What the house edge actually measures
The house edge is the average share of each bet that a game keeps over a very large number of rounds. It is usually quoted as a percentage of the amount wagered. A game with a 2% edge keeps, on average, 2 units for every 100 units bet. It does not say that a player loses 2% of their bankroll, and it does not say what will happen in any one session.
The idea is a direct application of expected value: multiply each possible result by its probability and add the results up. The house edge is the negative of that average, expressed per unit staked. This page is about understanding the arithmetic, not about finding a way around it. As far as the math goes, none exists.
Where the margin comes from: true odds versus payouts
Every casino bet has two numbers attached to it: the real probability of winning and the payout the game offers. If the payout matched the real odds exactly, the game would be fair and the edge would be zero. The edge appears because the payout is set a little lower than the fair figure.
European roulette is the cleanest example. The wheel has 37 pockets: the numbers 1 to 36 and a single zero. A bet on one number wins with probability 1/37. A fair payout would then be 36 to 1, meaning you would receive 36 times your stake in profit. The game pays 35 to 1.
Working out the expected result of a 1 unit bet:
- Win with probability 1/37 and gain 35 units.
- Lose with probability 36/37 and lose 1 unit.
- Expected value = (1/37 x 35) - (36/37 x 1) = (35 - 36)/37 = -1/37, which is about -2.70%.
An even-money bet on red is different on the surface, but the result is the same. There are 18 red pockets, so it wins with probability 18/37 and loses with probability 19/37. Expected value = (18 - 19)/37 = -1/37, again about -2.70%. The single zero is what pushes the losing side from 18/37 to 19/37, and that one pocket is the whole margin. A closer look at the wheel and each bet type is in the article on roulette probabilities.
The same idea in other games
The mechanism is always a payout that sits below the fair price, but the source of the gap varies.
- Roulette: the zero (or the zero and double zero on an American wheel) is not counted in the payout ratios. With two zero pockets the edge on the same bets is 2/38, or about 5.26%.
- Craps: the pass line wins with probability 244/495, about 49.29%, and pays even money. That gives an edge of roughly 1.41%.
- Blackjack: the edge comes from the order of play, since the player acts first and can bust before the dealer plays. It also depends heavily on rules such as the blackjack payout and what the dealer does on soft 17.
- Slots: the edge is whatever remains after the programmed return is subtracted from 100%. See the article on return to player.
Because the edge depends on the exact rules and pay tables, two games with the same name can have quite different margins.
Edge, hold and return to player
Three terms are often confused:
- House edge is the theoretical average margin on each unit wagered.
- Return to player (RTP) is the other side of the same number: RTP = 100% minus the house edge. A 96% RTP means a 4% edge.
- Hold is what the casino actually kept in practice, as a share of money exchanged. It will wobble around the theoretical edge, and it can also be affected by how players move money between bets.
The edge is a theoretical long-run figure. Hold is an observed figure over a specific period.
Why a small percentage is reliable in the long run
A 2.70% edge sounds minor, and in a single bet it is invisible: you either win or lose the whole stake. The edge only becomes a pattern when many bets are added together, which is the law of large numbers at work.
Suppose a player makes 1,000 even-money bets of 10 units each on a European wheel. Total wagered is 10,000 units. The expected loss is 2.70% of that, or 270 units. But each bet is close to a coin flip, so the typical spread around that expectation is large. The standard deviation of the total result is about 10 x the square root of 1,000, which is roughly 316 units. So a result anywhere from a sizeable profit to a loss well above 270 is plausible. That spread is why short-run results often look nothing like the average, and why individual winners are common even though the long-run average is negative for the player.
This is also where game variance enters. Variance describes how widely results scatter; the edge describes where the average sits. A high-variance game can have the same edge as a low-variance one and feel completely different to play.
What the edge does not do
- It does not make a particular spin or hand “due”. Each round is one of a series of independent events, and the wheel or deck has no memory of earlier results.
- It does not depend on the casino’s mood, time of day or the player’s recent luck. It is a property of the rules.
- Changing how much you bet, or varying bets after wins and losses, rescales the amounts but not the average percentage lost. The article on why betting systems cannot beat negative expectation covers that in detail.
Many mistaken beliefs about streaks and “hot” tables come from cognitive biases rather than from anything in the math, which is part of why the edge is so often underestimated.
Reading an edge figure sensibly
When you see a published edge or RTP, check what it assumes. For blackjack and video poker, the figure usually assumes a specific strategy played without mistakes; real play tends to produce a higher edge. For slots, the figure is a long-run average across a very large number of spins, so it says little about a short visit. For any game, the number is a description of an average, not a forecast of your result, and gambling outcomes are uncertain in a way that no calculation removes.
If gambling stops being a form of entertainment with a known cost, the article on responsible play lists warning signs and places to find support.