probability

You have a coin that lands heads with some unknown probability p. Build a fair 50/50 flip from it without knowing p. The von Neumann trick is two lines; the part that scores is explaining why the bias cancels and how many flips it costs.

Almost never, and the gap between score and probability quietly breaks thresholds, expected-value decisions, and customer trust. What calibration is, how to measure it, and the two fixes that work.

The base-rate trap is the classic, and it is not academic: it is exactly how a high-accuracy fraud or disease classifier drowns ops in false alarms. The worked numbers, the tree you draw on the whiteboard, and the two levers that actually fix it in production.

Picking the wrong distribution silently breaks your model: counts are not Gaussian, and treating them that way predicts negative events and underestimates the variance of busy periods. The decision tree by data type, the variance gotcha, and what each choice implies for the model you reach for.