What the house edge actually is

The house edge is not a fee, a commission or a cut taken from winnings. In almost every game it is a payout set slightly below the true odds of the event being bet on. Nothing is deducted, nothing is disclosed at the moment of settlement, and each individual bet is paid exactly as advertised. The advantage is built into the advertisement.

Consider the cleanest case. On a double-zero wheel a single number has thirty-eight pockets against it, so the true odds are thirty-seven to one. The payout is thirty-five to one. Two units of the honest price are withheld on every winning bet, which over thirty-eight spins comes to two units out of thirty-eight staked: 5.26%. Add a second zero to a wheel and you do not change the game's appearance at all, but you double its cost.

The figure is an average over all outcomes, not a charge on each play. A player betting one unit on a single number either loses one unit or gains thirty-five; they never lose 2.70 per cent of anything. What 2.70 per cent describes is the long-run rate at which stakes are converted into the operator's revenue, and that rate is what the operator, who is exposed to every bet placed all evening, actually experiences.

This is why edge per bet is a misleading way to compare games. A wheel resolving forty spins an hour at 2.70 per cent takes more from a given bankroll than a weekly draw at fifty per cent, because the wheel applies its small percentage forty times an hour and the draw applies its large one once a week. The quantity that matters to a player is edge multiplied by stake multiplied by the number of decisions, and games differ enormously in that third term.

A few bets carry no edge at all. The free odds wager taken behind an established craps line pays exactly true odds, so its expected value is zero. It exists because it cannot be made on its own: it must accompany a bet that does carry an edge, so the operator's percentage of total money on the table falls while the total money rises. A zero-edge bet inside a game is a marketing structure, not a flaw in the arithmetic.