To convert any roulette payout into house edge fast, do this: identify the bet’s true odds from the wheel layout, convert the payout to its implied “fair” probability, then compare the two. In practice, roulette is simpler: for any standard roulette bet on a given wheel, the house edge equals the fraction of outcomes reserved for the house (the green zero pockets) divided by total pockets—as long as the casino pays the standard table payout. That’s why European roulette (1 zero) is 1/37 = 2.70%, American roulette (0 and 00) is 2/38 = 5.26%, and triple-zero variants reach 3/39 = 7.69%.
The 30‑second method (works for any standard bet)
Roulette payouts are engineered so that, on a fair wheel with no green pockets, the expected value is about zero. The green pockets break that fairness. You can compute the house edge from any single bet in seconds:
- Count pockets on the wheel
– European: 37 pockets (0–36)
– American: 38 pockets (0, 00, 1–36)
– Triple-zero: 39 pockets (0, 00, 000, 1–36)
- Count how many numbers win your bet (W)
– Straight up: W = 1
– Split: W = 2
– Street: W = 3
– Corner: W = 4
– Six line: W = 6
– Dozen / Column: W = 12
– Even-money (red/black, odd/even, high/low): W = 18
- Use the standard payout multiplier (m)
– Straight: 35 to 1 (m = 35)
– Split: 17 to 1
– Street: 11 to 1
– Corner: 8 to 1
– Six line: 5 to 1
– Dozen/Column: 2 to 1
– Even-money: 1 to 1
- Compute expected value (EV) per 1 unit staked
– EV = (W/N) * m – (1 – W/N)
- House edge is simply: house edge = -EV
Because standard roulette payouts are calibrated to the 36 “non-zero” numbers, the result collapses neatly to:
- House edge = (number of zero pockets) / N
That’s the key shortcut: once you know how many green pockets are on the wheel, every standard bet has the same house edge.
Why payout tables “hide” the edge (and where it really comes from)
A common misconception is that the payout itself determines the edge. In roulette, the payout is mostly a reflection of the 36-number core of the game:
- On a hypothetical wheel with 36 numbers and no zeros, a straight-up bet has true odds 1 in 36. A “fair” payout would be 35 to 1 (you profit 35 and get your stake back), matching the standard table.
- Add a zero (European), and true odds become 1 in 37, but the payout stays 35 to 1. That mismatch creates the edge.
This is why you can compute the house edge without even referencing the payout once you assume the standard schedule: the zeros are the entire economic engine of roulette.
Worked examples: convert payout to edge (fast and explicit)
Example 1: European straight-up (35 to 1)
- N = 37, W = 1, m = 35
- EV = (1/37)*35 – (36/37)
- EV = (35 – 36) / 37 = -1/37
- House edge = 1/37 = 2.70%
Interpretation: for every 100 units wagered on average, the theoretical loss is 2.70 units, assuming random outcomes and standard rules.
Example 2: European red/black (1 to 1)
- N = 37, W = 18, m = 1
- EV = (18/37)*1 – (19/37)
- EV = -1/37
- House edge = 2.70% again
Key insight: even though the payout looks “fair” at 1:1, the extra losing outcome (0) is what you’re paying for.
Example 3: American dozen (2 to 1)
- N = 38, W = 12, m = 2
- EV = (12/38)*2 – (26/38)
- EV = (24 – 26)/38 = -2/38
- House edge = 2/38 = 5.26%
Same edge as any other standard American roulette bet.
The “implied probability” shortcut (when you only see the payout)
If you’re given a payout and want to sanity-check it, convert it to implied probability, then compare with the true probability from the wheel.
- For payout m to 1, the fair win probability would be about 1/(m+1).
– Example: 35 to 1 implies fair probability 1/36 (2.78%).
- True probability is W/N.
– European straight-up is 1/37 (2.70%).
- The gap between 1/36 and 1/37 is what produces the negative EV.
This shortcut is useful for spotting non-standard paytables. If a straight-up pays 34 to 1, the implied fair probability becomes 1/35, which is worse for the player than the standard 35 to 1.
When house edge is not uniform: special rules that change payouts
Roulette is “same edge on all bets” only under standard payouts and no special settlement rules. Two common rule families alter the expected loss on even-money bets:
La Partage (European)
If the ball lands on 0, even-money bets lose half the stake (instead of the full stake). Result:
- European even-money house edge becomes 1.35% (half of 2.70%).
En Prison (European)
If 0 hits, the even-money bet is “imprisoned” and either:
- released with no loss if the next spin wins, or
- lost if the next spin loses
Depending on the exact implementation, it typically yields the same 1.35% theoretical edge on even-money bets.
Important nuance: these rules usually apply only to even-money bets, not to dozens, columns, or inside bets—so edges differ by bet type when these rules are active.
Turning house edge into “what it costs you”: expected loss and volatility
House edge tells you the long-run rate of loss, not the short-run experience. Two players can face the same 2.70% edge but wildly different bankroll swings depending on bet type.
Expected loss (the cost rate)
Expected loss per spin = stake * house edge
- Example: 10 units on European roulette → expected loss ≈ 10 * 0.027 = 0.27 units per spin
Over 500 spins at 10 units:
- Total wagered = 5000 units
- Expected loss ≈ 5000 * 0.027 = 135 units
Volatility (how bumpy the ride is)
Even when EV is identical, variance differs:
- Straight-up bets: low hit frequency, large payouts → high variance
- Even-money bets: frequent small wins → lower variance
A practical way to quantify “bumpiness” is to compute standard deviation per spin from win/loss outcomes and payout size. To operationalize that quickly, click here for the variance calculator that shows how the same house edge can produce very different dispersion for a 1-number bet versus an even-money bet, which matters for bankroll drawdowns and session risk.
A quick checklist to compute edge correctly (and avoid common mistakes)
- Confirm the wheel type (European 37, American 38, triple-zero 39). The same payout implies different edges across wheels.
- Verify the bet uses the standard payout. Any deviation (e.g., 6 to 1 on a six-line, 34 to 1 on a straight) changes EV.
- Check for special zero rules (La Partage / En Prison) and whether they apply to your bet.
- Distinguish between:
– House edge (expected loss rate per unit wagered)
– Hit rate (W/N)
– Volatility (variance/standard deviation), which governs short-run outcomes
Final Thoughts
Roulette house edge is usually a one-step calculation: zeros divided by total pockets, because standard payouts are built around 36 numbers. The only time you need deeper math is when payouts or zero-handling rules differ—then converting payout and probability into EV exposes the true cost immediately.
