deviation) grows with the square root of the number of bets, while the expected loss grows with the number of bets itself. Early on the spread dwarfs the edge; later the edge dominates. Here is 1 coin per spin on single-zero red, with exact binomial chances of being ahead:
| Bets | Expected result | Typical spread (1 SD) | Chance of being ahead | |--:|--:|--:|--:| | 10 | −0.27 | ±3.2 | 34.4% | | 100 | −2.70 | ±10.0 | 35.5% | | 1,000 | −27.0 | ±31.6 | 18.8% | | 10,000 | −270 | ±100 | 0.33% |
After 10 bets about a quarter of sessions are exactly even, which is why the chance of being ahead is lower there than after 100. On the 15-slot wheel's T bet, with its higher edge, the chance of being ahead falls from 29.8% after 10 bets to 22.1% after 100 and 1.6% after 1,000. The bonus bet, at the same edge, keeps the chance alive longer (26.6% after 1,000 bets, 2.85% after 10,000) because one 14× hit covers many misses. The average cost is identical; only the spread differs. The gambler's fallacy article has more on streaks and short-run swings.
What the numbers don't tell you
The edge says what a game costs on average per coin wagered. It doesn't say what will happen tonight, and no way of sizing or timing bets changes it, as the betting systems article shows with Martingale and its cousins. For skill games the published figure assumes perfect play, so your real edge is that or higher.
What you can control is which game you play and how much you wager in total. cs2.casino shows each game's house edge and bet limits on the game, and over time the house wins. A lower edge means a smaller average cost per coin wagered, and fewer coins wagered means a smaller total.
