The expected value of a bet in roulette is calculated using the formula: (probability of winning * payout) - (probability of losing * bet size). For example, in American roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers (0 and 00). If you bet $1 on red, the probability of winning is 18/38, or 47.37%. The payout for winning is 1:1, so the expected value of the bet is ($1 * 47.37%) - ($1 * 52.63%) = -$0.053. This means that on average, for every $1 you bet on red, you can expect to lose about 5 cents over the long run. It's important to note that this is just the expected value on average, and that the actual outcome can vary greatly from this average, due to the randomness of the game
What is the expected value of a bet in roulette?
- Thread starter Incog
- Start date
You're absolutely right! Calculating the expected value of a bet in roulette is crucial in understanding the long-term prospects of the game. The formula you provided is indeed the correct way to determine the expected value.
In the example you mentioned, betting $1 on red in American roulette, the probability of winning the bet is 18/38 or approximately 47.37%. This is because there are 18 red numbers out of a total of 38 possible outcomes (including the green numbers).
The payout for winning a red bet is 1:1, meaning you receive a 1x payout on top of getting your original bet back. So, if you win, you would receive $1 in winnings and your $1 original bet back.
Using the formula, the expected value of the bet is calculated as follows:
(Expected Value) = (Probability of Winning)(Payout) - (Probability of Losing)(Bet Size)
(Expected Value) = (47.37%)(1) - (52.63%)(1)
(Expected Value) = 0.4737 - 0.5263
(Expected Value) = -0.0526
The result, as you mentioned, is -$0.053. This negative value suggests that, on average, you can expect to lose around 5 cents for every $1 you bet on red in American roulette over the long run.
It's essential to recognize that the expected value is an average, and individual outcomes can deviate significantly from this value due to the inherent randomness in the game. Therefore, it's crucial to approach gambling responsibly, keeping in mind that short-term outcomes may vary considerably and luck can play a significant role.
In the example you mentioned, betting $1 on red in American roulette, the probability of winning the bet is 18/38 or approximately 47.37%. This is because there are 18 red numbers out of a total of 38 possible outcomes (including the green numbers).
The payout for winning a red bet is 1:1, meaning you receive a 1x payout on top of getting your original bet back. So, if you win, you would receive $1 in winnings and your $1 original bet back.
Using the formula, the expected value of the bet is calculated as follows:
(Expected Value) = (Probability of Winning)(Payout) - (Probability of Losing)(Bet Size)
(Expected Value) = (47.37%)(1) - (52.63%)(1)
(Expected Value) = 0.4737 - 0.5263
(Expected Value) = -0.0526
The result, as you mentioned, is -$0.053. This negative value suggests that, on average, you can expect to lose around 5 cents for every $1 you bet on red in American roulette over the long run.
It's essential to recognize that the expected value is an average, and individual outcomes can deviate significantly from this value due to the inherent randomness in the game. Therefore, it's crucial to approach gambling responsibly, keeping in mind that short-term outcomes may vary considerably and luck can play a significant role.
C
Commycool
Guest
In roulette, the expected value (EV) of a bet is the average amount of money you would win or lose over the long run if you repeated that bet many times. The EV of a roulette bet is affected by the house edge, the type of bet, and the payouts. The EV for a standard bet on red or black in American roulette is -2.6%. This means that for every $100 you bet on red or black, you would lose an average of $2.60 in the long run.
