Billy Foster, PhD

Billy Foster

Clinical Assistant Professor of Economics at

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As a skeptic, I reject a sole time series of the past as an indication of future performance; I need a lot more than data. My major reason for this is the rare event, but I have others. On the surface, my statement here may seem to contradict earlier discussions, where I blame people from not learning enough from history. The problem is that we read too much into shallow recent history, with statements like ‘this has never happened before,’ but not from history in general… [H]istory teaches us that things that never happened before do happen. — Nassim Nicholas Taleb

Posts Tagged ‘gambling’

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?