That wager pays even money, that is, if you win, you get whatever you bet, and if you lose that same amount. What is your expected value for this bet?

Question

In roulette, you may bet whether the number that comes up is odd (or even). ( Remember that 0 does not count as either odd or even.) The wager pays even money, that is, if you win, you get whatever you bet, and if you lose, you lose that same amount. What is your expected value for this bet?

Answer 1

Hi Nya,

The answer for all of these types of expected value questions depends on the frequency you would encounter a win event versus a loss event. Let's say the wager was on a coin flip and you bet $1. The expected value would be $1 since there is a 50% chance of you walking away with $2 and a 50% chance of you walking away with $0.

Expected value is calculated by adding all the different possible outcomes multiplied by their probabilities. So in this case (.5 x $2) + (.5 x $1). For your specific example it would be determined by the number of options on a roulette wheel (generally 37). So you win on this bet in 18 outcomes (the even numbers) and lose on 19 outcomes (the odd numbers + 0). Putting it all together, your expected value is ((18/37) x (2 x wager [you receive the wager back and the winnings])) + ((19/37) x 0).

Hope this helps you understand expected value. Please PM me if you have any questions or if I wasn't clear.