Comments on: A new approach to the Monty Hall problem http://www.reenigne.org/blog/montyhall/ Stuff I think about Sun, 22 Jan 2012 21:39:31 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Andrew http://www.reenigne.org/blog/montyhall/comment-page-1/#comment-4063 Andrew Thu, 23 Jun 2011 13:37:36 +0000 http://www.reenigne.org/blog/?p=22#comment-4063 The first step isn't always the same, since there are two possibilities for what's behind the door that you chose (car or goat). They just look the same when you don't have all the information. The chance of winning isn't 50/50, as you can verify experimentally - changing doors does give you an advantage. Do you still think it's 50/50 if there are 100 doors and the host opens 98 "goat" doors? The first step isn't always the same, since there are two possibilities for what's behind the door that you chose (car or goat). They just look the same when you don't have all the information. The chance of winning isn't 50/50, as you can verify experimentally - changing doors does give you an advantage. Do you still think it's 50/50 if there are 100 doors and the host opens 98 "goat" doors?

]]> By: Alexandre da Cunha Serpa http://www.reenigne.org/blog/montyhall/comment-page-1/#comment-4062 Alexandre da Cunha Serpa Thu, 23 Jun 2011 12:24:03 +0000 http://www.reenigne.org/blog/?p=22#comment-4062 The main error in the current discussions of the Monty Hall Paradox/ Problem is that everyone is considering the problem as a “one step problem” whereas it is actually a “two step problem”. The first step is the irrelevant part of the problem and is the part in which you choose one out of three doors and then the show host opens the door that has the goat (out of the two doors that you did not choose). The second step is the part in which you choose to change doors or not (or, in other words, the step in which you choose one of two doors). Given that THE FIRST STEP IS ALWAYS THE SAME, i.e., you pick a door and the host opens, out of the two unchosen doors, the one that has the goat. Therefore THE FIRST STEP DOES NOT ADD ANYTHING UNKNOWN, it is thus irrelevant for the statistical calculations (it has a 1.0 probability). The first step shall then be disregarded, for it is just a technique to create the illusion of a more complicated game. The problem can be then focused on the second step, which always begins in the same manner: one of the three doors (the one that was opened by the host and which contains the goat) is out of the equation and you have to choose one out of two doors. That is it, there is no need for complex calculations, the actual game is quite simple: given those TWO doors, choose one! (the “change your first choice” thing is just to create a feeling of mistery/ risk that does not exist actually). It is then a very simple: 50/50 chance of winning the car or not. If you want to make things more complicated and actually discuss if the person is “changing” the doors, it remains the same, for you do NOT consider 3 choices, you only consider 2 choices (the third door is always opened and, thus, removed from the discussion). Then let’s say you initially chose (out of the 2 doors) the door with the car behind and you change, you lose, but if you do not change you win (50/50 chances). The same applies if you chose the door with the goat. The main error in the current discussions of the Monty Hall Paradox/ Problem is that everyone is considering the problem as a “one step problem” whereas it is actually a “two step problem”.
The first step is the irrelevant part of the problem and is the part in which you choose one out of three doors and then the show host opens the door that has the goat (out of the two doors that you did not choose).
The second step is the part in which you choose to change doors or not (or, in other words, the step in which you choose one of two doors).

Given that THE FIRST STEP IS ALWAYS THE SAME, i.e., you pick a door and the host opens, out of the two unchosen doors, the one that has the goat. Therefore THE FIRST STEP DOES NOT ADD ANYTHING UNKNOWN, it is thus irrelevant for the statistical calculations (it has a 1.0 probability).
The first step shall then be disregarded, for it is just a technique to create the illusion of a more complicated game.
The problem can be then focused on the second step, which always begins in the same manner: one of the three doors (the one that was opened by the host and which contains the goat) is out of the equation and you have to choose one out of two doors.
That is it, there is no need for complex calculations, the actual game is quite simple: given those TWO doors, choose one! (the “change your first choice” thing is just to create a feeling of mistery/ risk that does not exist actually).
It is then a very simple: 50/50 chance of winning the car or not.

If you want to make things more complicated and actually discuss if the person is “changing” the doors, it remains the same, for you do NOT consider 3 choices, you only consider 2 choices (the third door is always opened and, thus, removed from the discussion).
Then let’s say you initially chose (out of the 2 doors) the door with the car behind and you change, you lose, but if you do not change you win (50/50 chances). The same applies if you chose the door with the goat.

]]> By: mikey http://www.reenigne.org/blog/montyhall/comment-page-1/#comment-3894 mikey Mon, 11 Oct 2010 02:19:38 +0000 http://www.reenigne.org/blog/?p=22#comment-3894 Nice explanation. Just FYI, Monty Hall is a real person and hosted the game show 'Let's Make a Deal', on which this problem is based. Nice explanation.
Just FYI, Monty Hall is a real person and hosted the game show 'Let's Make a Deal', on which this problem is based.

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