### What does it take to be a hero? and other questions from statistical mechanics.

## 1 We only hear about the survivors

In the classic Star Trek episode Errand of Mercy, Spock computes the chance of success:

CAPTAIN JAMES T. KIRK : What would you say the odds are on our getting out of here?

MR. SPOCK : Difficult to be precise, Captain. I should say, approximately 7,824.7 to 1.

And yet they get out of there. Are Spock’s probability computations unreliable? Think of it another way. The Galaxy is a large place. There must be tens of thousands of Spocks, and Grocks, and Plocks out there on various missions. But we won’t hear (or don’t want to hear) about the failures. So they may all be perfectly good at probability theory, but we’re only hearing about the lucky ones. This is an example of survivor bias.

## 2 Simulation

We can model this. I’ve written a small battle simulator for a super-simple made up role-playing game...

And the rest of this article can be found at github

(Be sure to download the actual PDF if you want to be able to follow links.)

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