House edge
5.26%
= 2/38 of every unit you stake, on average
The Verification Venue · pointed at a thing everyone gets wrong
The Same Toll at Every Door
On an American roulette wheel, red/black and a lucky single number and a corner bet all carry the identical house edge: 5.26%, exactly 2/38. No bet is smarter than any other, and no system changes it. The edge lives in the wheel, not your choice. Pick a wheel and a bet below and watch it lock.
Roulette pays as if the wheel had only 36 pockets. An American wheel has 38 (the numbers 1 to 36, plus 0 and 00). A straight-up bet on one number pays 35:1, which would be a fair, break-even bet on a 36-pocket wheel. But there are two extra pockets you can also land on, so the true probability is 1/38, not 1/36. That gap, two pockets out of thirty-eight, is the entire house edge, and because every standard bet is shortchanged by the same two pockets, they all come out the same.
Bench 1 · recompute the edge from pockets and payout
Expected value per $1 staked
-$0.0526
win 18/38, lose 20/38
Try it: cycle through every American bet, straight-up, split, street, corner, six-line, column, dozen, red/black. The edge does not move. It reads 5.26% every single time. The folk belief that red/black is "safer odds" or a hunch number is "smarter" is simply false: the house takes the same 2/38 toll at every door.
Every bet, ranked · American double-zero
Watch the wall. On the American wheel every standard bet is a flat run at 5.26%, with one bar sticking out past it in red. Switch the wheel to European and the whole wall drops to 2.70%; switch to French and the even-money bets drop again, to 1.35%. Two honest complications finish the answer, and both matter more than which square you put your chips on.
Twist 1: one bet really is worse. None is better.
"Every bet is the same" is almost true, with one sucker exception
There is a single American bet that breaks the pattern, and it breaks it in the wrong direction. The five-number basket (covering 0-00-1-2-3 at once) pays 6:1. But a fair 36-pocket payout for a five-number cover would be 36/5 - 1 = 6.2:1. The casino rounds you down to 6, and that shortfall stacks on top of the usual two-pocket toll:
(5/38)(6) - (33/38)(1) = 30/38 - 33/38 = -3/38 = -7.89%
So the precise, quotable truth is not "all bets are equal." It is: no bet is better than 5.26%, and exactly one is worse. That still kills the superstition, because the superstition is always that some bet is smarter, and no bet is. The basket is a trap, not a shortcut. (It exists only on the American wheel; there is no 00 to combine on a European one.)
Twist 2: the real lever is the wheel, not the bet
Players agonize over the bet (provably pointless) and ignore the table (what matters)
Since no bet beats the edge, choosing a bet cannot help you. But choosing a wheel can, enormously, and it is the one lever players ignore. The edge is just the extra pockets over 36, divided by the total:
house edge = (N - 36) / N
American N=38 -> 2/38 = 5.26%
European N=37 -> 1/37 = 2.70% (one fewer zero)
French even-money, la partage -> 0.5/37 = 1.35%
Moving from an American double-zero wheel to a European single-zero wheel halves your expected loss, from 5.26% to 2.70%, by deleting one pocket. A French wheel with la partage ("the division") returns half your stake when the ball lands on zero, so even-money bets fall to 1.35%, a 4x improvement over American, achieved by changing nothing about how you bet. La partage only rescues the even-money bets, though: a straight-up on a French wheel is still 2.70%. The lesson is blunt. The bet you pick is decoration; the table you sit at is the decision.
| bet | pockets | pays | American 38 | Euro 37 | French la partage |
|---|
Twist 3: no betting system rescues you
The last hope people cling to is a system, and Martingale is the famous one: after every loss, double your bet, so the eventual win recovers everything plus one unit. It feels like a machine that prints small, reliable wins. It is, most of the time. What it cannot do is change the expected value. Every unit you stake still carries the same 2/38 loss, whatever pattern you stake it in. Run it below against flat betting and watch two things at once: the shape of outcomes changes completely, but the average loss per unit wagered lands on the same house-edge line in both.
Bench 2 · Martingale vs flat betting, red/black on an American wheel
Flat betting
run to compute
Martingale
run to compute
Both systems bleed at exactly the house edge. Martingale simply trades a wide spread of outcomes for a tall stack of small wins plus a rare, bankroll-erasing catastrophe (the long losing streak your finite bankroll and the table's maximum bet cannot ride out). It restructures when you win and lose, never whether. The expected loss stays pinned to the edge no matter the pattern.
The check: every number recomputed in front of you
Nothing here is a stored figure. For your current wheel and bet, the page derives the house edge from pocket counts and the posted payout, live, two ways: the per-bet EV, and the closed-form (N-36)/N.
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The offline gate reproduces every figure two independent ways and the Martingale convergence: node research/what-is-the-house-edge-in-roulette/verify-what-is-the-house-edge-in-roulette.mjs. Free choices & uncertainty. The house edge is a long-run expected value per unit staked, not a per-spin guarantee: variance is large, and a short session routinely ends well up or well down. Even-money bets share the identical edge but have far lower variance (you survive longer), which is a real difference in experience but not an odds advantage. The simulator uses a fixed table cap and bankroll for Martingale; changing them moves how often the rare ruin strikes, never the average loss. All payouts are the standard casino payouts; some casinos post slightly different rules (for instance, en prison instead of la partage), which land at the same 1.35% on even-money bets.
What's exactly true here, and what's a modelling choice
Exactly true (closed-form arithmetic). Every house edge on this page is exact and self-deriving from two integers and a payout. For a bet covering k of N pockets paying p:1, the edge is -[(k/N)·p - (N-k)/N]. Standard bets pay p = 36/k - 1 (a fair 36-pocket payout), so the edge collapses to (N-36)/N, which does not depend on k: that is why every standard bet is identical. American = 2/38 = 5.26%; European = 1/37 = 2.70%. The five-number basket pays 6:1 instead of its fair 6.2:1, so it alone reads 3/38 = 7.89%. French la partage refunds half the stake on the single zero for even-money bets, giving 0.5/37 = 1.35%.
A guarded claim, not a per-spin promise. "5.26%" is what the house keeps on average across many bets; on any one spin you win or lose the whole bet. Do not read it as "you lose 5.26% every spin." Short sessions deviate wildly, which is exactly why the game feels winnable.
Scope, kept honest. 5.26% is the American (double-zero) figure only; it is not "the" universal roulette edge. The European wheel is 2.70% and the wheel choice dwarfs the bet choice. La partage / en prison halves the edge only on even-money bets, not across the board. And lower-variance bets (even-money) are not better-odds bets: same edge, gentler ride.
A model, not arithmetic (the simulator only). Bench 2 is a Monte-Carlo draw, so its numbers wobble from run to run and converge to the edge as you add sessions. The Martingale "rare ruin" depends on the bankroll and table cap chosen; the invariance of the average loss does not. The point it demonstrates, that a system moves variance and not expected value, is a theorem, and the offline verifier pins the converged loss to 2/38 for both systems.