Roulette in Depth

European and American Roulette: The Effect of the Extra Zero

Compares single-zero (37 pockets) and double-zero (38 pockets) roulette, showing how one extra pocket roughly doubles the house edge on every standard bet.

On this page
  1. The one-pocket difference
  2. What the payouts assume
  3. The arithmetic for a $1 straight bet
  4. It applies to every standard bet
  5. A hypothetical hour at the table
  6. The five-number bet
  7. Why both versions exist
  8. What to take away

The one-pocket difference

Roulette is a game of chance with a built-in house edge. No strategy or timing changes the odds in the player’s favor over time, most players lose money in the long run, and nobody should gamble money they cannot afford to lose.

The two wheels most people hear about differ by a single pocket. A European (single-zero) wheel has 37 pockets: 1 to 36 plus one zero. An American (double-zero) wheel has 38: the same 36 numbers, a zero and a double zero. Both wheels pay the same amounts on winning bets, which is exactly why the extra pocket matters.

What the payouts assume

A straight-up bet on one number pays 35 to 1 on both wheels. That means a winning $1 bet returns $35 profit plus the original $1 stake.

On a 37-pocket wheel the chance of hitting a particular number is 1 in 37. A fair payout for a 1-in-37 chance would be 36 to 1, since you would risk one unit to win 36 on average once every 37 tries. The casino pays 35 instead, keeping the one-unit gap.

On a 38-pocket wheel the chance is 1 in 38, and a fair payout would be 37 to 1. The casino still pays 35, so the gap is two units.

The arithmetic for a $1 straight bet

On the single-zero wheel:

  • Win with probability 1/37, gaining $35.
  • Lose with probability 36/37, losing $1.
  • Expected result: (35 − 36) / 37 = −1/37, about −$0.027, or a 2.70% house edge.

On the double-zero wheel:

  • Win with probability 1/38, gaining $35.
  • Lose with probability 37/38, losing $1.
  • Expected result: (35 − 37) / 38 = −2/38 = −1/19, about −$0.053, or a 5.26% house edge.

The second figure is about twice the first (more precisely, 5.26 divided by 2.70 is a little under 2). One extra losing pocket costs the player roughly double.

It applies to every standard bet

The same pattern holds for the other regular bets, which reflects a uniform edge across bets on the same wheel. Take an even-money bet such as red. With 18 red pockets:

  • Single zero: win probability 18/37 (about 48.65%), lose 19/37 (about 51.35%).
  • Double zero: win probability 18/38 (about 47.37%), lose 20/38 (about 52.63%).

The expected loss on a $1 even-money bet is then 1/37 of a dollar on the first wheel and 2/38 of a dollar on the second, matching the straight-bet figures. The zeros are what make even-money bets not really even.

A hypothetical hour at the table

The numbers below are illustrative only. Suppose a player makes 100 spins at $10 each, so $1,000 in total is wagered.

  • Single zero: expected loss is $1,000 × 1/37, about $27.03.
  • Double zero: expected loss is $1,000 × 2/38, about $52.63.

These are averages across many sessions. Any single session can finish well above or well below them, because short-run results swing widely around the long-run expectation, a short-term fluctuation that can easily exceed the average. Over many spins, though, the law of large numbers pulls actual results toward the expected figure, and that figure is a loss.

The five-number bet

Many American-style layouts offer a bet on the five numbers 0, 00, 1, 2 and 3, paying 6 to 1. Its expected result per $1 is (5/38 × 6) − (33/38) = (30 − 33) / 38 = −3/38, which is about a 7.89% house edge. It is the only standard bet on that wheel that costs more than 5.26%, and it exists only because of the extra zero.

Why both versions exist

The two wheels have separate regional histories (part of roulette history), and which one a venue offers is a commercial and regulatory choice, not something a player can influence at the table. Some venues also offer rules that soften the zero’s effect on even-money bets, such as the French la partage rule.

What to take away

  • The only structural difference is one extra green pocket, but it changes the house edge from 1/37 to 2/38 on standard bets.
  • The pays are identical, so the player gets less for the same risk on the double-zero wheel.
  • Nothing about the wheel layout, the color of the pocket, or the previous spins can offset that cost.

If you are comparing the two for curiosity, remember that the lower figure is still a loss in expectation. The cheaper wheel is cheaper, not free, and the only reliable way to avoid losing money at roulette is not to wager it. Anyone who finds it hard to stop can contact a local support service.

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