Plinker

A Galton board you can rig. Balls bounce left or right at each peg; bars show the observed distribution, the white curve is the exact theoretical one.

Left-vs-right gap over time

Both panes plot the same number — how many more balls landed left than expected. Across: balls dropped, on a log scale. The band is the typical range: widening like √n above, shrinking like 1/√n below. Nothing pulls the line back to zero — it only crosses by wandering.

Balls

In flight

Mean

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Std dev

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Theory mean

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Theory SD

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Max |error|

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Board

Buckets 12

Peg rows 11

Link rows to buckets (rows = buckets − 1)

Frame

Spawning

Simulation clock

Speed 1.0× · 40/s

Instant mode (skip animation)

Space play/pause · → step one peg row · Shift+→ one frame. Pausing freezes every ball where it is. Stepping on an empty board releases one ball, so you can walk it down peg by peg.

Spawn points

Drag the funnels along the top of the board to reposition. Weight sets how often a spawn is used; bias is its chance of bouncing right at every peg.

Gates

Memory

Memory mode — pegs learn

Each peg remembers which way balls went through it and leans that way next time, so early luck compounds instead of averaging out. The white curve and the shaded band still show what independent trials would predict — watch the board walk away from them. Reset starts a fresh run and forgets everything, so a different side can win.

Display

Buckets show

Surplus / shortfall band Gap-over-time chart Theoretical curve Bucket labels & percentages Show pegs