Something is behind a door — cat or not-cat, starting at 1 : 1 odds. Five toggleable clue cards each multiply the odds: furry times 4, meows times 10, purrs times 8, barks times one twentieth, huge times one fifth. On a log-odds ruler from minus 6 to plus 6, each active clue lays down a bar segment end-to-end (+1.4, +2.3, +2.1, −3.0, −1.6 points) and a dot marks the net sum; readouts show the odds product, the points sum, and P(cat) = sigmoid(sum) as a probability bar. Adding up scores and passing the total through a sigmoid is exactly logistic regression.

The cat detector: evidence adds points

Something is behind the door — cat or not-cat? Start at 1 : 1. Each independent clue multiplies the odds — so on the log ruler, it just adds points. Toggle the clues.

Independent clues multiply the odds, so on the log ruler they add. “Add up the scores, then sigmoid” is logistic regression — and it is the same shape as the reward model's Bradley–Terry gap: the sigmoid just translates a total on the straight ruler back into a probability.