Billy Foster, PhD

Billy Foster

Clinical Assistant Professor of Economics at

Find me on:

           

Quotations

The ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else. Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. — John Maynard Keynes, The General Theory of Employment, Interest and Money (1935)

Expected Value and Fair Bets

Expected value is a concept that allows us to factor in the probability of an uncertain event into our calculations. Imagine that you have a summer roofing job in Sandy, Oregon. I chose Sandy because it gets 182 precipitation days per year so on any given day there is a 50% chance of not working due to the weather. If you get paid $80 per day worked and $20 when you do not work due to rain, what should you expect to make in a twelve-week summer? Let’s break this down into a smaller problem.

The expected value of any given workday is the average of the payment received for working ($80) and not working ($20), which is $50. This is because there is an equal chance of either type of day occurring. By extension, the expected value of a five-day work week is $250 and of total summer income is $3,000.

What does this have to do with betting? A fair bet has an expected value of zero. For example, a bet of $10 on a coin flip is fair. There is an equal chance of losing or gaining $10. The average of these two values (+10 and -10) is zero. Casinos make their money by offering unfair bets. The expected value of (almost) every casino bet is negative (and none of them are positive). They cannot collect a guaranteed profit from a fair game so they count on you to play a rigged one. What do you suspect about the expected value of casino profits?

Leave a Reply