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🎲 Coin & Dice Simulator

As the number of trials grows,
do results get closer to theoretical probability?

Flip a coin or roll a dice many times. The red dashed line is the theoretically expected probability. Watch whether the bar heights get closer to the dashed line as the number of trials increases (this is called the law of large numbers).

If you flip a coin once and get heads, you can't say "this coin always lands heads," right? Even 7 heads out of 10 flips could still easily be chance. When the number of trials is small like this, the result can stray from the theoretical probability by quite a lot.

But increase the number of flips to hundreds or thousands, and the story changes. The random ups and downs start to cancel each other out, and the proportion of each outcome (the relative frequency) gets closer and closer to the theoretical probability. This is called the law of large numbers.

Click the 1, 10, and 100 buttons in turn and watch how the bar heights approach the red dashed line. You'll see for yourself how it starts out jumpy and gradually settles down.

Theoretical probabilityActual relative frequency
Total trials
0
Click a button to start flipping!