Coin Flips and the Law of Large Numbers
Flip a coin again and again. The share of heads settles near one half, but the gap between heads and tails tends to widen.
0 flips: 0 heads, 0 tails (share 0.0%, gap 0)
Share of heads (dashed: 50%)
Heads − tails (dashed: ±√flips)
With a fair coin, the share of heads gets closer to 0.5 as flips accumulate (the law of large numbers). But the gap between heads and tails typically wanders by about the square root of the number of flips, so it tends to widen. The share is the gap divided by the number of flips, which is why it still settles near 0.5.
How to play
Press "Flip" for one coin, or "Auto" to keep going. The top chart shows the share of heads; the bottom one shows heads minus tails. Dashed lines are guides.
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With a fair coin, the share of heads gets closer to 0.5 as flips accumulate (the law of large numbers). But the gap between heads and tails typically wanders by about the square root of the number of flips, so it tends to widen. The share is the gap divided by the number of flips, which is why it still settles near 0.5.