In this thread, I'd like links or explanations of all the statistical techniques or other key pointers for game designers that have come up.

I'll start with the basics of binomial distributions. Suppose you have a die which might yield a success or might not. You roll some number of these. Each one has the same probability.

If you roll n dice, and each die has a probability p of being a success, the probability of rolling exactly k successes is (p^k) * ((1 - p)^(n - k)) * nCk. nCk (read "n choose k") can be found using pascal's triangle, which looks like this:

Code:

```
1
1 2 1
1 3 3 1
1 4 6 4 1
```

Suppose we flip four coins and count the heads. What is the probability that we get exactly two? Since the coins are independant and each have a 50% chance of coming up heads, the answer is (.5^2) * (.5^2) * 6. This equals .25 * .25 * 6, or .375.