Bayesian Connect 4

Your device secretly chose how good the computer is. Work out its skill from the way it plays.

How to play

You are red and go first. Tap a column to drop a disc; it falls to the lowest empty hole.
Make four in a row, across, down or diagonally, before the computer does.
The computer's skill is a secret number from 0 (plays at random) to 20 (sharp). Every move it makes updates the chart under the board: your belief about that skill.
The heat map shows where it will probably play next. On a computer, hover a column to preview its likely reply.
When the game ends you see its true skill, and whether your 80% range caught it.

Playing with a class? Tap Join a class room and enter the code you were given, and your games go on the class leaderboard.

Your move

The board

You are red. Tap a column to drop a disc.

Bayes' rule on the computer's last move

Prior Likelihood (rescaled to sum to 1) Posterior

computer's skill β (0 = random, 20 = sharp)

Why: how each column scored for the computer

Q = what a five-move lookahead expects (+1 a sure win, −1 a sure loss). A skilled player picks high-Q columns, so a high-Q move is evidence of skill.

Your read on the computer

Posterior mean 80% interval

after each of its moves

What the computer believes about you

Where it started What it believes now

your skill β

Games

You won

Computer won

Drawn

What is hidden, and how we learn it

Nothing on the board is hidden. The computer is: before the game, your device drew its skill β at random from 0 to 20 and told nobody.

Prior: every skill from 0 to 20 equally likely, which is exactly how it was drawn. Likelihood: how probable the column it chose would be at each skill. It scores every column, then plays column j with probability proportional to e^β·Q_j. Posterior: prior × likelihood, rescaled to sum to 1. It becomes the prior for its next move.

A forced or obvious move barely moves the posterior: every skill would have played it. A subtle good move, or a blunder, moves it a lot.