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Monty Hall, we have a PROBLEM
- Thread starter owslachief
- Start date
owslachief
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Re: Monty Hall, we have a PROBLEM
So about 4 months ago, I got an unsolicited Email from a service that claimed to have exclusive inside knowledge of upcoming college football games. The body of the message ended with a simple statement: "Hawaii will beat Colorado State", followed by a link to learn more. Not at all intrigued, I moved on. I got an IM a couple days later by my friend in Honolulu gloating over his proud alma mater's win over CSU.
About the same time next week another Email arrived: "Mark it: Eastern Michigan over Purdue". Sure enough, the following Saturday the Eagles pulled the upset. I resisted the urge to click the link, and did the same the next week when the Email from that service proclaimed "BYU will shock Wisconsin". When that indeed happened a couple days later, my resistance was wearing down. I opened the link and found "Inside Track to Fortune" making a pitch for its services.
But I'm extremely wary of these things and KNEW there's a catch to every get-rich-through-inside-knowledge scheme, so I made a vow to myself to stay the course the rest of the season and not give in.
Until Week 13. This time, instead of the usual Email, ITtF's message was "For a mere $100, get this week's shocking upset!". Knowing (by the way) by this time they'd been right all previous 12 weeks, the arguments for not going for it completely wore thin. I made my $100 online payment, received a somewhat reasonable upset prediction: Auburn over Alabama, and placed a $2,500 bet with a reputable sports betting service - putting my money on Auburn.
A moment of clarity soon found me, however. I realized I was most likely duped, and the relatively easy scam used to accomplish it.
What was this scheme?
So about 4 months ago, I got an unsolicited Email from a service that claimed to have exclusive inside knowledge of upcoming college football games. The body of the message ended with a simple statement: "Hawaii will beat Colorado State", followed by a link to learn more. Not at all intrigued, I moved on. I got an IM a couple days later by my friend in Honolulu gloating over his proud alma mater's win over CSU.
About the same time next week another Email arrived: "Mark it: Eastern Michigan over Purdue". Sure enough, the following Saturday the Eagles pulled the upset. I resisted the urge to click the link, and did the same the next week when the Email from that service proclaimed "BYU will shock Wisconsin". When that indeed happened a couple days later, my resistance was wearing down. I opened the link and found "Inside Track to Fortune" making a pitch for its services.
But I'm extremely wary of these things and KNEW there's a catch to every get-rich-through-inside-knowledge scheme, so I made a vow to myself to stay the course the rest of the season and not give in.
Until Week 13. This time, instead of the usual Email, ITtF's message was "For a mere $100, get this week's shocking upset!". Knowing (by the way) by this time they'd been right all previous 12 weeks, the arguments for not going for it completely wore thin. I made my $100 online payment, received a somewhat reasonable upset prediction: Auburn over Alabama, and placed a $2,500 bet with a reputable sports betting service - putting my money on Auburn.
A moment of clarity soon found me, however. I realized I was most likely duped, and the relatively easy scam used to accomplish it.
What was this scheme?
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WisconsinWildcard
The plural of anecdote is not data
owslachief
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Re: Monty Hall, we have a PROBLEM
As both the puzzle and Wildcard's answer are related to "The Gambler's Mistake", which was posed in the book Einstein's Riddle, well played
As both the puzzle and Wildcard's answer are related to "The Gambler's Mistake", which was posed in the book Einstein's Riddle, well played
Ralph Baer
Let's Go 'Tute!
owslachief
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Re: Monty Hall, we have a PROBLEM
Can you stand one more white hat/black hat problem?
There is a red herring involved (not counting the numbers involved), so caution ahead.
5 people have been notified that they have been awarded $15 million to split among them. There is a catch: Either a white hat or black hat is placed on each of their heads, and each must correctly identify which color hat he or she is wearing in order to get a share. Further, the prize official tells them they will be arranged in a straight queue, one behind the next, with the contestant in the back able to see all the contestants ahead of him/her, the one ahead of him/her will see the 3 ahead, and so forth. The guessing will start with the last person in line, and continue forward to the first person in line. Each contestant will hear all the guesses of the ones behind them, and whether or not they were correct.
All of the prize money will be awarded to split between the correct guessers.
The number of white or black hats will not be discovered until the end of the contest.
They are told that the contest will take place the next day. They are given the night to devise a plan. The brightest among them indeed comes up with a plan, but it will involve drawing straws.
So ...
(1) What is the collective plan, and (2) why must they draw straws?
Can you stand one more white hat/black hat problem?
There is a red herring involved (not counting the numbers involved), so caution ahead.
5 people have been notified that they have been awarded $15 million to split among them. There is a catch: Either a white hat or black hat is placed on each of their heads, and each must correctly identify which color hat he or she is wearing in order to get a share. Further, the prize official tells them they will be arranged in a straight queue, one behind the next, with the contestant in the back able to see all the contestants ahead of him/her, the one ahead of him/her will see the 3 ahead, and so forth. The guessing will start with the last person in line, and continue forward to the first person in line. Each contestant will hear all the guesses of the ones behind them, and whether or not they were correct.
All of the prize money will be awarded to split between the correct guessers.
The number of white or black hats will not be discovered until the end of the contest.
They are told that the contest will take place the next day. They are given the night to devise a plan. The brightest among them indeed comes up with a plan, but it will involve drawing straws.
So ...
(1) What is the collective plan, and (2) why must they draw straws?
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Re: Monty Hall, we have a PROBLEM
This makes no sense to me. The premise is that you want as many others to guess wrong as possible, so why would they work together to devise a plan? If they’re that cooperative that they’re going to work together, then they’re clearly altruistic enough that they’re willing to walk away with $3M each. If that is the case, then they just need at least one person to get it right, and then they can just divvy up the winnings $3M each after the fact. So the first guy just “guesses” the color of the hat in front of him, that guy gets his hat right, and everyone walks away with $3M no matter how many other people get it right.
I see no need for drawing straws.
This makes no sense to me. The premise is that you want as many others to guess wrong as possible, so why would they work together to devise a plan? If they’re that cooperative that they’re going to work together, then they’re clearly altruistic enough that they’re willing to walk away with $3M each. If that is the case, then they just need at least one person to get it right, and then they can just divvy up the winnings $3M each after the fact. So the first guy just “guesses” the color of the hat in front of him, that guy gets his hat right, and everyone walks away with $3M no matter how many other people get it right.
I see no need for drawing straws.
owslachief
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Re: Monty Hall, we have a PROBLEM
Actually, it is a strange problem because although competition is human nature, the fact is that for the good of each individual (save one potentially unfortunate soul), it's important that as many people as possible get their answers right. That plays a part in the solution to the puzzle, and the reason for drawing straws is a clue to the answer to the first question.
Let me rephrase this: If more than one person gets their answers wrong, the rest of the folks have a significantly smaller chance of answering correctly.
Finally I must apologize because there's one clarification that probably can't be merely assumed. It's in bold in my post.
The answer is here, cleverly camouflaged in white:
The plan is for the last person in line (the first to guess) to answer "white" if (s)he thinks the total number of black hats placed is odd, or "black" if (s)he think the number of black hats is even. Each deduces their answer based on what they heard behind them, combined with what they see in front of them.
So let's run this through: The last person in line, not knowing what color hat he's wearing and not having the benefit of hearing any guesses and responses so far, guesses the number of black hats is even, so he answers "black". "Correct" responds the official. The next person ahead of him hears this, looks ahead of her to see the worn hats remaining and will without hesitation gives her answer. She, and each person in front of her, will have all the information needed as the guessing moves forward.
An important point is even if the last person in line has guessed wrong, each person going forward will still have the information they need to guess correctly - it's just opposite of what they would have answered in the first scenario.
And all of this solves the second question: why draw straws? Because of course the last person in line only has a 50-50 chance of answering correctly. He will have to volunteer to be the last in line.
Actually, it is a strange problem because although competition is human nature, the fact is that for the good of each individual (save one potentially unfortunate soul), it's important that as many people as possible get their answers right. That plays a part in the solution to the puzzle, and the reason for drawing straws is a clue to the answer to the first question.
Let me rephrase this: If more than one person gets their answers wrong, the rest of the folks have a significantly smaller chance of answering correctly.
Finally I must apologize because there's one clarification that probably can't be merely assumed. It's in bold in my post.
The answer is here, cleverly camouflaged in white:
The plan is for the last person in line (the first to guess) to answer "white" if (s)he thinks the total number of black hats placed is odd, or "black" if (s)he think the number of black hats is even. Each deduces their answer based on what they heard behind them, combined with what they see in front of them.
So let's run this through: The last person in line, not knowing what color hat he's wearing and not having the benefit of hearing any guesses and responses so far, guesses the number of black hats is even, so he answers "black". "Correct" responds the official. The next person ahead of him hears this, looks ahead of her to see the worn hats remaining and will without hesitation gives her answer. She, and each person in front of her, will have all the information needed as the guessing moves forward.
An important point is even if the last person in line has guessed wrong, each person going forward will still have the information they need to guess correctly - it's just opposite of what they would have answered in the first scenario.
And all of this solves the second question: why draw straws? Because of course the last person in line only has a 50-50 chance of answering correctly. He will have to volunteer to be the last in line.
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Re: Monty Hall, we have a PROBLEM
Why? You said, "All of the prize money will be awarded to split between the correct guessers," so as long as 1 person gets it right, then ALL $15M is still awarded. If exactly one person gets it right, he gets $15M, and therefore each of these altruistic souls still gets $3M.
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owslachief
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Re: Monty Hall, we have a PROBLEM
The response to your point lies in the solution to the first question, but again I'll restate the clue:
The response to your point lies in the solution to the first question, but again I'll restate the clue:
So altruism and the best chance for personal gain actually depend on the same thing in this particular problem.
Re: Monty Hall, we have a PROBLEM
Otherwise, next problem?
I don't need a clue. I already gave a very simple, correct answer that guarantees that the group can split the full $15M. If you think my answer is wrong, feel free to show me why.
Otherwise, next problem?
owslachief
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Re: Monty Hall, we have a PROBLEM
* The contestants line up facing the person directly ahead of them. Let's say they're all facing east
* Each contestant has a hat placed on their head
* Each contestant gets one guess. They can't tell the person ahead of them what THAT person has on his/her head (does that help, and/or should that have been stated explicitly?)
At any rate, it's pretty slow around here, so I figured one puzzle would relieve the tedium. I'm always ready for the Next Problem.
I can't help but think that the problem I laid out may not have been clear about the rules? What if I state them this way:
* The contestants line up facing the person directly ahead of them. Let's say they're all facing east
* Each contestant has a hat placed on their head
* Each contestant gets one guess. They can't tell the person ahead of them what THAT person has on his/her head (does that help, and/or should that have been stated explicitly?)
At any rate, it's pretty slow around here, so I figured one puzzle would relieve the tedium. I'm always ready for the Next Problem.
Re: Monty Hall, we have a PROBLEM
I actually believe that you are misstating the problem. It should just be $3m for each person who gets his own hat correct, $0 for those who get their own hats wrong. THAT would give the group an incentive to get as many right as possible.
That way, if they don’t work together, each person’s expected value is 1.5M, a 50% chance of $3m. However, if they DO work together (and split the winnings evenly), then they can raise their expected value to 2.7m = 50% chance of 4 right ($12m) + 50% chance of 5 right ($15m). It’s also important that the first guy guesses not whether he THINKS the total number of black hats (including his own) is even or odd. He has to guess based on how many black hats he SEES (excluding his own).
I actually believe that you are misstating the problem. It should just be $3m for each person who gets his own hat correct, $0 for those who get their own hats wrong. THAT would give the group an incentive to get as many right as possible.
That way, if they don’t work together, each person’s expected value is 1.5M, a 50% chance of $3m. However, if they DO work together (and split the winnings evenly), then they can raise their expected value to 2.7m = 50% chance of 4 right ($12m) + 50% chance of 5 right ($15m). It’s also important that the first guy guesses not whether he THINKS the total number of black hats (including his own) is even or odd. He has to guess based on how many black hats he SEES (excluding his own).
owslachief
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Re: Monty Hall, we have a PROBLEM
Hey that's a good point. You've taken what I meant to be the red herring and actually made it matter, and I see from a competitive incentive perspective it can be refined to what you stated.
Have a good day.
Hey that's a good point. You've taken what I meant to be the red herring and actually made it matter, and I see from a competitive incentive perspective it can be refined to what you stated.
Have a good day.
