Probability is essential in Roulette betting as it informs players about the odds of winning for different bets. Each type of bet has specific winning probabilities based on the total outcomes on the wheel. For instance, in European Roulette, a straight-up bet on a single number has a winning probability of approximately 2.63%, given there are 37 pockets (0-36). Understanding these probabilities allows players to make informed betting decisions, evaluate risk versus reward, and develop strategies while managing their bankrolls.