What is American vs European Roulette?

The two standard roulette wheels differ by one pocket. A European wheel has 37 pockets: the numbers 1 to 36 and a single zero. An American wheel has 38: the same numbers plus both a single and a double zero. The bets, the layout and the payouts are otherwise the same. That extra pocket is not cosmetic. Payouts on both wheels are calculated as if the zeros did not exist, so adding a second zero increases the gap between the true chance of an outcome and what the bet pays, and it does so on every bet on the table rather than on one. This is the reason the single-zero wheel is generally the one to look for when both are offered side by side in the same lobby. Some single-zero tables add a rule that applies when zero lands — commonly returning half of an even-money bet, or holding it for the next spin — which changes the arithmetic further in the player's favour on those bets only. The wheel type and any zero rule are both stated in the table's own information panel, and they are the first two things worth checking before sitting down.