|
||
|
||
|
Server Time: 2/10/2012 10:23:46 PM PACIFIC |
 The Monty Hall Dilemma, Snorbolus, 8. May 2003 08:41 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Here is a statistical curiosity that, even now, I find surprising. I thought that it might be of interest to the group: On the show "Lets Make a Deal" a contestant is shown 3 doors. Behind one is the grand prize of a car, behind the other two are goats. The contestant gets whatever is behind the door they finally choose. However, after the contestant chooses a door, Monty opens one of the remaining two doors (Monty knows what is behind all of the doors and always opens one with a goat). After this, the contestant is given the option of (a) sticking with their original choice of door or (b) switching to the remaining closed door. We assume that the contestant never wants the goat. The dilemma is: should the contestant switch or not? What is the probability of winning the car if: (a) the contestant does not switch (b) the contestant does switch? Does it make a difference to the chance of winning the car if the contestant switches or not? Answers to follow. Snorbolus | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, shorn, 8. May 2003 08:54 | ||
| View ( Message | Thread ) | Return to Thread List | |
| The contestant should always switch because the likelihood of his first choice being correct on the first try was only 33.3%. Now the likelihood of the door left that he did not choose being the grand prize is 50%, so he should choose that door. Think of it in these terms. If there were 10 doors with 9 goats and 1 grand prize, and you selected one door and Monty eliminated 8 others, would you risk the chance that your first selection out of 10 was correct? Of course not. Well, with 3 doors, the situation is the same...the math is just a little closer. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Mark, 8. May 2003 09:24 | ||
| View ( Message | Thread ) | Return to Thread List | |
| on 8. May 2003 08:41 Snorbolus wrote: > Here is a statistical curiosity that, even now, I find surprising. I thought > that it might be of interest to the group: > > On the show "Lets Make a Deal" a contestant is shown 3 doors. Behind one is the > grand prize of a car, behind the other two are goats. The contestant gets > whatever is behind the door they finally choose. However, after the contestant > chooses a door, Monty opens one of the remaining two doors (Monty knows what is > behind all of the doors and always opens one with a goat). After this, the > contestant is given the option of (a) sticking with their original choice of > door or (b) switching to the remaining closed door. We assume that the > contestant never wants the goat. > > The dilemma is: should the contestant switch or not? > > What is the probability of winning the car if: > (a) the contestant does not switch > (b) the contestant does switch? > > Does it make a difference to the chance of winning the car if the contestant > switches or not? > > Answers to follow. > > Snorbolus Interesting question, You start out with 3 choices. Monty then eliminates 1 of the goat choices. Of the initial 3 choices, you will be right 1 in 3 tries, wrong 2 in 3. So you will be wrong 2 out of 3 times. After monty eliminates 1 goat, you will still have the wrong choice 2 out of 3 times. So by then switching to the other door, you will increase you odds of winning to 2:1 ( 2 out of 3 times). mark | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, GKrause, 8. May 2003 09:51 | ||
| View ( Message | Thread ) | Return to Thread List | |
| ROFL You should have seen some of the arguing that went on when this was brought up back in my undergraduate studies in math. Shorn's explanation is the easiest to grasp, but the point is: you always switch. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Schuster, 8. May 2003 09:55 | ||
| View ( Message | Thread ) | Return to Thread List | |
| 33% if you don't switch, 66% if you do switch. The odds of you picking it right on the first door are 1 in 3, so when he shows you one goat door, the odds of the grand prize being behind the remaining door are the remaining 2 in 3. But the real question is, who could pass up a free opportunity for a pet goat?! | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, chasepoker, 8. May 2003 10:13 | ||
| View ( Message | Thread ) | Return to Thread List | |
| It makes no difference your odds are still the same number of doors / number of cars. The fact that he is always going to bring it down to 2 doors does not affect the outcome You are just playing with numbers otherwise 7 High's Chasepoker | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Schuster, 8. May 2003 10:19 | ||
| View ( Message | Thread ) | Return to Thread List | |
| The difference is the fact that you picked the door first. Say I lay an entire deck out in front of you face down and tell you to pick a card. Then I look at your card, and look through the deck and pull out one other card, and I say that either the card you picked or the card I picked is the ace of spades. Which would you gamble on? For the door situation, it's like this. There is 1 correct door and 2 wrong doors. Whenever you first pick, you are 1 in 3 to pick the correct door. At this point, he will always open one of the wrong doors, and since there are two of them, there is always a wrong door to open. At this point, the door you picked is still 1 in 3 to be the correct door, but there is only one other door remaining. It's not a very intuitive concept, but it is correct. I think Snorbolus was in the mood for mischief when he posted this one! | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, chasepoker, 8. May 2003 10:20 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Have changed my mind you should change ! Or am i wrong ? 7 High's Chasepoker | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, stdioh, 8. May 2003 13:23 | ||
| View ( Message | Thread ) | Return to Thread List | |
| It's 1/3 to stay and 2/3 to switch. This is a very elementary problem. I will post a harder one for you brilliant poker minds to work through. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Wren, 8. May 2003 13:25 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Which one? The mathematicians/hats problem? Or perhaps the prisoner's dilemma? | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, stdioh, 8. May 2003 13:30 | ||
| View ( Message | Thread ) | Return to Thread List | |
| As above, the 3^n vs 3^(n+1) problem. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Wren, 8. May 2003 13:22 | ||
| View ( Message | Thread ) | Return to Thread List | |
| "But the real question is, who could pass up a free opportunity for a pet goat?!" LOL...that's the best answer I've heard yet ;D | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Nathaniel Brous, 8. May 2003 10:42 | ||
| View ( Message | Thread ) | Return to Thread List | |
| http://math.rice.edu/~ddonovan/montyurl.html For those interested in further explanations, they will beat it to death here. Note...try the third link first. - Nathaniel Brous | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, chasepoker, 8. May 2003 11:53 | ||
| View ( Message | Thread ) | Return to Thread List | |
| I stopped doing math when i was 16 and went the route of writing essays for history though always quite rated myself with numbers - guess i was wrong ! Great post though Snorbs got me thinking ! One quick question can you use this knowledge to help me improve my poker game ? 7 High's Chasepoker | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Don Quixote, 8. May 2003 13:43 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Interesting! Mathematics beyond 2+2 is always too abstract for me, but one poker related thought does come to mind. When you draw to a straight or to a flush on the flop, your odds are pretty good if you intend to draw on the turn also if you missed on the flop.. But, don't the odds on the turn then change for the worst? i.e., odds of hitting a four flush on the flop are 1.86 to 1 but on the turn they drop to 4.11 to 1. You would then have to readjust the odds of hitting on the turn to the pot odds at that moment. Now, back to Let's made a deal. The odds of selecting the correct door before Monty throws the monkey wrench into the works is 2 to 1. The contestants are now left with two doors from which to select. Don't your odds then change to 1 to 1? This is kind of the reverse of the above in that the odds would be better that you would select the proper door the second time around. With tongue slightly in cheek, is this what they mean by reverse implied odds? Don Quixote on 8. May 2003 11:53 chasepoker wrote: > I stopped doing math when i was 16 and went the route of writing essays for history though > always quite rated myself with numbers - guess i was wrong ! > > Great post though Snorbs got me thinking ! > > One quick question can you use this knowledge to help me improve my poker game ? > > 7 High's > Chasepoker | ||
| Return to Thread List | ||
| Re:Incorrect analysis C here for the correct one, Cpt Kernow, 9. May 2003 02:47 | ||
| View ( Message | Thread ) | Return to Thread List | |
| I think the analysis that you have 1in3 to stick and 2in3 to switch is mistaken. What is importnat to remember is that you are given two opportunities to act. These opportunities are independent of each other. This is the pertinent fact. Just as if I flip a coin and it comes up heads, this had no bearing on the statistical likely hood of heads coming up on the next coin flip. On your first choice you have a 1-3 chance of correct of choosing the right door. Monty opens a door. You now have another chance to act (stick or switch) the odds for this event are entirely independent of the first moment of choice. There are 2 doors, behind one is a car. The probability therefore for either choice is now exactly 50%. This second choice is entirley independent of the first choice. | ||
| Return to Thread List | ||
| no, it isn't, Easy E, 9. May 2003 04:49 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Your second action did not change the probability, at the beginning when you picked your door, that the car was only 33% likely to be behind your door. Monty's revealing of the goat makes it 67% likely that the opposite door had the car behind it IN THE FIRST PLACE. The actions are NOT independent of one another, in that the probabilities do NOT change. You would have only a 50/50 chance if Monty opened the goat door FIRST, and THEN asked you to pick your door. | ||
| Return to Thread List | ||
| Re: Re:Incorrect analysis C here for the correct one, stdioh, 9. May 2003 09:00 | ||
| View ( Message | Thread ) | Return to Thread List | |
| I'll never undersant why so many humans have trouble with this. Simply put: You pick a door and there is a 2/3 chance that it is in one of the other 2 doors. There is a 1/1 chance that at least one of those other doors has nothing behind it, so he will always be able to open one of those doors. You also have the information that one of those doors without anything behind it, and not the one that you have chosen will be opened. The prizes do not move. Thus, nothing changes the fact that there is still a 2/3 chance that it is behind one of the doors that you did not pick. To make it *even easier* to understand, what if there were 1000 doors? Now you pick one door and Montey opens 998 of the remaining doors and you have the option of staying or switching...do you still think you have a 50% chance of being right? Obviously you only have a 1/1000 chance of picking the right door at first, so the only way you are on the prize is if you were initially correct. Now when you switch you have a 999/1000 chance of being right. Now see that when you have 4 doors and he opens 2 of them you have a 1/4 chance of being right initially, so if you switch you have a 3/4 chance of being right. Now see that when you have 3 doors and he opens 1 of them, you have a 1/3 chance of being right initially, so if you switch you have a 2/3 chance of being right. If you genuinely believe that in the 1000 door example you have a 50% chance of being right, then I would like to invite you over to my house to play this game - I will lay you favourable odds :) | ||
| Return to Thread List | ||
| Re: Re:Incorrect analysis C here for the correct one, shorn, 9. May 2003 09:08 | ||
| View ( Message | Thread ) | Return to Thread List | |
| If he accepts, I want a piece too. :) | ||
| Return to Thread List | ||
| Because it's "counterintuitive", Easy E, 9. May 2003 11:13 | ||
| View ( Message | Thread ) | Return to Thread List | |
| to realize that the two picking actions are NOT independent of one another. | ||
| Return to Thread List | ||
| Re: Re:Incorrect analysis C here for the correct one, Schuster, 9. May 2003 11:15 | ||
| View ( Message | Thread ) | Return to Thread List | |
| You'd better really clean up -- setting up 1000 doors would be expensive!!! Lee | ||
| Return to Thread List | ||
| Cleaning up ( final comment ), chasepoker, 9. May 2003 13:22 | ||
| View ( Message | Thread ) | Return to Thread List | |
| YOU WOULD HAVE TO CLEAN UP WITH A 1000 DOORS THATS 999 GOATS AND WHOLE LOAD OF GOAT S*** I LOVE ALL THESE POSTS BUT I RECKON IT IS POKER TIME !!!! > You'd better really clean up -- setting up 1000 doors would be expensive!!! | ||
| Return to Thread List | ||
| Re: Cleaning up ( final comment ), shorn, 9. May 2003 13:29 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Chase...u crack me up. Damn straight though. It is poker time! | ||
| Return to Thread List | ||
| Re: Cleaning up ( final comment ), 4 POKER, 9. May 2003 13:33 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Agreed. 4 POKER | ||
| Return to Thread List | ||
| Re: Cleaning up ( final comment ), 4 POKER, 9. May 2003 13:36 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Ok, so it looks like it's just Shorn, Chasepoker and myself for now... what are we going to talk about, theory, bad beats, psychology, what? (LOL). I'm game. 4 POKER | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Wren, 8. May 2003 13:24 | ||
| View ( Message | Thread ) | Return to Thread List | |
| I still can't figure out why people find this problem so tricky. Figuring out what to do during daylight savings is much less intuitive to me. I have to rely on the old "Spring Forward, Fall Back" saying :O) | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, David R, 8. May 2003 13:43 | ||
| View ( Message | Thread ) | Return to Thread List | |
| I think we are making a poor assumption. I own three cars and no goats, therefore I stick with my original selection which gives me a 66.66% chance of getting my first goat. Besides, it may be a magic goat. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, stdioh, 8. May 2003 13:51 | ||
| View ( Message | Thread ) | Return to Thread List | |
| The problem assumes that the choser is socially well adjusted :) | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Wren, 8. May 2003 13:59 | ||
| View ( Message | Thread ) | Return to Thread List | |
| LOL | ||
| Return to Thread List | ||
| Hey, it could be true love...., Easy E, 9. May 2003 04:50 | ||
| View ( Message | Thread ) | Return to Thread List | |
| who could be against THAT? Well, not knowing David, maybe SPCA | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, Snorbolus, 8. May 2003 14:03 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Pretty much everybody who posted got the right answers so I won't belabor them. I posted because I encountered this dilemma for the first time last night and it boggled my mind. I find it completely counter intuitive. Even after working through the probabilities I did not believe my answer until I ran a simulation and got the same result. One of my colleagues is still unconvinced - and has suggested that the simulation may be rigged as some sort of elaborate hoax. Thanks for your replies, Snorbolus | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, ice, 8. May 2003 16:25 | ||
| View ( Message | Thread ) | Return to Thread List | |
| id pick the door lacking goat like noises coming from behind... or do they gag the goats? hmm...or maybe the door with goatlike noises is just a recording to throw you off from picking it... since DAVID R wants the goat, he'd probably be most likely to pick the car. *********** ¡¢£ßøx | ||
| Return to Thread List | ||
| If the goatlike noises came from the car door, Easy E, 9. May 2003 04:51 | ||
| View ( Message | Thread ) | Return to Thread List | |
| would you ask for the goat door back? | ||
| Return to Thread List | ||
| Do it with a deck of cards, Easy E, 9. May 2003 04:52 | ||
| View ( Message | Thread ) | Return to Thread List | |
| 3 cards: 2 deuces and an Ace. Run through the scenarios about 20 times with him. That should do the trick..... Then, get a poker game started. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, stdioh, 9. May 2003 09:02 | ||
| View ( Message | Thread ) | Return to Thread List | |
| Put money on trials of it with him. Lay him favourable odds. Tell him that you'll play the game and he never switches and every time that he is correct you'll pay him off 55%, but every time that he is incorrect he pays you off 45%. If he really thinks that it is 50/50, you can make some money off of this sap. | ||
| Return to Thread List | ||
| Re: The Monty Hall Dilemma, stdioh, 9. May 2003 09:04 | ||
| View ( Message | Thread ) | Return to Thread List | |
| You also might want to try logic on your friend. If you never switch, then you win when the car is behind the door you pick initially and you lose if it is somewhere else. Thus resolve in your mind that you will never switch and pick a door. It doesn't matter which one he opens now, you still have a 1/3 chance. Thus always switch. | ||
| Return to Thread List | ||
| POKER FORUM HOME | POKER FORUM | LINK TO US | ARCHIVE | ONLINE POKER | Copyright 2002, United Poker Forum |
|
Getting Started |
UPF Tournaments |
Poker News, Views, Rules |
Poker Strategy & Psychology |
Money and Bankroll Poker Bonuses & Promotions | World Series of Poker (WSOP) | Play Online Poker | Poker Odds & Statistics | Tournament Poker | Poker Books, Videos & Learning Tools Looking for a Poker Game | Poker Bad Beats | Not Quite Poker | Quizzes and Polls | Forum Suggestions & Bugs |
|
|
|
|
Interesting Links: Online Poker | Free Poker Games | United Poker Network | Find Vancouver Businesses |
|