Billy Foster, PhD

Billy Foster

Clinical Assistant Professor of Economics at

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Ask a physicist how long it would take a bowling ball to land if you dropped it from the roof of your house. He will happily assume that your house is located in a vacuum, and then proceed to calculate the right answer. Ask an engineer to predict the path of a billiard ball after it is struck at a certain angle. He will assume that there is no such thing as friction, and the accuracy of his prediction will give him no cause for regret. Ask an economist to predict the effects of a rise in the gasoline tax. He will assume that all people are rational and give you a pretty accurate response. — Steven E. Landsburg, The Armchair Economist (1993)

Posts Tagged ‘probability’

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?