# Can you solve this riddle? #2 **URL:** \ **Category:** In My Humble Opinion\ **Created:** [May 4, 2015, 2:07pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240 "2015-05-04T14:07:12Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [May 4, 2015, 7:37pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/61 "2015-05-04T19:37:36Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Seriously, dude, LET’S DO THIS! Nice try, Lefty. But there is one constant in the Monty Hall dilemma: _The ones with the incorrect reasoning are precisely the ones who refuse to bet real money on it._ ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [May 4, 2015, 7:39pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/62 "2015-05-04T19:39:48Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Folly, try it out. I’ve got a deck of cards in front of me, for real, and I just chose one at random. I want you to make 51 different guesses as to what it might be. Of your 51 guesses, I’ll eliminate 50. > > (To make it easier, instead of writing 51 cards, you can just tell me which one you’re declining to guess, e.g., say, “I’m guessing every card except the 6 of diamonds”) > > Seriously, dude, LET’S DO THIS! I don’t get to be 51 people, I get to be one person. Let’s say I’m the very first person. I say Ace of Spades. Put a card to the side. The next card you deal is me. Let’s put that into the Folly circle of isolation. You look at the remaining cards. By some miracle, contestant Folly has not been eliminated. So, where’s the Ace of Spades. In the Folly circle of isolation? Or put to the side. What are the probabilities of both? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 7:39pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/63 "2015-05-04T19:39:56Z")
> [@septimus](#): > > Nice try, Lefty. But there is one constant in the Monty Hall dilemma: _The ones with the incorrect reasoning are precisely the ones who refuse to bet real money on it._ 😃 Someone else is welcome to try. We can do it many times. Septimus, you wanna make 51 guesses? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 7:41pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/64 "2015-05-04T19:41:44Z")
> [@Folly](#): > > I don’t get to be 51 people, I get to be one person. That’s fine. I’m asking you to tell me what all 51 people say. MOST OF THE TIME YOU ARE GOING TO BE ELIMINATED. WE ARE NOT TALKING ABOUT THOSE TIMES. But if you tell me what all 51 say, I’ll eliminate 50 of them, and give a choice to that one remaining person. Try it my way, see what happens. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [May 4, 2015, 7:44pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/65 "2015-05-04T19:44:51Z")
> [@Left\_Hand\_of\_Dorkness](#): > > That’s fine. I’m asking you to tell me what all 51 people say. > > MOST OF THE TIME YOU ARE GOING TO BE ELIMINATED. WE ARE NOT TALKING ABOUT THOSE TIMES. > > But if you tell me what all 51 say, I’ll eliminate 50 of them, and give a choice to that one remaining person. > > Try it my way, see what happens. Try it my way. What are the probabilities between the Folly circle of Isolation and the card put off to the side. The card I _know_ you cannot check to see if its the Ace of spades to check if I’ve lost. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [May 4, 2015, 7:47pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/66 "2015-05-04T19:47:09Z")
[quote=“Left\_Hand\_of\_Dorkness, post:64, topic:719240”] MOST OF THE TIME YOU ARE GOING TO BE ELIMINATED. WE ARE NOT TALKING ABOUT THOSE TIMES. QUOTE] That’s right we are choosing between a time I’m not eliminated because I got very lucky and a time I’m not eliminated because the “untouched card” is the winner. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [May 4, 2015, 7:49pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/67 "2015-05-04T19:49:06Z")
> [@Terr](#): > > OK let’s see: Let’s. > [@Terr](#): > > 1. I have nothing, Bob has nothing, unchosen door has car … > B. When Monty opens Bob’s door that means that (3) above is eliminated. … And ? Take your time. (Hint: what about scenario 2?) > [@Terr](#): > > QED Quod est demens ? > [@Terr](#): > > Not really sure why people are having a problem with this. 😃 ---
**Author:** ![Terr](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Terr](https://boards.straightdope.com/u/Terr)\ **Post date:** [May 4, 2015, 7:49pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/68 "2015-05-04T19:49:43Z")
See post #57. So far I see it as the simplest explanation. Show me where it is wrong. ---
**Author:** ![Terr](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Terr](https://boards.straightdope.com/u/Terr)\ **Post date:** [May 4, 2015, 7:52pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/69 "2015-05-04T19:52:34Z")
> [@septimus](#): > > … And ? Take your time. (Hint: what about scenario 2?) What about scenario 2? It is still viable. So is scenario 1. Either one can happen, and the chances of either are the same. That’s the point. ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [May 4, 2015, 7:52pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/70 "2015-05-04T19:52:35Z")
So I was wrong. It’s better to switch. It’s interesting how what seems insignificant turns out to make the difference. Switching is better for the contestant give the offer to switch 2/3 of the time. I’m not understanding the 50% or the 80% figures some others have come up with. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [May 4, 2015, 7:53pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/71 "2015-05-04T19:53:02Z")
> [@Martian Bigfoot](#): > > Hey, **Folly**! Good news: The two of us are on the show together. Let’s make a deal: If either of us wins, we’ll split the car. You get the front half, I get the back half. Sounds good? Cool, let’s work together on this. > > OK, there are three doors. We get to pick two of them. Awesome, that gives us a 2/3 chance of getting the car. > > Now, Monty opens my door… bummer, there’s a goat behind it. Ah, well, no matter. Still your door to go. Sounds to me like we still have out 2/3 chance. Agreed? Tell you what, though, I’ve been thinking about this. If you win the car, just keep it. I don’t really want half a car anyway. > > Now tell me how this is different from the scenario in the OP. It’s different because I get to be two people. Of course that would double my chances. ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [May 4, 2015, 7:53pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/72 "2015-05-04T19:53:16Z")
> [@Terr](#): > > Not really sure why people are having a problem with this. Then I take it you’ve never discussed probability before. The greatest minds in the world have problems with probability. But damn it, your post has swayed me. If I am the contestant left, 1/3 of all outcomes have been eliminated. OK, now it’s you, \*\*Folly \*\*and me against everyone else. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 7:53pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/73 "2015-05-04T19:53:38Z")
> [@Folly](#): > > Try it my way. What are the probabilities between the Folly circle of Isolation and the card put off to the side. > The card I _know_ you cannot check to see if its the Ace of spades to check if I’ve lost. I don’t understand your way, honestly–I don’t know what you mean when you say “Put a card to the side. The next card you deal is me. Let’s put that into the Folly circle of isolation.” But I make a promise. If you’ll just goddamned give my way a go, and then explain your way, I’ll try your way. Just give a goddamned go already! ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [May 4, 2015, 7:54pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/74 "2015-05-04T19:54:22Z")
> [@Greg\_Charles](#): > > So I was wrong. It’s better to switch. It’s interesting how what seems insignificant turns out to make the difference. > > Switching is better for the contestant give the offer to switch 2/3 of the time. I’m not understanding the 50% or the 80% figures some others have come up with. Are you talking about the original Monty Hall problem? Because that’s the answer to the original, not the OP. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 7:54pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/75 "2015-05-04T19:54:45Z")
> [@Terr](#): > > See post #57. So far I see it as the simplest explanation. Show me where it is wrong. Post 50 examines all the possibilities; take a look at that one to see where you’re wrong. Or pick some cards, any 51 cards, and see how it plays out! ---
**Author:** ![Don\_t\_Panic](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/don_t_panic/32/398_2.png) [@Don\_t\_Panic](https://boards.straightdope.com/u/Don_t_Panic)\ **Post date:** [May 4, 2015, 7:56pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/76 "2015-05-04T19:56:40Z")
> [@Folly](#): > > It’s different because I get to be two people. Of course that would double my chances. But that’s my point. In the scenario in the OP, you do effectively get to be two people. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [May 4, 2015, 7:59pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/77 "2015-05-04T19:59:45Z")
> [@bup](#): > > OK, now it’s you, \*\*Folly \*\*and me against everyone else. Not quite. In addition to your incorrect answer of 50%, we have votes for 33% and 80%, but only a few for the correct answer: 67%. @ **Terr** : If you’re sincere about wanting to learn, perform the step-by-step exercise in #47. That will lead you to your error. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 8:00pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/78 "2015-05-04T20:00:09Z")
> [@Martian Bigfoot](#): > > But that’s my point. In the scenario in the OP, you do effectively get to be two people. Well…sort of. I think that confuses things. SOMEBODY TAKE MY CARD CHALLENGE, DAMMIT! I really think the odds here will demonstrate, but if I make all the choices myself, it’ll be hard to follow. Choose 51 cards! ---
**Author:** ![Terr](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Terr](https://boards.straightdope.com/u/Terr)\ **Post date:** [May 4, 2015, 8:01pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/79 "2015-05-04T20:01:06Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Post 50 examines all the possibilities; take a look at that one to see where you’re wrong. Post 50 is unnecessarily complex. Mine is simple. There are only 3 possibilities. No dice throwing two times. Monty, by selecting the other guy and not me eliminates one. 2 are left. Each one had equal chance of occurring before and still has equal chance of occurring. So the probability is 1/2. Same with your card example. Instead of 3 possiblities, there are 52 each one with the initial probability of 1/52. By eliminating 50 players, Monty reduces the number of possibilities to 2. Each one is equally likely NOW. So the probability is still 1/2. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [May 4, 2015, 8:03pm UTC](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240/80 "2015-05-04T20:03:41Z")
> [@Terr](#): > > Same with your card example. Instead of 3 possiblities, there are 52 each one with the initial probability of 1/52. By eliminating 50 players, Monty reduces the number of possibilities to 2. Each one is equally likely NOW. So the probability is still 1/2. Put up or shut up. You’re giving orders to 51 people to choose different cards. Which one will they not choose? [Previous page](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240.md?page=3) [Next page](https://boards.straightdope.com/t/can-you-solve-this-riddle-2/719240.md?page=5)