Program logic bugs vs input/environmental errors

[Timon Gehr via Digitalmars-d]

On 10/08/2014 02:37 AM, H. S. Teoh via Digitalmars-d wrote:
> On 10/08/2014 12:10 AM, Nick Sabalausky wrote:
> [...]
>> I've managed to grok it, but yet even I (try as I may) just cannot
>> truly grok the monty hall problem. I *can* reliably come up with the
>> correct answer, but *never* through an actual mental model of the
>> problem, *only* by very, very carefully thinking through each step of
>> the problem. And that never changes no matter how many times I think
>> it through.
> [...]
>
> 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
> in the given scenario. Of course, this scenario is also often told in a
> deliberately misleading way -- the fact that the host *never* opens the
> right door is often left as an unstated "common sense" assumption,
> thereby increasing the likelihood that people will overlook this minor
> but important detail.
>
>
> T
>

The problem with this explanation is simply that it is too long and 
calls the overly detailed reasoning a 'secret'. :o)
It's like monad tutorials!