House edge
The house edge is the share of each amount staked that the rules of a game are expected to retain once every outcome has been weighted by its probability. It is fixed entirely by the difference between the prize a game pays and the prize a game with no edge would have to pay for the same result. On a wheel of thirty-seven pockets that pays 35 to 1 on a single number, that difference works out at exactly one part in thirty-seven, or 2.70 %. per unit staked
The figure is derived in full, from the pocket count upward, on the House edge entry.
Topic chapters
Probability
What a probability is, how outcomes are counted, and how a bet's average result is worked out.
Lotteries and Draws
Counting selections, dividing pools, and how a draw game's return is fixed before any tier is set.
Odds and Prices
How prices are written in the three common notations, and what a price implies about probability.
House Advantage
The structural difference between the prize a game pays and the prize a fair game would pay.
Variance and Streaks
How far results scatter around their average, and how that scatter behaves as trials accumulate.
Games and Rules
The specifications, mappings and rules that decide what a game returns and how often it returns it.
Recently added entries
The eight entries written most recently, in the order they were written. This index keeps no publication calendar.
Editorial note
Two conventions govern everything printed here. The first is that a percentage is meaningless without the quantity it is a percentage of, so every figure on this site is printed with the base it is measured against: per unit staked, per spin, per draw, per market. A 4 % figure per unit staked and a 4 % figure per hour of play are not the same number and cannot be compared. The second is that every figure is derived on the page that states it, from assumptions written out in full, rather than asserted or attributed to an outside authority.
Applying those conventions to commercial games produces one plain arithmetic result, which is stated here once rather than repeated on every page. Every game offered commercially pays less on a winning result than a game with no edge would have to pay. That gap is not an incidental feature of any particular game; it is the mechanism by which the game produces revenue, and it is fixed in the rules before any play occurs. Because the gap is fixed and each trial is independent of the last, the expected result of continued play is a loss proportional to the total amount staked, and the proportion of trials that finish in loss approaches certainty as the count of trials rises. No sequence of stakes, no pattern of timing and no run of prior results alters that arithmetic, and nothing on this site should be read as suggesting otherwise.
This index describes how these figures are calculated and where the rules that fix them came from. It does not describe how to play any game, and it recommends nothing.