# Expected Value: a crash course

When analyzing politics I think largely in terms of expected value. This is a really useful tool I recommend for anyone interested in logical thinking, and it comes up in how I write on this blog. This post is a crash course in the subject.

In mathematics, specifically probability, the expected value of something is the most probable outcome of a given action. It is calculated by multiplying every possible outcome by its respective probability and adding those together. As a simple example, imagine flipping a coin and betting a dollar it will land on heads. If you are right (50% chance), you get a $1, and if you are wrong (50% chance) you get -$1. So the expected value is ($1)*(50%) – ($1)*(50%) = \$0. For another example consider a standard six-sided die. The expected value of what you will role is determined by multiplying the numbers on each face by one-sixth and adding them together, which provides a value of 3.5.

In both of these situations the expected value is actually a value that is impossible to get. Rather it is the average outcome of the action is repeated an infinite number of times. This helps tell one the real value of their investment—lottery tickets are a good example. Because the chance of winning the lottery is so small it dwarfs the potential winnings and it always costs money to buy a tick, the expected monetary value of a lottery ticket is always negative.

In the coming weeks I will try to post a few examples of how I use expected value to think about particular events.

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