What “bias” really means

A fair coin has P(Heads) = 0.5. A biased coin sets P(Heads) = p, where p≠0.5. It does not mean “every five flips contain exactly three heads.” Bias changes long-run frequency, not short-run patterns.

Why expose bias at all? Teaching, prototyping, and controlled activities. It’s a feature for experiments, not for gambling.

Streaks aren’t proof of bias

Humans overreact to streaks. Five heads in a row from a fair coin? Not shocking. What matters is sample size and expected variance. With only 10 flips, 7–3 outcomes are common. With 1,000 flips, the proportion tightens around the true p.

Read the stats like an adult

• Proportion after n flips is an estimate of p; it has uncertainty.
• Cumulative chart is your friend: if it drifts, ask whether sample size explains it.
• Replicability matters: share the link so others can observe the same sequence under the same seed.

Bias with integrity

If you enable bias (say 60% heads):

• State it clearly to participants.
• Use it for pedagogical goals (weighted decisions, experiments).
• Keep the seed visible so anyone can replay your run.

The motion should look honest

People trust motion cues. Our coin tosses upward, flips fast, bounces once or twice, then rolls to a stop. Impacts trigger distinct sounds; the final “ring” is subtle. It’s still 2D, but the timing and cues make it believable.

A quick classroom activity

1. Run 20 fair flips; mark heads and tails bars.
2. Predict whether 20 more flips will “even out.”
3. Turn on 60% bias and repeat; compare convergence.
4. Share both links so students can replay on their phones.

Limits and honesty

We promise determinism with seeds and a natural animation, not cryptographic security. For high stakes, use certified hardware RNGs and publish seeds plus logs.