## Three Card Rinsel, anyone?

Message boards : Cafe SETI : Three Card Rinsel, anyone?
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rinselberg
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Message 12936 - Posted: 8 Jan 2007, 9:24:13 UTC

I'm not generally one for puzzles or brain teasers, but I just ran into one that is elegant in its simplicity, yet profound in its implications.

Consider a deck of only three playing cards. One of the cards is a Joker. The other two cards could be anything - even duplicates of each other - anything but another Joker. Three cards, one Joker.

You play this game with a computer. The computer can only play fairly and exactly by the rules. The computer deals the cards face down in front of you, Left, Center and Right. The computer is perfectly randomized so that before the deal, the probability that the Joker will be dealt in any particular order (Left, Center or Right) is always one chance in three. After the deal, the computer always knows which card is the Joker.

The cards have been dealt. This is what the computer "sees" ...

Your objective is to select the Joker. You are perfectly versed in the rules of the game and about how the computer is programmed. But you cannot predict the outcome of the computer's randomizing calculations. At this point you can't do any better than a random selection of your own, so you point to one of the cards - Left, Center or Right. It doesn't make the slightest difference which one. Let's say you select the card on the Left.

This is what you see. You select the card on the Left ...

There is only one Joker, so whichever card you selected, at least one and possibly both of the other cards are losers. Whichever card you selected, the computer responds by facing one of the other cards and showing you a loser. If, on the strength of one chance in three, you selected the card that the computer knows is the Joker, then the computer has one additional computation to perform. It must decide which one of the two cards that you didn't select - both cards, losers - to reveal to you. It does so in a perfectly random way. It performs the software equivalent of flipping a coin to determine which one of the two losers to face.

After the computer shows you a loser, and only two cards remain face down, you have an option: You can play the card that you selected - or you can switch (renege) and play the last remaining card.

The computer has faced a loser from the cards that you didn't select (Center; Right). Should you play your selection - the card on the Left - or should you switch and play the last remaining card - the card in the Center ..?

You want to win. So what decision do you make? Or does it even make any difference to your odds of winning, whether you play your selection, or renege and play the other card?

Instead of posting, why not just send me an email via rinselberg2@sbcglobal.net ..? I will post only a statistical breakdown of the responses - no user names.

Images: Iraq Playing Cards. Courtesy of WNBC, New York City, New York.
ID: 12936 ·
GalaxyIce
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Message 12948 - Posted: 8 Jan 2007, 23:32:44 UTC

It is quite obvious that you should renege and play another other card since it has a better chance of getting the Joker than no chance at all if you stay with the losing card.

Secondly, why would I want to send you an email and reveal my own email address to you? Are you going to spam me or sell my email address on to other spammers?

ID: 12948 ·
rinselberg
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Joined: 16 Oct 06
Posts: 115
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Message 12949 - Posted: 8 Jan 2007, 23:59:52 UTC - in response to Message 12948.

It is quite obvious that you should renege and play another other card since it has a better chance of getting the Joker than no chance at all if you stay with the losing card.

Secondly, why would I want to send you an email and reveal my own email address to you? Are you going to spam me or sell my email address on to other spammers?

Aside from a sort of general caution (which I understand), why would you think that a bona fide SETI@home beta tester like me would want to spam you or sell your email address to other spammers? Have you looked at my other message board posts? They're almost all under the "Number crunching" category. Evidence of a straightforward and honest beta test volunteer. A somewhat iconoclastic personal style, perhaps - but my substance - as far as my beta test activities - is rock solid. I stand on my record.

If this message board had a PM (Private Message) option, I would have invited PMs instead of emails.

I was hoping that someone might enjoy responding to me about this card game puzzle without posting or adding a visible message - so as to not "let the cat out of the bag" about the answer(s) to the puzzle. Hence, the suggestion of an email or PM. I'm interested in how different people think and express themselves via the Internet. I did get three PMs on the subject from another forum where I posted the same material.

But it's clear that I did not make the objective of this clear enough for you. I guess I did not describe the game clearly enough for you. It's not just about that particular configuration of cards that I presented, where the Joker is the Center card and the human player starts by selecting the card on the Left. I was trying to cover the general case. Remember, there is sure to be one Joker. The player picks one of the cards, initially, and then the computer responds. It's possible that the player unknowingly selects the Joker (on the strength of one chance in three) - or - in the case that I illustrated with those playing card images - it's possible that the player unknowingly selects one of the two other card-values that I defined from the very outset as losers.

Does this make it more understandable for you - as to what kinds of reponses I was looking for?

More than anything else, it was just fun for me to put this together as carefully as I did with my own words and images - and some links to other web pages on this topic - which, sooner or later I would post here, or PM/email as my reply to anyone who finds the puzzle of some interest. Everyone has their own idea of fun ..?

Yours truly.
ID: 12949 ·
GalaxyIce
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Joined: 10 Oct 06
Posts: 555
Credit: 54,802
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Message 12982 - Posted: 10 Jan 2007, 0:08:15 UTC - in response to Message 12949.

Does this make it more understandable for you - as to what kinds of reponses I was looking for?

I'm not sure it really does. It's a rather long explanation about choices involving just three cards and I fear I don't have the attention span to go over it again with your added qualification to find the complications which I obviously can't see.

I think the biggest block to my thought process here is your choice to use an image of Saddam Hussein. I expect you didn't realize he was hung recently and controversy about his death is still raging.

Or is using this card part of your weird game?

ID: 12982 ·
rinselberg
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Joined: 16 Oct 06
Posts: 115
Credit: 233,455
RAC: 0
Message 12986 - Posted: 10 Jan 2007, 1:03:07 UTC - in response to Message 12982.

For sure, I got the news about the recently late Saddam Hussein.

The Iraq cards are what is called a "subtext" - meaning an implicit or unspoken message - perhaps even veiled or cloaked message of a literary text.

But that doesn't mean I was trying to be any more than just casually or slightly political - I'm not going to try to subvert this forum for repeated political harangues, as sometimes happens in the "Cafe" part of other technical forums.

I've had eight responders in all. You're the first one to comment on the style of the card images that I selected. And the first one to respond from the other side of the Atlantic. Which adds a little bit to my "fun".

But - if we could get past the specific card images that I selected - it really is a bonafide puzzle. Of the seven other responders, four got it right and three got it wrong. As for me - I got it wrong when I first ran into it a few weeks ago during a science segment on cable TV.

I'm going to hold out for a bit and see if any other beta testers are prompted to respond - then I will post a link to my own little explanatory essay about the solution to the puzzle. No more card images or political subtexts ...

I appreciate your interest - the worst thing about these forums is to not have anyone respond at all.

ID: 12986 ·
GalaxyIce
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Joined: 10 Oct 06
Posts: 555
Credit: 54,802
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Message 12988 - Posted: 10 Jan 2007, 1:38:13 UTC - in response to Message 12986.

I appreciate your interest - the worst thing about these forums is to not have anyone respond at all.

It's a good job I posted then.

What was on the cards was irrelevant, I was just fishing for more information from you in an expected explanation, which you duly gave.

You see, I think the three got it wrong because they don't understand the game. The answer to the game is very simple, as soon as you can work out what is supposed to be going on. 'That' is the real challenge to your game.

It's a bit like life. Nobody really knows what it's all about. If they did, they might start to enjoy it.

ID: 12988 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 13022 - Posted: 10 Jan 2007, 19:36:32 UTC

I've sent you an email. I quite enjoyed trying to solve that. I think I have the answer, but not that confident about it; look forward to hearing the solution.

This takes me back to queuing theory when a man faced a queue with 10 people waiting for ice cream at a ice cream van - calculate the probability that he will join the queue, as opposed to walking off and deciding not to queue. Arrrgh! What if the queue was 15 people? Aarrrrrrrghhhh!

ID: 13022 ·
GalaxyIce
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Joined: 10 Oct 06
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Message 13056 - Posted: 11 Jan 2007, 12:45:22 UTC - in response to Message 13022.

I've sent you an email. I quite enjoyed trying to solve that. I think I have the answer, but not that confident about it; look forward to hearing the solution.

Thank you for your reply rinselberg. I was pleased to see I had solved this correctly. It's actually a very good puzzle and I would be pleased to try out any more you have. Thanks.

ID: 13056 ·
rinselberg
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Joined: 16 Oct 06
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Credit: 233,455
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Message 13089 - Posted: 12 Jan 2007, 3:00:28 UTC
The text passage describes a probability puzzle involving a game with three cards, one of which is a Joker. The player selects a card, and the computer reveals a non-Joker card from the remaining two. The player then has the option to stick with their original choice or switch to the other remaining card. The puzzle asks whether it makes a difference to the player's odds of winning if they switch or stick with their original choice.
single_question_with_answer

the passage contains a single mathematical question (whether it makes a difference to switch or stick) and provides an answer in the form of a discussion and email exchange, where the correct answer is revealed to be that switching increases the probability of winning.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Three Card Rinsel, anyone?

Message boards : Cafe SETI : Three Card Rinsel, anyone?
Message board moderation

AuthorMessage
rinselberg
Volunteer tester

Joined: 16 Oct 06
Posts: 115
Credit: 233,455
RAC: 0
Message 12936 - Posted: 8 Jan 2007, 9:24:13 UTC

I'm not generally one for puzzles or brain teasers, but I just ran into one that is elegant in its simplicity, yet profound in its implications.

Consider a deck of only three playing cards. One of the cards is a Joker. The other two cards could be anything - even duplicates of each other - anything but another Joker. Three cards, one Joker.

You play this game with a computer. The computer can only play fairly and exactly by the rules. The computer deals the cards face down in front of you, Left, Center and Right. The computer is perfectly randomized so that before the deal, the probability that the Joker will be dealt in any particular order (Left, Center or Right) is always one chance in three. After the deal, the computer always knows which card is the Joker.

The cards have been dealt. This is what the computer "sees" ...

Your objective is to select the Joker. You are perfectly versed in the rules of the game and about how the computer is programmed. But you cannot predict the outcome of the computer's randomizing calculations. At this point you can't do any better than a random selection of your own, so you point to one of the cards - Left, Center or Right. It doesn't make the slightest difference which one. Let's say you select the card on the Left.

This is what you see. You select the card on the Left ...

There is only one Joker, so whichever card you selected, at least one and possibly both of the other cards are losers. Whichever card you selected, the computer responds by facing one of the other cards and showing you a loser. If, on the strength of one chance in three, you selected the card that the computer knows is the Joker, then the computer has one additional computation to perform. It must decide which one of the two cards that you didn't select - both cards, losers - to reveal to you. It does so in a perfectly random way. It performs the software equivalent of flipping a coin to determine which one of the two losers to face.

After the computer shows you a loser, and only two cards remain face down, you have an option: You can play the card that you selected - or you can switch (renege) and play the last remaining card.

The computer has faced a loser from the cards that you didn't select (Center; Right). Should you play your selection - the card on the Left - or should you switch and play the last remaining card - the card in the Center ..?

You want to win. So what decision do you make? Or does it even make any difference to your odds of winning, whether you play your selection, or renege and play the other card?

Instead of posting, why not just send me an email via rinselberg2@sbcglobal.net ..? I will post only a statistical breakdown of the responses - no user names.

Images: Iraq Playing Cards. Courtesy of WNBC, New York City, New York.
ID: 12936 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 12948 - Posted: 8 Jan 2007, 23:32:44 UTC

It is quite obvious that you should renege and play another other card since it has a better chance of getting the Joker than no chance at all if you stay with the losing card.

Secondly, why would I want to send you an email and reveal my own email address to you? Are you going to spam me or sell my email address on to other spammers?

ID: 12948 ·
rinselberg
Volunteer tester

Joined: 16 Oct 06
Posts: 115
Credit: 233,455
RAC: 0
Message 12949 - Posted: 8 Jan 2007, 23:59:52 UTC - in response to Message 12948.

It is quite obvious that you should renege and play another other card since it has a better chance of getting the Joker than no chance at all if you stay with the losing card.

Secondly, why would I want to send you an email and reveal my own email address to you? Are you going to spam me or sell my email address on to other spammers?

Aside from a sort of general caution (which I understand), why would you think that a bona fide SETI@home beta tester like me would want to spam you or sell your email address to other spammers? Have you looked at my other message board posts? They're almost all under the "Number crunching" category. Evidence of a straightforward and honest beta test volunteer. A somewhat iconoclastic personal style, perhaps - but my substance - as far as my beta test activities - is rock solid. I stand on my record.

If this message board had a PM (Private Message) option, I would have invited PMs instead of emails.

I was hoping that someone might enjoy responding to me about this card game puzzle without posting or adding a visible message - so as to not "let the cat out of the bag" about the answer(s) to the puzzle. Hence, the suggestion of an email or PM. I'm interested in how different people think and express themselves via the Internet. I did get three PMs on the subject from another forum where I posted the same material.

But it's clear that I did not make the objective of this clear enough for you. I guess I did not describe the game clearly enough for you. It's not just about that particular configuration of cards that I presented, where the Joker is the Center card and the human player starts by selecting the card on the Left. I was trying to cover the general case. Remember, there is sure to be one Joker. The player picks one of the cards, initially, and then the computer responds. It's possible that the player unknowingly selects the Joker (on the strength of one chance in three) - or - in the case that I illustrated with those playing card images - it's possible that the player unknowingly selects one of the two other card-values that I defined from the very outset as losers.

Does this make it more understandable for you - as to what kinds of reponses I was looking for?

More than anything else, it was just fun for me to put this together as carefully as I did with my own words and images - and some links to other web pages on this topic - which, sooner or later I would post here, or PM/email as my reply to anyone who finds the puzzle of some interest. Everyone has their own idea of fun ..?

Yours truly.
ID: 12949 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 12982 - Posted: 10 Jan 2007, 0:08:15 UTC - in response to Message 12949.

Does this make it more understandable for you - as to what kinds of reponses I was looking for?

I'm not sure it really does. It's a rather long explanation about choices involving just three cards and I fear I don't have the attention span to go over it again with your added qualification to find the complications which I obviously can't see.

I think the biggest block to my thought process here is your choice to use an image of Saddam Hussein. I expect you didn't realize he was hung recently and controversy about his death is still raging.

Or is using this card part of your weird game?

ID: 12982 ·
rinselberg
Volunteer tester

Joined: 16 Oct 06
Posts: 115
Credit: 233,455
RAC: 0
Message 12986 - Posted: 10 Jan 2007, 1:03:07 UTC - in response to Message 12982.

For sure, I got the news about the recently late Saddam Hussein.

The Iraq cards are what is called a "subtext" - meaning an implicit or unspoken message - perhaps even veiled or cloaked message of a literary text.

But that doesn't mean I was trying to be any more than just casually or slightly political - I'm not going to try to subvert this forum for repeated political harangues, as sometimes happens in the "Cafe" part of other technical forums.

I've had eight responders in all. You're the first one to comment on the style of the card images that I selected. And the first one to respond from the other side of the Atlantic. Which adds a little bit to my "fun".

But - if we could get past the specific card images that I selected - it really is a bonafide puzzle. Of the seven other responders, four got it right and three got it wrong. As for me - I got it wrong when I first ran into it a few weeks ago during a science segment on cable TV.

I'm going to hold out for a bit and see if any other beta testers are prompted to respond - then I will post a link to my own little explanatory essay about the solution to the puzzle. No more card images or political subtexts ...

I appreciate your interest - the worst thing about these forums is to not have anyone respond at all.

ID: 12986 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 12988 - Posted: 10 Jan 2007, 1:38:13 UTC - in response to Message 12986.

I appreciate your interest - the worst thing about these forums is to not have anyone respond at all.

It's a good job I posted then.

What was on the cards was irrelevant, I was just fishing for more information from you in an expected explanation, which you duly gave.

You see, I think the three got it wrong because they don't understand the game. The answer to the game is very simple, as soon as you can work out what is supposed to be going on. 'That' is the real challenge to your game.

It's a bit like life. Nobody really knows what it's all about. If they did, they might start to enjoy it.

ID: 12988 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 13022 - Posted: 10 Jan 2007, 19:36:32 UTC

I've sent you an email. I quite enjoyed trying to solve that. I think I have the answer, but not that confident about it; look forward to hearing the solution.

This takes me back to queuing theory when a man faced a queue with 10 people waiting for ice cream at a ice cream van - calculate the probability that he will join the queue, as opposed to walking off and deciding not to queue. Arrrgh! What if the queue was 15 people? Aarrrrrrrghhhh!

ID: 13022 ·
GalaxyIce
Volunteer tester

Joined: 10 Oct 06
Posts: 555
Credit: 54,802
RAC: 0
Message 13056 - Posted: 11 Jan 2007, 12:45:22 UTC - in response to Message 13022.

I've sent you an email. I quite enjoyed trying to solve that. I think I have the answer, but not that confident about it; look forward to hearing the solution.

Thank you for your reply rinselberg. I was pleased to see I had solved this correctly. It's actually a very good puzzle and I would be pleased to try out any more you have. Thanks.

ID: 13056 ·
rinselberg
Volunteer tester

Joined: 16 Oct 06
Posts: 115
Credit: 233,455
RAC: 0
Message 13089 - Posted: 12 Jan 2007, 3:00:28 UTC
user
The text passage describes a probability puzzle involving a game with three cards, one of which is a Joker. The player selects a card, and the computer reveals a non-Joker card from the remaining two. The player then has the option to stick with their original choice or switch to the other remaining card. The puzzle asks whether it makes a difference to the player's odds of winning if they switch or stick with their original choice.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question (whether it makes a difference to switch or stick) and provides an answer in the form of a discussion and email exchange, where the correct answer is revealed to be that switching increases the probability of winning.