Rules Desk
House edge is arithmetic, not luck
The edge on a wheel is a property of the gap between the number of pockets and the payout offered on hitting one.
House edge is not a force acting on a session and it is not a description of how a night went. It is a subtraction, and it can be carried out in a line.
Take a single-zero wheel. The ring holds thirty-seven pockets: one to thirty-six plus a green zero. A wager on one number therefore comes home once in thirty-seven attempts, on average, over a long run.
Now take the payout. That wager is paid at thirty-five to one, meaning thirty-five units returned in profit on a one-unit stake, plus the stake itself.
The gap between those two figures is the entire mechanism. There are thirty-six ways to lose and one way to win, and the win pays thirty-five rather than thirty-six. The shortfall of one unit, spread across the thirty-seven possible pockets, is the edge.
Every proposition on that cloth resolves to the same shortfall, which is why the even-money wagers, the columns, the dozens and the single numbers all carry the same edge on a single-zero wheel despite paying wildly different amounts. The payouts are computed as if the green pocket were not there.
The double-zero wheel adds a second green pocket without changing the payout table. There are now thirty-eight pockets and the single number still pays thirty-five to one, so the shortfall is two units rather than one, and the edge is correspondingly larger.
Two consequences follow, and both are frequently misstated. The edge describes a long-run average, so it forecasts nothing at all about a given spin or a given evening. And it is a fixed property of the payout table, so no pattern of stakes alters it: staking more, staking less, or staking in a sequence all leave the subtraction exactly where it was.