Estimating the chances of something that hasn’t happened yet
This reminds me of a different "rule of 3": If you want to compare two things (e.g., "is my new code faster than my old code"), a very simple approach is to measure each three times.  If the all three measurements of X are smaller than all three measurements of Y, you have X < Y with 95% confidence.<p>This works because the probability of the ordering XXXYYY happening by random chance is 1/(6 choose 3) = 1/20 = 5%.  It's quite a weak approach -- you can get more sensitivity if you know something about the measurements (e.g., that errors are normally distributed) -- but for a quick-and-dirty verification of "this should be a big win" I find that it's very convenient.