The expected value of a roulette bet is the average amount of money a player can expect to win or lose over time, based on the probabilities of different outcomes and the payouts for each bet.
The expected value is calculated by multiplying the probability of each possible outcome by the corresponding payout and then summing all of these values. This results in a positive or negative number, which represents the expected profit or loss for the player.
The expected value is important because it helps players determine the overall risk and potential reward of their bets. It also allows them to make more informed decisions about which bets to place and how much to wager.
The expected value can vary significantly depending on the type of bet. For example, inside bets (such as betting on a specific number) have lower probabilities but higher payouts, resulting in a higher expected value. Outside bets (such as betting on red or black) have higher probabilities but lower payouts, resulting in a lower expected value.
No, it is not possible for a player to have a positive expected value in roulette. This is because the payouts for all bets are slightly lower than the true odds of winning, giving the casino a slight advantage in the long run. This is known as the "house edge" and it ensures that the casino will always make a profit over time.