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house edge
edge = -E[unit]House edge is the single number that makes a commercial game commercial. It is not a fee, a commission taken from winnings, or a setting that responds to how a session is going. It is the arithmetic difference between what an outcome is worth and what the game pays for it.
Derived from the payout table
Take any bet, list its outcomes, attach the payout the rules specify, and compute the expected value per unit staked. Negate it and express it as a percentage. That is the house edge, and there is nothing else in it. A game designer sets the edge by choosing payouts that are slightly short of the true odds — usually by paying as though one or two outcomes did not exist.
This is why the edge can be stated before the game opens, why it does not depend on the player, and why no sequence of results changes it. Results vary around it; the number itself is a property of the rules.
single zero: 37 pockets, even-money bet covers 18 E = (18 - 19) / 37 = -1/37 = -2.7027% edge 2.70% double zero: 38 pockets, even-money bet covers 18 E = (18 - 20) / 38 = -2/38 = -5.2632% edge 5.26% the rules changed by one pocket; the cost to the bettor nearly doubled
Edge, hold and RTP
Three figures are quoted in this area and they mean different things. House edge is expected loss per unit staked. Return to player is its complement, the share of stake returned on average, so an edge of 4% and an RTP of 96% are the same statement. Hold is different again: it is an observed accounting figure, the share of the money brought to a table or machine that was not carried away, and it is normally much larger than the edge because the same money is staked repeatedly.
| figure | denominator | nature |
|---|---|---|
| house edge | total amount staked | fixed by the rules, computable in advance |
| return to player | total amount staked | the complement of edge, same information |
| hold | money brought to the game | observed after the fact, depends on how long play lasted |
Return to player over what horizon
An RTP figure is an average over an enormous number of rounds — the kind of horizon a machine reaches over its service life and an individual never does. Over a few hundred rounds the distribution of results is wide enough that the average is nearly invisible inside it. This is not a caveat attached to the figure; it is what the figure means.
It follows that RTP says nothing at all about a session, and that two machines with the same RTP can produce completely different experiences depending on how the return is distributed. That second quantity is volatility, and it is treated in the reel machines entry.
Per round or per hour
Edge is quoted per unit staked, but exposure accumulates per round, and rounds arrive at very different rates. A game with a low edge played several hundred times an hour can cost more than a game with a high edge played slowly. Comparing edges without comparing round rates compares the wrong quantity.
game A: edge 1.4%, 60 rounds/hour, 10 units per round expected cost = 0.014 x 60 x 10 = 8.4 units per hour game B: edge 5.3%, 12 rounds/hour, 10 units per round expected cost = 0.053 x 12 x 10 = 6.4 units per hour the lower edge is the more expensive game as played
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Last modified 17 August 2026.