Re: Monty Hall, we have a PROBLEM
spell check can be a necessary but not a sufficient condition of accuracy sometimes....
spell check can be a necessary but not a sufficient condition of accuracy sometimes....
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Monty Hall, we have a PROBLEM
- Thread starter owslachief
- Start date
unofan
Well-known member
So this obviously fabricated story is making the rounds. I do have a question that I didn't see brought up in any of the few dozen comments that I could stomach reading, and I would put it to this audience:
In decimal notation, doesn't "999" also include implied operators? That is, isn't 999 really just shorthand for 9x100 + 9x10 + 9?
(and now my head hurts from thinking about the number 10, which is really 1x10+0. But you can't use "10" in the definition of itself, so we should really break that down as 1x (1x10+0)+0, but....)
In decimal notation, doesn't "999" also include implied operators? That is, isn't 999 really just shorthand for 9x100 + 9x10 + 9?
(and now my head hurts from thinking about the number 10, which is really 1x10+0. But you can't use "10" in the definition of itself, so we should really break that down as 1x (1x10+0)+0, but....)
unofan
Well-known member
I suppose, but you could break it out in an infinite number of ways (999 is also 1+1+1+1.... or 111 x3x3 or 10x10x9 + 9 x 10 x 9), so I'm not understanding why that matters or where you're going with it.
Last edited:
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
In front of you are two boxes. Box A is transparent and you can see it contains $1,000. Box B is opaque and the host tells you it contains either $1 million or nothing. The host offers you a choice: you can either take both Box A and Box B, or just take Box B.
Here's the catch: the host is a mindreader. And a darn good one. As far as anyone can tell he is never wrong. If he predicts you'll take both Box A and Box B, he puts nothing in Box B. If he predicts you'll take just Box B, he puts the million inside. He has already loaded the boxes backstage and can't change them now.
Which is the best play?
Technically, either play can logically be the better play. If you just take Box B and he predicted it, bam, million dollars, end of story. However, if he predicted that and the boxes are already loaded, might as well take both and score an extra thousand as well.
In front of you are two boxes. Box A is transparent and you can see it contains $1,000. Box B is opaque and the host tells you it contains either $1 million or nothing. The host offers you a choice: you can either take both Box A and Box B, or just take Box B.
Here's the catch: the host is a mindreader. And a darn good one. As far as anyone can tell he is never wrong. If he predicts you'll take both Box A and Box B, he puts nothing in Box B. If he predicts you'll take just Box B, he puts the million inside. He has already loaded the boxes backstage and can't change them now.
Which is the best play?
Technically, either play can logically be the better play. If you just take Box B and he predicted it, bam, million dollars, end of story. However, if he predicted that and the boxes are already loaded, might as well take both and score an extra thousand as well.
Re: Monty Hall, we have a PROBLEM
That is what I was thinking. Glad to know I am not completely nuts.
That is what I was thinking. Glad to know I am not completely nuts.
But if we're all nuts, is the sane one nuts?
Re: Monty Hall, we have a PROBLEM
However, you can take both boxes, so you get a grand either way. The "bonus" is the possible million.
However, you can take both boxes, so you get a grand either way. The "bonus" is the possible million.
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
On the other hand, the only way for you to score the full $1,001,000 involves the host making an incorrect prediction (he calls just B and loads the million, you take both,) which we can assume is impossible.
On the other hand, the only way for you to score the full $1,001,000 involves the host making an incorrect prediction (he calls just B and loads the million, you take both,) which we can assume is impossible.
Re: Monty Hall, we have a PROBLEM
But that's on him. Now, if the question was:
Take A OR B, one box has 1K, the other has 1MM, OR take a 3rd option that would reward you with, say, 300K...now it becomes an "expected value" problem.
But that's on him. Now, if the question was:
Take A OR B, one box has 1K, the other has 1MM, OR take a 3rd option that would reward you with, say, 300K...now it becomes an "expected value" problem.
Handyman
Hug someone you care about...
Re: Monty Hall, we have a PROBLEM
But either way, if you take both you are guaranteed money so there is no real "loss". If, say, by taking both you run the risk of getting zero (because you would pick the box with nothing) then there is a dilemma but I would just pick both without hesitation and get straight cash homie.
The host "reading your mind" is a red herring. So what, he has to put money in one box and you know it is there you lose nothing by taking both.
But either way, if you take both you are guaranteed money so there is no real "loss". If, say, by taking both you run the risk of getting zero (because you would pick the box with nothing) then there is a dilemma but I would just pick both without hesitation and get straight cash homie.
The host "reading your mind" is a red herring. So what, he has to put money in one box and you know it is there you lose nothing by taking both.
Re: Monty Hall, we have a PROBLEM
except he knew you were thinking that way before he loaded the boxes.
except he knew you were thinking that way before he loaded the boxes.
Handyman
Hug someone you care about...
Re: Monty Hall, we have a PROBLEM
Yes but we know one of the boxes has the thousand dollars in it cause it is transparent and we see it. It doesnt matter if the host is a mindreader I still get a thousand bucks as long as I choose both boxes. The only way to possibly get no money is to chose Box B and the host predicted that and puts nothing in it. If you take both you are guaranteed to not walk away empty handed.
Under what circumstances is it smarter to just take Box B only? You are leaving $1000 on the table on the off chance you can outwit the host and get a million but if you can outwit the host to get that million why not also get another $1000?
Yes but we know one of the boxes has the thousand dollars in it cause it is transparent and we see it. It doesnt matter if the host is a mindreader I still get a thousand bucks as long as I choose both boxes. The only way to possibly get no money is to chose Box B and the host predicted that and puts nothing in it. If you take both you are guaranteed to not walk away empty handed.
Under what circumstances is it smarter to just take Box B only? You are leaving $1000 on the table on the off chance you can outwit the host and get a million but if you can outwit the host to get that million why not also get another $1000?
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
You're backwards. If the host predicts you'll pick only B, he will have the million inside.
The idea is that this is a paradox with two perfectly rational lines of thinking:
Line 1: Since the boxes are already set, taking both boxes gets you $1,000 more than taking just Box B regardless of what the host predicted. Either he predicted you'd take just B and it's $1,001,000 vs. $1,000,000, or he predicted you'd take both and it's $1,000 vs. $0.
Line 2: It is impossible to get either of $1,001,000 or $1,000,000 by taking both boxes, since this means the host would predict it and not put the million in Box B. Thus, taking just Box B for $1,000,000 is the only logical move.
You're backwards. If the host predicts you'll pick only B, he will have the million inside.
The idea is that this is a paradox with two perfectly rational lines of thinking:
Line 1: Since the boxes are already set, taking both boxes gets you $1,000 more than taking just Box B regardless of what the host predicted. Either he predicted you'd take just B and it's $1,001,000 vs. $1,000,000, or he predicted you'd take both and it's $1,000 vs. $0.
Line 2: It is impossible to get either of $1,001,000 or $1,000,000 by taking both boxes, since this means the host would predict it and not put the million in Box B. Thus, taking just Box B for $1,000,000 is the only logical move.
Handyman
Hug someone you care about...
Re: Monty Hall, we have a PROBLEM
But you still get $1000. I am not backwards...you never said the goal was to maximize your money. There is no incentive not to take both boxes under any circumstance. If you do, you either get $1000 or $1,001,000. There is zero chance you get $0 so you win
There is no paradox. Take both boxes and get paid
(now if you take logic out of the equation, then yes there technically is two parallel lines of thinking but in reality you would be foolish to do otherwise)
But you still get $1000. I am not backwards...you never said the goal was to maximize your money. There is no incentive not to take both boxes under any circumstance. If you do, you either get $1000 or $1,001,000. There is zero chance you get $0 so you win
There is no paradox. Take both boxes and get paid
(now if you take logic out of the equation, then yes there technically is two parallel lines of thinking but in reality you would be foolish to do otherwise)
Re: Monty Hall, we have a PROBLEM
Not sure I agree here. In effect, you are asked to "invest" $1,000 based on your assessment of the host's mind-reading capabilities. If you believe the host can indeed read minds, then you forego the $1,000 in order to get a chance to win $1,000,000, and pick B, since that will be your thinking all along, and you hope you are right in thinking that the host can read your mind.
If you do not believe that the host can read minds, you pick both boxes, and you get $1,000 more than you would have gotten had you picked only B.
It depends ultimately whether you are more loss averse, or more opportunity seeking.
But you still get $1000. I am not backwards...you never said the goal was to maximize your money. There is no incentive not to take both boxes under any circumstance. If you do, you either get $1000 or $1,001,000. There is zero chance you get $0 so you win
There is no paradox. Take both boxes and get paid
(now if you take logic out of the equation, then yes there technically is two parallel lines of thinking but in reality you would be foolish to do otherwise)
Not sure I agree here. In effect, you are asked to "invest" $1,000 based on your assessment of the host's mind-reading capabilities. If you believe the host can indeed read minds, then you forego the $1,000 in order to get a chance to win $1,000,000, and pick B, since that will be your thinking all along, and you hope you are right in thinking that the host can read your mind.
If you do not believe that the host can read minds, you pick both boxes, and you get $1,000 more than you would have gotten had you picked only B.
It depends ultimately whether you are more loss averse, or more opportunity seeking.