Re:350,757 coin flips show coins tend to land the same-side ...
by matsemann on Tuesday October 10, 2023 @12:33PM
(#37834298)
I've never been happy with that explanation. I don't get why the host would not just open a single door, that's what the host does in the other scenario to me.
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Re:350,757 coin flips show coins tend to land the same-side ...
by cstrahan on Tuesday October 10, 2023 @12:45PM
(#37834436)
> that's what the host does in the other scenario to me.
Is it, though? It seems apparent that, after the first guess, the host opens all but the last two doors, which just so happens to be 1 door.
To check the math:
Start with the $NUM_DOORS open doors. Now open all but the last two. So that’s $NUM_DOORS-2, which is 3-2, which equals 1 open door.
Re:350,757 coin flips show coins tend to land the same-side ...
by matsemann on Tuesday October 10, 2023 @02:07PM
(#37835406)
My interpretation of the host opening a single door and asking if you want to switch is equally valid when you expand it to 100 doors.
Re:350,757 coin flips show coins tend to land the same-side ...
by joshuamorton on Tuesday October 10, 2023 @02:14PM
(#37835490)
Sure, it could be that the host only opens one door, or it could be that he opens all but one door. In every case, however, it is better to switch. The all-but-one example is hyperbolic but still follows precisely the same mathematical rules. Your interpretation is valid, but so is the all-but-one example, and they all lead to the same result, it's just more obvious when you open nearly all the doors.