QuoteOriginally posted by: outrunThe optimal strategy is deduced from the game rules and turns out to be independent of the game state.That seems right to me, but let's look at the reasoning of Andrew Vazsonyi here. He assumes that the prize is behind door #1, and that I guess one of the three doors. "Then suppose I guess Door #1. This is the first branch of my tree. The host will not open Door #1, but he may open Door #2 or #3. Suppose he opens #2, and I switch to Door #3, then I lose." But suppose I guess Door #2, and the host reveals #3. "What if I switch to #1 and win? Much better. Now suppose I guess #3, the third branch of the tree. The host opens #2, I guess #1 and win. I can't believe it. Two of the three branches of the tree lead to winning. So the probability is 2/3 if I switch".He says nothing about the rule. The only information he gives us is that the game show host, who knows where the car is, opens a door containing a dud.Is Vazsonyi's reasoning correct?

QuoteOriginally posted by: daveangelQuoteOriginally posted by: And2QuoteOriginally posted by: daveangelwhen monty hall opens the dud that new informationI would say the opposite. The monty hall is guaranteed to reveal dud, you know it upfront - no new information there for the decision.Therefore you can decide your strategy upfront (to always switch or not)... may go something like this: - There are only 2 final states in the game: you either win or lose. - If you never switch, you win only in 1/3 cases (if your original choice was correct), and thus lose in 2/3. - If you always switch, you lose only in 1/3 cases (if your original choice was correct), and thus win in 2/3.In the new version you do get new information, and thus can change the decision... except in this particular case it is irrelevant as the game stops if the second contestant wins. So, you can still chose the strategy upfront and it would go like this: - There are 3 final outcomes: you win, second contestant wins, you both lose. - If you never switch, you win only in 1/3 cases (if your original choice was correct), and thus lose in 2/3. - If you always switch, you lose in 1/3 cases (if your original choice was correct), and in 1/3 (of irrelevant) cases when the second contestant is correct, thus you win in 1/3of course there is new information when monty reveals the empty door. if the game was such that you chose one of 3 doors and then are invited to stick or chose another then there is no new information. however, when monty opens door, he shows you one of the two doors that don't have the prize.I'm with daveangel on this.When the other contestant opens the door and it's a dud, the two remaining doors are each equally likely to hold the prizeIt's a 50-50 choice

QuoteOriginally posted by: ppauper...When the other contestant opens the door and it's a dud, the two remaining doors are each equally likely to hold the prizeIt's a 50-50 choiceThis is exactly what I said, expect you don't need any information, beside the fact that one of the doors was opened.E.g., you can construct a machine which as an input has only one button. You press it once, it says "Chose door #1", you press twice it says "Switch the door". This machine does not need any more information to play optimally at both of these games, and in the original game it wins in 2/3 of the time, and in the new one it wins 1/2 of the time.

many years ago (1998) I built a simple Monte Hall Monte Carlo simulation for my webpage, I think it was in javascript...I remember it fitted the conclusion: one should switch door (standard Monte Hall )I think the code disappeared when I at some point did some revolutionary changes of my webpage, looks like only 3 empty doors left, and no code? (but why did I put 3 horses there, was it one horse behind each door? what door was the small horse behind?) I wonder what distance this small horse has covered; running back and forth during all these years...yes depends on your pixel size"Then the game show host open a certainly empty door. "

QuoteOriginally posted by: Collectormany years ago (1998) I built a simple Monte Hall Monte Carlo simulation for my webpage, I think it was in javascript...I remember it fitted the conclusion: one should switch door (standard Monte Hall )I think the code disappeared when I at some point did some revolutionary changes of my webpage, looks like only 3 empty doors left, and no code? (but why did I put 3 horses there, was it one horse behind each door? what door was the small horse behind?) I wonder what distance this small horse has covered; running back and forth during all these years...yes depends on your pixel size"Then the game show host open a certainly empty door. "your old website indulges in time travel as well. i have just been to feb 2, 116

QuoteOriginally posted by: daveangelQuoteOriginally posted by: Collectormany years ago (1998) I built a simple Monte Hall Monte Carlo simulation for my webpage, I think it was in javascript...I remember it fitted the conclusion: one should switch door (standard Monte Hall )I think the code disappeared when I at some point did some revolutionary changes of my webpage, looks like only 3 empty doors left, and no code? (but why did I put 3 horses there, was it one horse behind each door? what door was the small horse behind?) I wonder what distance this small horse has covered; running back and forth during all these years...yes depends on your pixel size"Then the game show host open a certainly empty door. "your old website indulges in time travel as well. i have just been to feb 2, 116It all started when someone actually opened that last door!

Quoteyour old website indulges in time travel as well. i have just been to feb 2, 116Ahh, I just tried setting my computer clock/year to 1998, and 1999. The year function then works very well on my old webpage, it is when it switches to 2000 the year problem start ....rember the big 2000 scare, how computer systems should break down and the world end....the world did not end, but we are still seeing the ripple effects of the 2000 problem. Unfortunately setting the year to 1998 did not make the Monte Hall simulation work, it is likely gone...the horses are out!