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Pastimes : Let's Talk About Our Feelings!!! -- Ignore unavailable to you. Want to Upgrade?

To: Chuzzlewit who wrote (33623)	4/3/1999 12:46:00 PM
From: rudedog	Respond to of 108807

Statistically I think you improve your chances by switching your choice - since on your first call you had a .33 chance but on your second call you get .5. But it seems intuitively perverse.

To: Chuzzlewit who wrote (33623)	4/3/1999 9:30:00 PM
From: nihil	Read Replies (1) \| Respond to of 108807

'Fraid you have to hang with your original curtain. Before you chose the probability of your choice eventually being RR was .3333... After the lifting of the third curtain, the probability of your choice being right is .50. And the probability of switching to the remaining unpicked choice appears to be .5. Except -- if Monte was fair and rational (watch the name!)-- the probability of his lifting the RR curtain was 0.00. His disclosure had a probability of one after you have picked your original curtain. Of course rational greedy Monte doesn't want to give away RR's. The rotten guy would only ask you to switch if you had picked the RR. Your a priori prob of picking the RR and not having a curtain lifted was zero. The a priori probability of picking RR and having a curtain lifted was 1. Before I turned down the remaining curtain I would ask Monte if he was a follower of Ayn Rand (like Alan Greenspan)? If he said yes (he'd have to tell the truth), I'd stick with the original curtain. If he said no, I'd stick anyway, but fear the possibility that he was a decent man who would not lead me astray. If I was a beautiful woman, I'd make clear to him that I was his before the show. If I were a beautiful man, and thought that he was gay .... Anyway, you get my point. It's very rare that the probability model dictates the answer to a 3D problem.

To: Chuzzlewit who wrote (33623)	4/4/1999 6:51:00 PM
From: BGR	Respond to of 108807

CTC, If that's the curtain I chose first, I will switch, as it improves the probability of my success from 1/3 to 1/2. If that's not the curtain I chose first, I may or may not switch, the probabilities remain the same at 1/2. -BGR. PS: OK, saw your response, which I need to think over!

To: Chuzzlewit who wrote (33623)	4/5/1999 3:51:00 AM
From: On the QT	Read Replies (1) \| Respond to of 108807

Hi Chuzz First let me say that Edwarda made me aware of your misunderstanding with the SI Web Robot, saw JBN response, could not have phrased it better! Now to the challenge you threw out to the thread, the responses I read are somewhat different then mine. I have not seen your response and of course would appreciate hearing from you and others on this as well. I don't know if anyone submitted anything to you along these lines: Lets rephrase the problem. If we ( let's call us " the house") had a bag of marbles, in this, the first case, three marbles, one black and the others white, and we were to ask someone, (let's call that person " the player ") to sight unseen, reach in and correctly pick the black marble, the chances of the player being successful would be one chance in three. The correct odds are 2-1. In a fair game the house would have to pay back a total of $3.00 for every $1.00 played. A dollar bet will return $ 3.00 on average for every $3.00 bet. In the long run it would be a break even situation. Nothing has changed in the player's hand. We don't know if the player has a black or white marble, we do know however that the player has a one chance out of the original three in being right and the player should be paid off at the 2-1 odds. Nothing we do to the remaining marbles in the bag can change the original choice in the players hand and the original fair odds. We know that the original choice had a one chance of three in being correct. Now if we were to say that the hand that held the original choice would be right choice one out of three selections then the remaining marbles in the bag would be right choice two out of every three selections. We could also say the bag containing the remaining marbles would contain the black marble 2 out 3 times. Now if we were to eliminate the white marble from the bag we would not reduce the chances of finding the black marble in the bag. The chances of finding the black marble in the hand would be 1 in 3 and finding the black marble in the bag would still be 2 in 3. Therefore, if the player were than given a second choice to whether to accept the original choice in the player's hand, which we know to have a one chance in three to be correct or to choose the bag which we know to have a 2 out 3 chance to be correct, the choice is obviously to reject the marble in hand and opt for the remaining marble in the bag. Now back to the original problem. Assuming that Monty did not know if the contestant correctly picked the curtain with the RR, before opening the curtain of the contestant's first choice, Monty offers the contestant a second choice. Before we get to that, it is important to know that the contestant had one chance out of three in picking the curtain that contains the RR. There is nothing that Monty can do to change what is behind that curtain ( unless of course he cheats, we will assume that is not part of the problem.) Nothing that he does with the remaining two curtains can change the original odds of the contestant's first choice. That original choice has a one chance of three to succeed in selecting the curtain with the RR behind it. Monty instructs his assistant to go behind the curtain of each of the remaining two curtains and unveil one of the curtains that does not have the RR behind it. We know by opening the curtain that did not have the RR behind it, that this does not change the fact that the RR has a 2 out 3 chance of being behind one of the two curtains that the contestant did not choose as the first choice. Therefore, given the second opportunity to choose again under this scenario the first choice would always have a one chance of three of being successful and the second different choice would have a 2 chance of 3 in being successful. The contestant should change from the original choice to the only remaining choice. Best Regards, QT