Galton Board Distribution Lab

Galton rows

Bins = rows + 1

Galton pRight

pRight: 0.50

Balls per batch

Drop to populate Galton + (optional) u-samples.

Animation speed

Speed: 1.00

Risk generation method

Dropped balls generate u-samples; distributions update live.

Sim samples (MC/LHS)

Simulate replaces/extends u-samples.

PIT uniformization

Make pRight/rows affect cost shape (OFF) vs correct uniform u (ON).

Risk distribution

Theory vs empirical updates instantly.

Apply to cost as

Direct: $ | Delta: $Δ | Mult: factor.

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Units

Applies to Base + Budget inputs and cost-like params.

Base cost

Anchor for delta/mult mapping + auto-fit.

Budget threshold

Used for exceedance + auto-fit target.

Target P-level

P80 → –

Uncertainty

CV-ish: 0.15

Right-tail

Skew: 0.55

Simulate replaces samples

Recommend ON for learning (clean comparisons).

Last drop explained

Drop a ball to see: bin → u → Q(u) → cost

Galton balls: 0

u-samples: 0

E[cost]: –

P(cost > budget): –

Skew(cost): –

Tail(P95/P50): –

Galton Board —

Tap/click to drop a ball. “Last Path” highlights the most recent route.

Galton Histogram —

Bin index k on X-axis (0…rows). This is the binomial shape (normal-ish when rows are larger).

Cost PDF (Histogram + Theory) —

Budget is shown as a vertical line. Changing distribution/params/base/apply mode remaps instantly.

Cost S-Curve (CDF) Interactive

P10/P50/P80/P90: –

Distribution Explanation –

What you’re seeing –

Drop balls or simulate u-samples to see interpretation + convergence notes.

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