Small experiments, serious curiosity.

Three statistical ideas to play with: a distribution forming, π from random points, and a game against Gaussian noise.

Each peg is a coin flip, so the pile at the bottom approaches a Normal distribution; the dashed line is that Gaussian. Bias weights the coin.

Bias

Speed

Balls

Mean bin

0.00

Throw random darts at a square. Four times the share that lands inside the quarter-circle estimates π, and the error shrinks roughly like 1/√n.

π estimate

—

Darts thrown

Relative error

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The opponent computes exactly where the ball will arrive, μ, then aims at μ + σz with z ~ N(0, 1). At σ = 0 it never misses. AI’s mind shows the bell it samples from. First to 7 wins.

AI noise σ

You · CPU

0 · 0

Rally

Best

σ (px)

Small experiments, serious curiosity.

Galton board

Monte Carlo π

Pong vs. a Gaussian