Roulette

European roulette — stack chips on numbers, colours, odds and dozens, spin the wheel and chase 35-to-1.

The wheel's mathematics is unusually blunt. A European wheel has 37 pockets and pays 35 to 1 on a single number, which leaves a house edge of 2.7 percent on every bet on the table. The American wheel adds a double zero, giving 38 pockets and an edge of 5.26 percent.

Every betting system fails against that for the same reason: the edge applies per spin, and no combination of bet sizes changes the expected value of the next one. Martingale doubling feels like it works because it wins small amounts often, and it ends the way it must — at the table limit, or the end of a bankroll, after a run that was always going to arrive.