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Mathematics
Plinko probability
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One path, one outcome
100 balls fall through the board in sequence. Pause or slow down to observe; results update as each ball leaves the last peg.
Changing rows, probability or seed starts a new sample and clears the comparison.
- Recorded
- 0
- Not yet recorded
- 0
- Mean
- —
- Sample standard deviation
- —
- Standard error
- —
Mean n·p: 6
Standard deviation √(np(1−p)): 1.732
- Current sample
- 0 · 0%
- Theoretical probability
- 22.6%
Pin a sample, then drop more balls to compare frequencies on the same axis.
Each row is a left-or-right choice. Only balls that have left the last peg count in the sample. The curve shows theoretical probabilities; a small sample does not necessarily resemble it.
Model notes
- Each row is a Bernoulli trial with the same probability of going right. Choose 1–26 rows and probability 0–1; a seed makes the trial sequence reproducible.
- Probability determines the path in advance. Parabolic motion illustrates falling between pegs; it is not a mechanical collision solver. Results are recorded on leaving the last peg, before the ball comes to rest.
- Pause both the feeder and motion, release a single ball or a sequence of 100. Batch drops retain the same random sequence and counting rules; slow speed lets you inspect each stage. Changing parameters resets the sample and cancels the batch.
- Sample, comparison and theory share a fixed frequency axis from 0 to 100%. Sample SD uses N−1; SEM = SD/√N. For 0 or 1 balls the model returns 0 by convention; the UI shows — for an empty sample.
- The limit is 9,999 balls in one bin and up to 64 moving balls. Reopening pauses the simulation so observation can continue.