My Chance 3 — Lottery and betting odds mathematics | mychance3.com
The European wheel has 37 pockets and a 2.70% house edge; the American wheel adds a double zero, has 38 pockets and holds 5.26% on nearly every bet.
Roulette odds come from pocket counts. A European single-zero wheel has 37 pockets — 18 red, 18 black and one green zero. An American wheel adds a double zero for 38 pockets while the payouts stay the same, and that single extra pocket is the entire difference between the two games.
Take an even-money bet such as red. On the European wheel it wins 18 times out of 37 and pays 1-to-1, leaving the house 2.70% of every unit over the long run. On the American wheel the same bet wins 18 times out of 38, and the unchanged payout lifts the house edge to 5.26% — nearly double, on almost every bet on the layout.
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The break-even test from numbers games applies unchanged. A fair 1-in-6 bet must pay 5-to-1 for zero expected value; paying only 4-to-1 leaves an expected loss of 16.7% of every unit staked. Roulette's single-number bet works the same way: the payout is set as if there were 36 pockets, and the zero — or two zeros — is the margin.
Volume does not rescue a negative edge. In a fair 1-in-6 game repeated 1,000,000 times, wins average 166,667 with a standard deviation of about 373 — long runs cluster tightly around the expectation. With a house edge in the formula instead of fairness, the same clustering works against the player, session after session.
Compared with a 500-to-1 pick-3 straight carrying a 50% expected loss, even the American wheel is cheap per unit staked — 5.26% against 50% is an order-of-magnitude difference. The pick-3 odds page derives that 50% figure, and the odds calculation guide shows how to run the same comparison for any game.
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