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
If the host picks randomly, then you will indeed not see better odds. 1/3 chance your original has prize, 1/3 the switched one has the prize, and 1/3 the one the host picked has the prize.
But the host didn’t pick randomly, they are guaranteed to always pick one without the prize. This changes the probability of all steps that proceed the host’s selection.
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