More tries, steadier
Show on a big screenAfter one toss, the share of heads is 0 or 1. That is nowhere near the middle.
- A made-up run of twenty tosses, not a real toss.
- After 1 toss the share is 0 or 1.
- After 10 tosses the share wobbles near the middle.
- After 20 tosses it sits at 0.45, close to 0.5 but not on it.
What settling looks like
The share of heads is heads so far ÷ tosses so far. The running share is that share after each toss. To settle is to change less and less.
Toss once: the share is 0 or 1. Toss ten times: it is usually near the middle. Toss twenty, then a hundred. The running share keeps moving, but its swings usually shrink.
The share keeps moving
Smaller swings are not stillness. A run can look settled at toss 200. It can still move at toss 201. A late, small move is normal.
| After this many tosses | Running share |
|---|---|
| 1 | 1.0 |
| 10 | 0.5 |
| 20 | 0.45 |
Rule: More tries steady the share. They never fully still it. Each try is blind to the ones before it.
Blind here means earlier tries have no effect on a try.
The worked-out chance comes from counting the set-up. For a fair coin, that chance is 1/2. Law of large numbers — many tries bring the share near that chance. The share need not equal that chance exactly.
Drag the slider. Watch the line settle.
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Try the lab to finish this lesson.