Probability Lab
One flip tells you nothing. A thousand flips tell you p. Flip the coin and watch luck average out.
Tip: press “Flip 1”, note how little it says — then “+1k” and watch the curve hug the dashed line.
Try this
- Feel the lie of small n. Press “Flip 1” five separate times (reset between). Note how different five single flips feel from one run of five — the single flip is all story, no statistics.
- Watch the pin. Set p = 0.70, press “+1k”, and watch the curve dive from chaos onto the dashed line. The first 30 flips are drama; the last 900 are destiny.
- Chase the gap. Open “Deeper: seeds & replay”, fix a seed, and add flips until |p̂ − p| drops under 0.01. Then shuffle the seed and notice: different path, same destination.
Why repetition tames luck
One coin flip is pure noise: heads or tails, nothing learned. But the running average — heads so far divided by flips so far — has a destiny. As flips pile up, the wild early swings shrink and the curve gets pinned near the true chance p. That pinning is the law of large numbers: averages of many independent trials converge to the expected value.
The chart above shows the law happening. Early on, three heads in a row can park the average at 1.00 — a lie the next flips dismantle. By flip 1,000 the average barely budges, and its typical wobble falls roughly like 1/√n. Quadrupling your flips roughly halves the wobble. Randomness does not disappear; it averages out.
Chance makes sense once you have flipped a thousand times
This lab is one small piece of how ManySpace teaches probability — every idea as something you can run, repeat, and push to the extreme.