Roulette is a popular casino game that involves a spinning wheel and a ball. The mathematics behind roulette is based on probability theory. The basic formula for calculating the probability of winning on a single number bet in European roulette is P = 1/37, since there are 37 pockets （numbers 0 to 36）. For American roulette, which has an additional double zero （00）, the probability becomes P = 1/38. 
Another important formula is the expected value （EV）, which helps players understand their long-term losses. For a straight-up bet on a single number in European roulette, the EV can be calculated as EV = （35 * 1/37） + （-1 * 36/37） = -0.027, meaning a house edge of about 2.7%. Similarly, for American roulette, the house edge is higher due to the extra zero.
Players often use strategies like the Martingale system, which involves doubling bets after losses. However, mathematical analysis shows that no strategy can overcome the house edge in the long run, as each spin is independent and the odds are fixed. |
