Coin Flipper

Coin Flipper

Coin Flipper flips a virtual coin with an animation and tracks the running count of heads and tails.

How to use it

1. Flip the coin.
2. Read the result and the running tally.
3. Keep flipping to watch the ratio settle.

What the running tally demonstrates

Each flip is independent with a 50% chance either way. The tally is interesting because it shows two things people routinely confuse. The proportion of heads converges toward one half as you flip more, which is the law of large numbers.

The absolute difference between heads and tails does not converge. It tends to grow. So you can be forty flips ahead on heads while the ratio steadily approaches 50%, because forty is a shrinking share of a growing total. Expecting the counts to even out is the gambler's fallacy, and it is wrong.

When it helps

• Settling a decision fairly.
• Demonstrating probability to someone.
• Generating a random binary choice.
• Watching the law of large numbers actually happen.

Common mistakes

• Believing a run of heads makes tails more likely. The coin has no memory.
• Expecting the counts to equalise. The ratio converges, the raw difference does not.
• Using a coin flip for a decision you actually care about. If you feel disappointed by the result, you already knew your answer.