owslachief
occupe toi de tes oignons
Last edited:
USCHO Fan Forum
This is a sample guest message. Register a free account today to become a member! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!
-
The USCHO Fan Forum has migrated to a new plaform, xenForo. Most of the function of the forum should work in familiar ways. Please note that you can switch between light and dark modes by clicking on the gear icon in the upper right of the main menu bar. We are hoping that this new platform will prove to be faster and more reliable. Please feel free to explore its features.
Monty Hall, we have a PROBLEM
- Thread starter owslachief
- Start date
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
You're arrested, thrown in jail, and given the death penalty.
The executioner, however, allows you to make one final statement in your last words. If it is a true statement, you'll be hanged. If it is false, you'll be beheaded.
Your statement should be "You're going to behead me." He would have to behead you to make it true, which means he should have hanged you instead. If he hangs you, then it was a false statement and he should have beheaded you instead.
You're arrested, thrown in jail, and given the death penalty.
The executioner, however, allows you to make one final statement in your last words. If it is a true statement, you'll be hanged. If it is false, you'll be beheaded.
Your statement should be "You're going to behead me." He would have to behead you to make it true, which means he should have hanged you instead. If he hangs you, then it was a false statement and he should have beheaded you instead.
owslachief
occupe toi de tes oignons
Jimjamesak
Already insane, UAA making it worse
Re: Monty Hall, we have a PROBLEM
Very similar to Pinocchio saying "My nose will grow now!"
Re: Monty Hall, we have a PROBLEM
I have some reservations about Twitch Boy's auction, in white, in case anyone hasn't read his explanation:
In the abscence of spite, the key is that you only bid $99 if you're the *first* bidder. Even if the other guy has only bid $1 before your $99 bid, it would still be in his best interest to go ahead and bid $100 to improve his net position by $1 (form $1 lost to breaking even). In the real world, I wouldn't bid $99 even on the first bid with a 10-foot pole. Even if there's only a 0.0001% chance that there's a spiteful bidder in the room, throwing your hat into the ring at all exposes you to a huge potential loss, because as soon as the second bidder goes to $100, the infinite loop begins where bidding higher is not spiteful but is actually in both of your own self interests. Even if there's only that 0.0001% chance of a truly spiteful bidder, I guarantee there's at least a 10% chance of a moronic bidder who would bid $100 not out of spite but because he didn't know any better.
Therefore, the optimal bid is not to bid at all.
I have some reservations about Twitch Boy's auction, in white, in case anyone hasn't read his explanation:
In the abscence of spite, the key is that you only bid $99 if you're the *first* bidder. Even if the other guy has only bid $1 before your $99 bid, it would still be in his best interest to go ahead and bid $100 to improve his net position by $1 (form $1 lost to breaking even). In the real world, I wouldn't bid $99 even on the first bid with a 10-foot pole. Even if there's only a 0.0001% chance that there's a spiteful bidder in the room, throwing your hat into the ring at all exposes you to a huge potential loss, because as soon as the second bidder goes to $100, the infinite loop begins where bidding higher is not spiteful but is actually in both of your own self interests. Even if there's only that 0.0001% chance of a truly spiteful bidder, I guarantee there's at least a 10% chance of a moronic bidder who would bid $100 not out of spite but because he didn't know any better.
Therefore, the optimal bid is not to bid at all.
P
Priceless
Guest
Re: Monty Hall, we have a PROBLEM
The only winning move is not to play.
The only winning move is not to play.
Re: Monty Hall, we have a PROBLEM
Reminds me of that childhood game, "let's have a contest to see who can hit each other the softest. You go first."
When I hear / read about stuff parents of young children worry about today, I'm amazed that any of my peers and me made it to adulthood!
Reminds me of that childhood game, "let's have a contest to see who can hit each other the softest. You go first."
When I hear / read about stuff parents of young children worry about today, I'm amazed that any of my peers and me made it to adulthood!
Re: Monty Hall, we have a PROBLEM
ah but they'd never answer "no" in the first place, would they? They'd more likely respond with "I always tell the truth" or some other such non-truthful evasion.
I'll skip all the obvious political jokes too.
ah but they'd never answer "no" in the first place, would they? They'd more likely respond with "I always tell the truth" or some other such non-truthful evasion.
I'll skip all the obvious political jokes too.
XYZ
Smoking in the selection room.
My bad on that. Didn't really read it as I assumed it was the version I had seen before in which #3 was not a given.
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
The following statement is true.
The previous statement is false.
The following statement is true.
The previous statement is false.
Re: Monty Hall, we have a PROBLEM
Or you can just skip a step: This statement is false.
Re: Monty Hall, we have a PROBLEM
So you say...but how reliable are you? did you discover that truth on your own, or is it from sometihing you read on the internet and re-posted without checking its validity first?
So you say...but how reliable are you? did you discover that truth on your own, or is it from sometihing you read on the internet and re-posted without checking its validity first?
Last edited:
Re: Monty Hall, we have a PROBLEM
Something about this thread reminds me of the story of Carl Friedrich Gauss as an elementary school student. Even at that age, he knew more than his teacher.
His harried teacher finally thought of a way to quiet the precocious child. "Add the numbers from 1 to 100" he instructed, hoping to gain a few moments' respite from the child's unrelenting questions.
"Oh, that's easy," supposedly replied the young Gauss. "You take 1+99, 2+98, 3+97, ... and that get's you to 4,900. Add 50 to get 4,950. Then it depends upon whether you said '1 to 100' or '1 through 100' which would make it 5,050."
Something about this thread reminds me of the story of Carl Friedrich Gauss as an elementary school student. Even at that age, he knew more than his teacher.
His harried teacher finally thought of a way to quiet the precocious child. "Add the numbers from 1 to 100" he instructed, hoping to gain a few moments' respite from the child's unrelenting questions.
"Oh, that's easy," supposedly replied the young Gauss. "You take 1+99, 2+98, 3+97, ... and that get's you to 4,900. Add 50 to get 4,950. Then it depends upon whether you said '1 to 100' or '1 through 100' which would make it 5,050."
Ralph Baer
Let's Go 'Tute!
Re: Monty Hall, we have a PROBLEM
http://www.heretical.com/pound/dollar.htmlI have some reservations about Twitch Boy's auction, in white, in case anyone hasn't read his explanation:
In the abscence of spite, the key is that you only bid $99 if you're the *first* bidder. Even if the other guy has only bid $1 before your $99 bid, it would still be in his best interest to go ahead and bid $100 to improve his net position by $1 (form $1 lost to breaking even). In the real world, I wouldn't bid $99 even on the first bid with a 10-foot pole. Even if there's only a 0.0001% chance that there's a spiteful bidder in the room, throwing your hat into the ring at all exposes you to a huge potential loss, because as soon as the second bidder goes to $100, the infinite loop begins where bidding higher is not spiteful but is actually in both of your own self interests. Even if there's only that 0.0001% chance of a truly spiteful bidder, I guarantee there's at least a 10% chance of a moronic bidder who would bid $100 not out of spite but because he didn't know any better.
owslachief
occupe toi de tes oignons
Another paradoxical scenario was used (unsuccessfully) by the doomed right after sentencing. A creative judge handed him an unusual sentence: he was to be executed during a one-week window, and the day of his execution was to be a surprise.
The man reasoned his salvation as follows: if I survive until the last day, next Friday, then I know it's Friday i'm to die, and it's no longer a surprise. So I can't die on Friday. Thursday then becomes the last possible day, but then the same reasoning applies as for Friday! Safe in the knowledge that he can inductively apply that back through the entire week, he serenely waited out the week, until Friday came. In the morning, the executioner arrived, to the doomed man's complete surprise.
owslachief
occupe toi de tes oignons
Xml Something about this thread reminds me of the story of Carl Friedrich Gauss as an elementary school student. Even at that age, he knew more than his teacher.
His harried teacher finally thought of a way to quiet the precocious child. "Add the numbers from 1 to 100" he instructed, hoping to gain a few moments' respite from the child's unrelenting questions.
"Oh, that's easy," supposedly replied the young Gauss. "You take 1+99, 2+98, 3+97, ... and that get's you to 4,900. Add 50 to get 4,950. Then it depends upon whether you said '1 to 100' or '1 through 100' which would make it 5,050."[/QUOTE]
Yep the 100 x (avg. of #s between 1 and 99, which is 50)
His harried teacher finally thought of a way to quiet the precocious child. "Add the numbers from 1 to 100" he instructed, hoping to gain a few moments' respite from the child's unrelenting questions.
"Oh, that's easy," supposedly replied the young Gauss. "You take 1+99, 2+98, 3+97, ... and that get's you to 4,900. Add 50 to get 4,950. Then it depends upon whether you said '1 to 100' or '1 through 100' which would make it 5,050."[/QUOTE]
Yep the 100 x (avg. of #s between 1 and 99, which is 50)
Last edited:
FlagDUDE08
Banned
Re: Monty Hall, we have a PROBLEM
There are all kinds of series like that. Adding numbers = n(n+1)/2; the square of n is the summation (x = 1 to n) of 2x-1; so on and so forth.
Here's an interesting problem: On a site called moola.com, there is a game called Gold Rush. The idea is that you get "gold bars" weighed from 1 to 6, as does your opponent. Bars from 1 to 6 are up for grabs in each round. Whomever puts down the highest weight takes the round's pot. Ties put everything into the pot and carries over to the next round. How do you get yourself to win that?
There are all kinds of series like that. Adding numbers = n(n+1)/2; the square of n is the summation (x = 1 to n) of 2x-1; so on and so forth.
Here's an interesting problem: On a site called moola.com, there is a game called Gold Rush. The idea is that you get "gold bars" weighed from 1 to 6, as does your opponent. Bars from 1 to 6 are up for grabs in each round. Whomever puts down the highest weight takes the round's pot. Ties put everything into the pot and carries over to the next round. How do you get yourself to win that?
Twitch Boy
Defacing this tagline is a MAX foul
Re: Monty Hall, we have a PROBLEM
You're at a party. I'll bet you $100 that at least two of the people in the room share a birthday.
How many people would need to be present for it to be an unfavorable bet for you?
Just 23. At 23 it's about a 50/50 shot that there will be a matching birthday. At 30 there's about a 70% chance of a match. At 50 it's a 97% chance.
Imagine it this way: the guests enter one at a time and state their birthday. If anyone repeats a birthday...THE ROOM EXPLODES!
First guest = can be any date. 365/365 odds of no match. (Assuming no leap years.)
Second guest = has to dodge the first date. 365/365 * 364/365 odds of no match.
Third guest = has to dodge the first and second dates. 365/365 * 364/365 * 363/365 odds of no match.
...
Tenth guest = has to dodge nine dates. 365/365 * 364/365 * ... * 356/365 odds of no match.
...
Twentieth guest = has to dodge NINETEEN dates. 365/365 * 364/365 * ... * 346/365 odds of no match.
It may seem like only a few days to dodge, but try dodging them 23 times in a row. Or 30. Or 50.
You're at a party. I'll bet you $100 that at least two of the people in the room share a birthday.
How many people would need to be present for it to be an unfavorable bet for you?
Just 23. At 23 it's about a 50/50 shot that there will be a matching birthday. At 30 there's about a 70% chance of a match. At 50 it's a 97% chance.
Imagine it this way: the guests enter one at a time and state their birthday. If anyone repeats a birthday...THE ROOM EXPLODES!
First guest = can be any date. 365/365 odds of no match. (Assuming no leap years.)
Second guest = has to dodge the first date. 365/365 * 364/365 odds of no match.
Third guest = has to dodge the first and second dates. 365/365 * 364/365 * 363/365 odds of no match.
...
Tenth guest = has to dodge nine dates. 365/365 * 364/365 * ... * 356/365 odds of no match.
...
Twentieth guest = has to dodge NINETEEN dates. 365/365 * 364/365 * ... * 346/365 odds of no match.
It may seem like only a few days to dodge, but try dodging them 23 times in a row. Or 30. Or 50.
Re: Monty Hall, we have a PROBLEM
The Birthday Problem hurts my head. It's awesome though.
The Birthday Problem hurts my head. It's awesome though.