Program logic bugs vs input/environmental errors

[Dominikus Dittes Scherkl via Digitalmars-d]

On Wednesday, 8 October 2014 at 01:22:49 UTC, Timon Gehr wrote:
>> The secret behind the monty hall scenario, is that the host is 
>> actually
>> leaking extra information to you about where the car might be.
>>
>> You make a first choice, which has 1/3 chance of being right, 
>> then the
>> host opens another door, which is *always* wrong. This last 
>> part is
>> where the information leak comes from.  The host's choice is 
>> *not* fully
>> random, because if your initial choice was the wrong door, 
>> then he is
>> *forced* to pick the other wrong door (because he never opens 
>> the right
>> door, for obvious reasons), thereby indirectly revealing which 
>> is the
>> right door.  So we have:
>>
>> 1/3 chance: you picked the right door. Then the host can 
>> randomly choose
>> 	between the 2 remaining doors. In this case, no extra info is
>> 	revealed.
>>
>> 2/3 chance: you picked the wrong door, and the host has no 
>> choice but to
>> 	pick the other wrong door, thereby indirectly revealing the
>> 	right door.
>>
>> So if you stick with your initial choice, you have 1/3 chance 
>> of
>> winning, but if you switch, you have 2/3 chance of winning, 
>> because if
>> your initial choice was wrong, which is 2/3 of the time, the 
>> host is
>> effectively leaking out the right answer to you.
>>
>> The supposedly counterintuitive part comes from wrongly 
>> assuming that
>> the host has full freedom to pick which door to open, which he 
>> does not
But yes. He has. It makes no difference.
If he would ever open the right door, you would just take it too.
So if the win is behind the two doors you did not choose first,
you will always get it.

> The problem with this explanation is simply that it is too long 
> and calls the overly detailed reasoning a 'secret'. :o)

So take this shorter explanation:

"There are three doors and two of them are opened, one by him
and one by you. So the chance to win is two out of three."
It doesn't matter if he uses his knowledge to open always a
false door. It only matters that you open your door AFTER him,
which allows you to react on the result of his door. If you
open the door first, your chance is only 1/3.