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Roulette house edge per bet, with the arithmetic shown
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The roulette house edge is usually stated as a single figure per wheel: 2.70% European, 5.26% American. That is correct and slightly hides why. The edge is identical for every bet on a given wheel because of how the payouts were set, and seeing the working for each bet makes the whole game clearer. Here it is, row by row.
The method
For any bet, expected profit per £1 staked = P(win) × payout − P(lose) × 1.
A negative result is the house edge. On a 37-pocket wheel, P(win) = numbers covered ÷ 37.
European wheel, 37 pockets
| Bet | Covers | P(win) | Payout | Expected profit per £1 | Edge |
|---|---|---|---|---|---|
| Straight-up | 1 | 1/37 | 35 | 35/37 − 36/37 = −1/37 | 2.70% |
| Split | 2 | 2/37 | 17 | 34/37 − 35/37 = −1/37 | 2.70% |
| Street | 3 | 3/37 | 11 | 33/37 − 34/37 = −1/37 | 2.70% |
| Corner | 4 | 4/37 | 8 | 32/37 − 33/37 = −1/37 | 2.70% |
| Six line | 6 | 6/37 | 5 | 30/37 − 31/37 = −1/37 | 2.70% |
| Dozen | 12 | 12/37 | 2 | 24/37 − 25/37 = −1/37 | 2.70% |
| Even-money | 18 | 18/37 | 1 | 18/37 − 19/37 = −1/37 | 2.70% |
Every row ends at −1/37. That is not a coincidence; it is the design. Each payout is (36 − numbers covered) ÷ numbers covered, the fair odds for a 36-pocket wheel, applied to a 37-pocket one.
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French even-money with La Partage
On a zero, half the stake is returned. Expected profit per £1 on red: 18/37 × 1 − 18/37 × 1 − 1/37 × 0.5 = −0.5/37 = −1.35%. The one standard bet with a different, lower, edge. Inside bets, dozens and columns are unchanged on a French table.
American wheel, 38 pockets
Same payouts, one more pocket. Straight-up: 35/38 − 37/38 = −2/38 = −5.26%. Red: 18/38 − 20/38 = −2/38. Every standard bet: −5.26%.
The basket, 0-00-1-2-3 at 6:1: 5/38 × 6 − 33/38 × 1 = 30/38 − 33/38 = −3/38 = −7.89%. The one bet that gives up more than the wheel's share, because 6:1 is a long way below the fair 6.6:1.
Multiplier tables, briefly
A 29:1 straight-up on 37 pockets, with no multiplier, would be 29/37 − 36/37 = −7/37 = −18.9%. The struck-number multipliers pull that back; the published straight-up returns are 96.50% to 97.10% depending on the table, so the net edge on straight-ups is 2.90% to 3.50%. Outside bets are unchanged. The exact figure depends on multiplier frequencies the provider sets.
What the table tells you
Pick the wheel, not the bet, to change the price. On a given single-zero table every row costs the same, except the even-money row on a French table, which costs half. On an American table every row costs nearly double and the basket costs almost three times. That is the entire economics of roulette in one column.
Put it into practice
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People also ask
How is the roulette house edge calculated?
Expected return per £1 is (chance of winning × payout) minus (chance of losing × 1). On a European straight-up that is (1/37 × 35) − (36/37 × 1) = −1/37 = −2.70%. The same working gives −2.70% for every standard bet on that wheel.
Is the house edge the same as the RTP?
They are two sides of one number. RTP 97.30% means the house edge is 2.70%; the return plus the edge is 100%.