The long run, not the next flip
A fair coin is a model: each flip is an even chance, and heads does not owe you a tails. The pine bars are that model. Your flips will miss them, then wander closer. They will not alternate to “catch up.”
Chance Lab
Watch chance settle into a rule
Flip, roll, and compare what happened with what the model said would happen. Short runs lie. Long runs tell the truth about the share — never about the next trial.
- Trials
- 0
- Widest gap
- —
- Usual wobble
- —
Ready when you are
A fair coin. Nothing tossed yet.
Slow enough to follow
Each run adds this many. Reset starts a fresh experiment. Up to 100,000.
How the trials landed
Share of all trials so far, beside the model.
ObservedExpected
Copper is what you got. Pine is what the model expects. Matching bars means the sample agrees with the theory.
| Outcome | Count | Observed | Theory | Gap |
|---|---|---|---|---|
| Heads | 0 | — | 50.0%1/2 | — |
| Tails | 0 | — | 50.0%1/2 | — |
A short classroom sequenceShowHide
- Stay on the coin. Press Step ten times. Notice the gap can be huge and still be fair.
- Set speed to Watch, run 100, and look at the coin as the bars chase 50%.
- Switch to two dice before running. Which pine bar is tallest, and why is it not “luck”?
- Slide heads to 70%, reset is automatic, then add 100 flips. Can you already see the tilt?
- Add 5,000 more. The wobble number shrinks like one over the square root of the trial count.