Comments on: Analysis of Strategies for the n-Door Monty Hall Problem http://someoneandanyone.wordpress.com/2008/05/21/analysis-of-strategies-for-the-n-door-monty-hall-problem/ "I walk slowly, like one who comes from so far away he doesn't expect to arrive." Mon, 27 Oct 2008 18:20:20 +0000 http://wordpress.com/ hourly 1 By: Charles http://someoneandanyone.wordpress.com/2008/05/21/analysis-of-strategies-for-the-n-door-monty-hall-problem/#comment-180 Charles Thu, 28 Aug 2008 00:27:37 +0000 http://someoneandanyone.wordpress.com/?p=29#comment-180 I believe that if you want to maximize the probability of your current choice being C, you must switch at every stage, i.e., if you believed that the game was going to end at a random time. Also, I believe the path you follow while switching doors matters, and that your analysis of strategy four is imprecise (though you are correct that by the last door, it is inferior to strategy two). Intuitively, strategy two is the best if you know the game will proceed until the last door: you choose a random door with P of C 1/n. While losing doors are revealed, this probability will never change so long as it is your choice. P of C for the other closed doors will rise each time a losing door is opened. When you make the switch to the final door, it has P of C (n-1)/n ... but only if you stayed with your initial door for the rest of the game. Do you see why this casts some doubt on your analysis of strategy four? I believe that if you want to maximize the probability of your current choice being C, you must switch at every stage, i.e., if you believed that the game was going to end at a random time.

Also, I believe the path you follow while switching doors matters, and that your analysis of strategy four is imprecise (though you are correct that by the last door, it is inferior to strategy two).

Intuitively, strategy two is the best if you know the game will proceed until the last door: you choose a random door with P of C 1/n. While losing doors are revealed, this probability will never change so long as it is your choice. P of C for the other closed doors will rise each time a losing door is opened. When you make the switch to the final door, it has P of C (n-1)/n … but only if you stayed with your initial door for the rest of the game. Do you see why this casts some doubt on your analysis of strategy four?

]]>