I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?
In: Mathematics
The key to the difference (and how it suddenly started making sense to me) is that Monty Hall, the game show host, knows where the prize is, and he’ll *always* open a door that leads to a goat. He’s not picking randomly, which is why the odds change from the first pick to the second pick.
The other replies go into the specifics of the calculation, but this explains *why* there’s a difference.
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