Is there a law that says if you do enough trials, rare things happen?

I’m trying to make a video about loaded dice, and at one point in the video we roll about 200 dice, take all the sixes, roll those again, and take all the sixes and roll those a third time. We had one die that came up 6 three times in a row, which is obviously not unusual because there should be a 1/216 chance of that happening and we had about 200 dice. So how do I explain that it’s not unusual? It doesn’t quite seem like the Law of Large Numbers. I want to say something like “If you do enough tests, even unlikely things are bound to happen” but my partner said people might take issue with the “bound to” terminology.

Is there a standard way to state this concept?


Law of truly large numbers:

“with a sample size large enough, any outrageous thing is likely to happen.”

Source : Link , Question Author : Cassandra Gelvin , Answer Author : Emilio M Bumachar

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