Comments on: The best game-show math brain teaser and the controversey that surrounded the answer http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/ School Safe Puzzles and Games for Kids of all ages Wed, 01 Feb 2012 04:15:27 +0000 hourly 1 http://wordpress.org/?v=3.0.2 By: LydiaFre http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-85455 LydiaFre Sat, 17 Dec 2011 05:38:20 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-85455 I'd say yes because door 1, which you picked first had a 1 out of 3 (33.3%) chance of having the car. Now, with only 2 doors to chose from, the other door has a 1 out of 2 (50%) chance of being correct. The odds are in your favor if you switch your choice. I’d say yes because door 1, which you picked first had a 1 out of 3 (33.3%) chance of having the car. Now, with only 2 doors to chose from, the other door has a 1 out of 2 (50%) chance of being correct. The odds are in your favor if you switch your choice.

]]> By: wyrdo http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-84422 wyrdo Wed, 23 Feb 2011 23:40:34 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-84422 I agree for the most part with fanfan. It's nice to know that my opinion (which I fully believe to be the mathematically correct one) is shared by at least one other person on this site. :-) fanfan could very well be correct about the psychology angle, but my understanding of how these game shows operate, at least in the USA where I am, is that because of a controversy back in the 50s over the show "Twenty-One" (see wikipedia), no one on the show including the show host has access to info that's supposed to be hidden. That is to say: in order to prevent even the illusion of the possibility of rigging the show, the things that are supposed to be hidden/random/unknown really *are* hidden/random/unknown. And, from what little game theory I can remember, in a situation like that, you're best game strategy is to be truly random. So: don't *always* change your original guess and don't *always* stick with your original guess. Rather: completely ignore you're original guess (since it was based on different odds) and make a new random choice (50%/50%) using a coin or something. I don't know if would fanfan agree with me on that part, but it's cool either way. I don't want to start a dispute with fanfan over that point. I'm just relieved that there's at least one other person out there that understands that once one door has been opened and you're given the opportunity to change your guess, the old 1/3, 1/3, 1/3 odds no longer applies and we have a brand new probability problem with 50%/50%. :-) -- Furry cows moo and decompress. I agree for the most part with fanfan. It’s nice to know that my opinion (which I fully believe to be the mathematically correct one) is shared by at least one other person on this site. :-)


fanfan could very well be correct about the psychology angle, but my understanding of how these game shows operate, at least in the USA where I am, is that because of a controversy back in the 50s over the show “Twenty-One” (see wikipedia), no one on the show including the show host has access to info that’s supposed to be hidden. That is to say: in order to prevent even the illusion of the possibility of rigging the show, the things that are supposed to be hidden/random/unknown really *are* hidden/random/unknown.


And, from what little game theory I can remember, in a situation like that, you’re best game strategy is to be truly random. So: don’t *always* change your original guess and don’t *always* stick with your original guess. Rather: completely ignore you’re original guess (since it was based on different odds) and make a new random choice (50%/50%) using a coin or something.


I don’t know if would fanfan agree with me on that part, but it’s cool either way. I don’t want to start a dispute with fanfan over that point.


I’m just relieved that there’s at least one other person out there that understands that once one door has been opened and you’re given the opportunity to change your guess, the old 1/3, 1/3, 1/3 odds no longer applies and we have a brand new probability problem with 50%/50%. :-)


–
Furry cows moo and decompress.

]]> By: fanfan http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-84418 fanfan Wed, 23 Feb 2011 22:32:55 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-84418 Let us start by assuming that we cannot second guess the motive of the show host in changing the game rules: a. By offering a 2nd choice, the game rules have been changed, from a 1 in 3 choice, to a 50:50 probability choice, having no relationship at all to the earlier 1 in 3 starter (it is as if this did not exist at all). In this case, it remains a 50:50 probability, and there is no point in changing the original choice. b. If the game host has a motive, it would, by the very nature of these programs, to prolong delivery of the reward, and not make it too easy for the contestants. This motive would have a higher probability, looking at the very nature of man. In that case, in case the contestant had initially made a wrong choice with the 1 in 3 option, the probability should be less than 50% that, instead of promptly declaring the contestant failed, and extending the program, that the host would try to give a second chance with a new 50:50 option. In this case, the host is attempting misdirection, to create self-doubt in the contestant. So, in this scenario too, contestant should stick to original choice. Let us start by assuming that we cannot second guess the motive of the show host in changing the game rules:
a. By offering a 2nd choice, the game rules have been changed, from a 1 in 3 choice, to a 50:50 probability choice, having no relationship at all to the earlier 1 in 3 starter (it is as if this did not exist at all). In this case, it remains a 50:50 probability, and there is no point in changing the original choice.
b. If the game host has a motive, it would, by the very nature of these programs, to prolong delivery of the reward, and not make it too easy for the contestants. This motive would have a higher probability, looking at the very nature of man. In that case, in case the contestant had initially made a wrong choice with the 1 in 3 option, the probability should be less than 50% that, instead of promptly declaring the contestant failed, and extending the program, that the host would try to give a second chance with a new 50:50 option. In this case, the host is attempting misdirection, to create self-doubt in the contestant. So, in this scenario too, contestant should stick to original choice.

]]> By: XSLT brain teaser « Tech Team http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-84230 XSLT brain teaser « Tech Team Fri, 07 Jan 2011 03:32:42 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-84230 [...] address values “n/a”, “na” and “Dr”. This reminds me of the game show brain teaser where by stepping through the scenarios in a logical fashion gives the correct answer; trying to [...] [...] address values “n/a”, “na” and “Dr”. This reminds me of the game show brain teaser where by stepping through the scenarios in a logical fashion gives the correct answer; trying to [...]

]]> By: Benson http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83637 Benson Fri, 17 Sep 2010 20:16:16 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83637 experiment, I have summed up the proof in a very simple sentence. Not everybody is expected to grasp it, so there is no need to be on the defensive if you didn't. Derogatory terms won't help your case either. As for the dog walking far INTO the woods, maybe you'd like to share the details of your experiment. A good laugh won't hurt us. experiment, I have summed up the proof in a very simple sentence. Not everybody is expected to grasp it, so there is no need to be on the defensive if you didn’t. Derogatory terms won’t help your case either.


As for the dog walking far INTO the woods, maybe you’d like to share the details of your experiment. A good laugh won’t hurt us.

]]> By: experiment http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83636 experiment Fri, 17 Sep 2010 18:30:59 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83636 and wyrdo, you are embarrassing yourself. The challenge is not to prove that the wrong answer is correct, the challenge is to understand why switching doors gives one a 2/3 chance of winning. There are many great explanations here. good luck. and wyrdo, you are embarrassing yourself. The challenge is not to prove that the wrong answer is correct, the challenge is to understand why switching doors gives one a 2/3 chance of winning. There are many great explanations here. good luck.

]]> By: experiment http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83635 experiment Fri, 17 Sep 2010 18:24:32 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83635 hmm, so its seems you agree with me about the doors while showing no proof or reason for your thinking but do not know how far a dog can walk into the woods. OK, brainiac. Maybe you should stick to the word search puzzles. hmm, so its seems you agree with me about the doors while showing no proof or reason for your thinking but do not know how far a dog can walk into the woods. OK, brainiac. Maybe you should stick to the word search puzzles.

]]> By: Benson http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83621 Benson Thu, 16 Sep 2010 16:14:51 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83621 It is obvious that we have to switch as door 2 now has the probability doors 2 and 3 combined. Despite the GED, why do some people find it so hard to understand? This has nothing to do with dogs walking far into the woods. But you still can do what science always dictates, run the experiment. To better understand: make it a cocker spaniel and a medium sized forest. Explain to the dog that its grandmother is waiting for it at the other side of the woods. Make sure you give it plenty of food and water. We would not want some lame dog excuses like no food or water ruining the experiment. Then equip it with a tracking device to find out how far a dog can run into the woods. Don't bother telling anybody the results as I doubt that anybody would be interested in them, that is unless they are craving for a good laugh. end of story It is obvious that we have to switch as door 2 now has the probability doors 2 and 3 combined.


Despite the GED, why do some people find it so hard to understand? This has nothing to do with dogs walking far into the woods. But you still can do what science always dictates, run the experiment. To better understand: make it a cocker spaniel and a medium sized forest. Explain to the dog that its grandmother is waiting for it at the other side of the woods. Make sure you give it plenty of food and water. We would not want some lame dog excuses like no food or water ruining the experiment. Then equip it with a tracking device to find out how far a dog can run into the woods.


Don’t bother telling anybody the results as I doubt that anybody would be interested in them, that is unless they are craving for a good laugh.


end of story

]]> By: wyrdo http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83608 wyrdo Thu, 16 Sep 2010 04:37:25 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83608 There are many, many answers that indicate that you will have a 2/3 (66%) chance of getting the car if you switch. This is one of those times when people let themselves fail to "see the forest for the trees". I mean--if you think about it for a moment, how could your choosing door one over door 2 possibly have any impact on the odds that it will have a car or a goat? All the "monte hall" simulations in the world aren't going to help you work out the odds because, in this instance, you're basing them on a false premise. What really happens is this: as soon as the host reveals there is a goat behind one of the doors, the original problem: ( 33+1/3% car, 33+1/3% goat, 33+1/3% goat ) goes away. Supposing the host reveals a goat behind the 3rd door, we now have: ( 50% car, 50% goat, goat *for sure* ) The goat we can see doesn't figure into our probability calculations. And which door we choose has no affect on the probability that we get a car or a goat. How could it? In an instance such as this, game theory tells us the best play is to make the decision truly random: "let the chips fall where they may" as they say. So you should do a heads pick door 1, tails pick door 2 type of thing. ----------------------------------------- I have to say, the frequency with which people get this wrong is very depressing. But on the plus side, I'm starting to understand why casinos succeed in pulling in so much cash. Various people that think they are smart are unable to detect a run-of-the-mill trick question, and they think their choice can somehow affect the odds. That's insane. I want to open my casino now please. -- Furry cows moo and decompress. There are many, many answers that indicate that you will have a 2/3 (66%) chance of getting the car if you switch. This is one of those times when people let themselves fail to “see the forest for the trees”. I mean–if you think about it for a moment, how could your choosing door one over door 2 possibly have any impact on the odds that it will have a car or a goat? All the “monte hall” simulations in the world aren’t going to help you work out the odds because, in this instance, you’re basing them on a false premise.


What really happens is this: as soon as the host reveals there is a goat behind one of the doors, the original problem:


( 33+1/3% car, 33+1/3% goat, 33+1/3% goat )


goes away. Supposing the host reveals a goat behind the 3rd door, we now have:


( 50% car, 50% goat, goat *for sure* )


The goat we can see doesn’t figure into our probability calculations. And which door we choose has no affect on the probability that we get a car or a goat. How could it?


In an instance such as this, game theory tells us the best play is to make the decision truly random: “let the chips fall where they may” as they say. So you should do a heads pick door 1, tails pick door 2 type of thing.
—————————————–
I have to say, the frequency with which people get this wrong is very depressing. But on the plus side, I’m starting to understand why casinos succeed in pulling in so much cash. Various people that think they are smart are unable to detect a run-of-the-mill trick question, and they think their choice can somehow affect the odds. That’s insane. I want to open my casino now please.
–
Furry cows moo and decompress.

]]> By: experiment http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83607 experiment Thu, 16 Sep 2010 03:31:24 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83607 Ok, 2 more ways to look at this. 1. The key is that the host KNOWINGLY exposes a goat. He exposes a goat no matter what the contestant chose. If the host DID NOT know where the car is and the exposed door could be either car or goat then it would be 50/50 that the contestant had the car door IF a goat was exposed. 2.Doors 2 and 3 must be one of 3 combinations goat goat goat car car goat The host automatically eliminates a goat from whichever combination exists leaving: goat car car 2 OUT OF 3 chance that a car is left. end of story Ok, 2 more ways to look at this.
1. The key is that the host KNOWINGLY exposes a goat. He exposes a goat no matter what the contestant chose. If the host DID NOT know where the car is and the exposed door could be either car or goat then it would be 50/50 that the contestant had the car door IF a goat was exposed.


2.Doors 2 and 3 must be one of 3 combinations
goat goat
goat car
car goat
The host automatically eliminates a goat from whichever combination exists leaving:
goat
car
car
2 OUT OF 3 chance that a car is left.


end of story

]]> By: experiment http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83605 experiment Thu, 16 Sep 2010 02:05:32 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83605 it replaces: HOW FAR CAN A DOG WALK INTO THE WOODS? it replaces:
HOW FAR CAN A DOG WALK INTO THE WOODS?

]]> By: experiment http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83604 experiment Thu, 16 Sep 2010 02:00:12 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83604 ok, really all you PHD's, professors, MIT guys, highest IQ lady, etc, why is this so hard to understand and explain, apparently most cannot do what science always dictates, run the experiment. To better understand, make it ten doors, one car, nine goats. Contestant picks a door, host removes 8 goats doors. One of two things just happened: 1.contestant picked the one car door out of ten doors-10% chance 2.contestant picked one of the nine goats doors-90% chance That means the other door the host left is one of two things: 1.a goat-10%chance 2.a car-90% chance GET TEN PIECES OF PAPER, ONE CAR, NINE GOATS,PICK ONE.AFTER THE HOST REMOVES THE EIGHT GOAT DOORS IT BECOMES BLATANTLY, GLARINGLY, RIDICULOUSLY OBVIOUS WHERE THE CAR IS(90% OF THE TIME ON AVERAGE). JUST DO IT. My G.E.D. came in real handy here, it helped me understand this immediately, some people are just thinking too much instead of running the experiment. This is actually my favorite brainteaser of all time now ok, really all you PHD’s, professors, MIT guys, highest IQ lady, etc, why is this so hard to understand and explain, apparently most cannot do what science always dictates, run the experiment. To better understand, make it ten doors, one car, nine goats. Contestant picks a door, host removes 8 goats doors. One of two things just happened:
1.contestant picked the one car door out of ten doors-10% chance
2.contestant picked one of the nine goats doors-90% chance
That means the other door the host left is one of two things:
1.a goat-10%chance
2.a car-90% chance
GET TEN PIECES OF PAPER, ONE CAR, NINE GOATS,PICK ONE.AFTER THE HOST REMOVES THE EIGHT GOAT DOORS IT BECOMES BLATANTLY, GLARINGLY, RIDICULOUSLY OBVIOUS WHERE THE CAR IS(90% OF THE TIME ON AVERAGE). JUST DO IT.


My G.E.D. came in real handy here, it helped me understand this immediately, some people are just thinking too much instead of running the experiment.
This is actually my favorite brainteaser of all time now

]]> By: drshacket http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83594 drshacket Tue, 14 Sep 2010 17:00:54 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83594 Stay with the same door. Your odds were 33%. Now with door number 3 revealed (also 33%), your odds of having selecting the right door increased by 33%. Therefore, your odds of winning is now cumulative, to 66%, buy staying with door number 1. Stay with the same door. Your odds were 33%. Now with door number 3 revealed (also 33%), your odds of having selecting the right door increased by 33%. Therefore, your odds of winning is now cumulative, to 66%, buy staying with door number 1.

]]> By: smartguy http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83179 smartguy Wed, 23 Jun 2010 23:14:19 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83179 Here is another way of looking at it - sorry if anyone has already mentioned it. Suppose you have a deck of playing cards with 51 Aces and 1 King. All the cards are faced down. You are asked to select a card that you think is the King. I then turn over 50 cards, showing 50 Aces. Now surely if you are given the opportunity of changing your card, you would do so - as the chance of you selecting the king at the start was 1 in 52. It would be very unlikely that you chose the King at the beginning. The same principle applies here. Here is another way of looking at it – sorry if anyone has already mentioned it. Suppose you have a deck of playing cards with 51 Aces and 1 King. All the cards are faced down. You are asked to select a card that you think is the King. I then turn over 50 cards, showing 50 Aces. Now surely if you are given the opportunity of changing your card, you would do so – as the chance of you selecting the king at the start was 1 in 52. It would be very unlikely that you chose the King at the beginning. The same principle applies here.

]]> By: kaxxito http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/comment-page-2/#comment-83155 kaxxito Mon, 21 Jun 2010 17:26:41 +0000 http://www.smart-kit.com/s313/the-best-simple-math-brain-teaser-and-the-controversy-that-surrounded-the-answer/#comment-83155 sorry for my english. suppose in game are 2 players. David and John. David choosed door number 1, and John choosed door number 2. both of them has 33% chance to win. then host opened door number 3 and there was nothing. after that David's and John's chances will be equal. David and John are in equal positions, everything effects on them identically, so if one's winning probability increases, seconds will increase too. my answer is: it has no matter to change answer sorry for my english. suppose in game are 2 players. David and John. David choosed door number 1, and John choosed door number 2. both of them has 33% chance to win. then host opened door number 3 and there was nothing. after that David’s and John’s chances will be equal. David and John are in equal positions, everything effects on them identically, so if one’s winning probability increases, seconds will increase too. my answer is: it has no matter to change answer

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