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RE: OT On the subject of logic & riddles page 6This is a discussion thread · 105 replies DPCondit: [nq:1]Monte's motives are at issue because it matters if he always gives you the choice or only gives you the ... he only offered the change when you had won, then you would lose 100% of the time by switching. R8480[/nq]If Monty has an option on whether to give you a choice at all, then that would introduce new variables, the answer would certainly not be so cut and dried. However, the assumption is that Monty will always show you one of the doors, and always give you a choice. My point is (which only holds true if Monty ALWAYS reveals a door, and ALWAYS gives you a choice), that how he picked what door to reveal is irrelevant.
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DPCondit: [nq:2]That is an important key point. Monty will never open ... he will always open a door with a booby prize.[/nq][nq:1]Note that although it is a key point, it isn't stated in the problem. That is part of the reason ... the other two doors where Monty knows the prize isn't. He then offers to let you switch doors. Should you?[/nq] Assuming that he ALWAYS shows you a door, and ALWAYS gives you a choice, the answer is yes. [nq:1]B) A prize is behind one of three doors. You choose one of the three. Monty doesn't know where the ... shows you what is behind it. The prize isn't there. He then offers to let you switch doors. Should you?[/nq] Assuming that he ALWAYS shows you a door, and ALWAYS gives you a choice, the answer is yes, same as the previous question. It does not matter how he arrived at the choice of doors. YOUR initial choice is still only 1/3rd chance of being correct.
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da pickle: [nq:1]Monte's motives are at issue because it matters if he always gives you the choice or only gives you the ... he only offered the change when you had won, then you would lose 100% of the time by switching. R8480[/nq]Suppose there is a fourth door!!! A trap door that Monte can control with a toe switch in his shoe. If he has 4 pounds (exactly) available to make it work.
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ruylopez: [nq:1]The motivations are irrelevant, whether the door is picked at random is irrelevant. If it was random, and Monty accidentally ... accident) is not the big prize, it is always a 2/3rds chance that the remaining door IS the big prize.[/nq]No! In the case where the door is selected randomly, it doesn't matter if you switch or not. Borrowing Lester's syle of showing this so well: Let's say the prize is behind 1. You pick / Monty shows / Result of switch == door 1 door 2 LOSS door 1 door 3 LOSS door 2 door 1 NO CHOICE door 2 door 3 WIN door 3 door 1 NO CHOICE door 3 door 2 WIN These are the only possible situations. When Monty shows you the prize the game is over. If Monty shows you a booby, in four sitations you are faced with a choice. Switching wins in two, and loses in two. The fact that he shows you a booby every time is why the problem works. Posted using RecPoker.com - http://www.recpoker.com
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DPCondit: [nq:2]The motivations are irrelevant, whether the door is picked at ... a 2/3rds chance that the remaining door ISthe big prize.[/nq][nq:1]No! In the case where the door is selected randomly, it doesn't matter if you switch or not. Borrowing Lester's ... two, and loses in two. The fact that he shows you a booby every time is why the problem works.[/nq] Wrong! You are showing two choices for when you correctly picked door 1. You would in reality only be offered one choice to switch when you picked door 1, not two. His choice of revealing door 2 or door 3 are 50% each, but HE IS ONLY GOING TO PICK ONE OF THEM. Therefore it would be correctly illustrated as Monty reveals EITHER door 2 or door 3, HE CANNOT REVEAL BOTH, so adding this as two outcomes CANNOT BE CORRECT.
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ruylopez: [nq:2]The fact that he shows you a booby every time is why the problem works.[/nq][nq:1]Wrong! You are showing two choices for when you correctly picked door 1. You would in reality only be offered ... reveals EITHER door 2 or door 3, HE CANNOT REVEAL BOTH, so adding this as two outcomes CANNOT BE CORRECT.[/nq] But here he has added new information, because it is possible that the door he opened had contained the prize. In the other scenario you get NO information from Monty opening a door, because you already knew he would show you a booby prize. In this situation you are being offered a parlay of the other two doors. Here you are not. You HAVE been given some information, but only that it is not behind the opened door. Switching is no longer giving you a parlay of those two doors, there are now only two doors in the game. The information you now have is that it is behind one of the two remaining doors. Either is equally likely. It's gonna take a sim to prove it, but I'd lay cash I'm right this time. Posted using RecPoker.com - http://www.recpoker.com
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ruylopez: .. I can show two choices for the door 1 situation here because I have also shown two choices for the other doors. Because they exist in this version of the problem. It is still perfectly balanced.It is key that the game ends, as it obviously would, if Monty shows you the prize. Obviously it would be a dumb show if, after showing you the correct door, you could just pick that one, as you suggest, and get it right every time. Posted using RecPoker.com - http://www.recpoker.com
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DPCondit: [nq:2]Wrong! You are showing two choices for when you correctly ... REVEAL BOTH, so addingthis as two outcomes CANNOT BE CORRECT.[/nq][nq:1]But here he has added new information, because it is possible that the door he opened had contained the prize. ... Either is equally likely. It's gonna take a sim to prove it, but I'd lay cash I'm right this time.[/nq] All right I guess if you did each one twice for each door you picked, that you would have four unknown choices, and of the unknown choices, 50% would be correct. Damn, I can't believe that I screwed that one up. Yes, it needs to be stated in advance that Monty may only choose a door with a goat. Peace, you got me this time! Good luck, Don
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DPCondit: It appears that I got this one wrong. If he picks randomly, and you know this, all other conditions being the same, then it evidently becomes a 50% choice between switching or not switching.Sorry. The humbled one, Don
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HeatSearch: I have followed this thread for many years without responding, so I thought I would finally chime in. I understand the math for switching doors which seems simple enough. The truth however, if one is actually on the game show is quite different. Information we have: (1) promise land is behind one of three doors (2) Monty will always show us one door that is not the richesQuestion: Should you switch? Answer: Makes no difference Solution: When Monty shows us the dead door he increases our chances from 1 in 3 up to 1 in 2. We still have no more information as to which door of the two remaining is the fruit than we did when we started. Stick with your original pick or switch to the new door you win half of the time. Regards, David
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