Grammar Nazis - public service or public enemy?
Comments
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Assume you pick door 1
Possible scenarios (all equally likely)
Prize is behind 1: Stick you win, Change you lose
Prize is behind 2: Stick you lose, Change you win
Prize is behind 3: Stick you lose, Change you win
So, not knowing where the prize is, if you change then you win in 2 of 3 cases.0 -
dhope wrote:DonDaddyD wrote:Nah, there are two remaining doors. So assuming one has the prize and the other contains the got the actual real term odds are 50:50.
From the quizmasters perspective the odds may apper to be 5% because he knows the answer and he hasn't given an answer.
The contestant is just being dicked with so doesn't know what to think.
For the outsider looking in there is now only 1 right answer and 1 wrong answer so it's 50:50.
Yep, that's what most assume at first, myself included.
having 2 remaining doors doesn't mean the odds are 50/50. If you started with 2 doors then yes, but you started with 3 and the quizmaster has opened a door based on his knowledge of the winning door, which is what skews the odds.
3 doors = 1 in three chance
Quiz master opens a door, knowing it is the wrong door.
2 door = 1 in 2 or 50:50 (from the perspective of the player)
Hypothetically, what if the quiz master opens the last remaining wrong door. What are the odds then? If its 'evens' because the player is now going to open the right door. Then by adding 1 wrong door (and the player doesn't know which is right and which wrong) then the odds go back to 50:50. So going back to the 3 door, 2 door thing.... If there are 3 doors and 1 is removed the odds are 50:50.
I think.Food Chain number = 4
A true scalp is not only overtaking someone but leaving them stopped at a set of lights. As you, who have clearly beaten the lights, pummels nothing but the open air ahead. ~ 'DondaddyD'. Player of the Unspoken Game0 -
Listen carefully to confirm which of the two little doors are the source of the sound of the bleating goats, then pick the big Up & Over door with CO fumes belching out of it. No?
DHope is correct, but it's still only a statistical probability of being right and only a muppet would expect stats to get them anywhere.0 -
dhope wrote:Assume you pick door 1
Possible scenarios (all equally likely)
Prize is behind 1: Stick you win, Change you lose
Prize is behind 2: Stick you lose, Change you win
Prize is behind 3: Stick you lose, Change you win
So, not knowing where the prize is, if you change then you win in 2 of 3 cases.
The prize can't be behind door 3 - you know that already
There is no benefit to changing“New York has the haircuts, London has the trousers, but Belfast has the reason!0 -
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DonDaddyD wrote:dhope wrote:DonDaddyD wrote:Nah, there are two remaining doors. So assuming one has the prize and the other contains the got the actual real term odds are 50:50.
From the quizmasters perspective the odds may apper to be 5% because he knows the answer and he hasn't given an answer.
The contestant is just being dicked with so doesn't know what to think.
For the outsider looking in there is now only 1 right answer and 1 wrong answer so it's 50:50.
Yep, that's what most assume at first, myself included.
having 2 remaining doors doesn't mean the odds are 50/50. If you started with 2 doors then yes, but you started with 3 and the quizmaster has opened a door based on his knowledge of the winning door, which is what skews the odds.
3 doors = 1 in three chance
Quiz master opens a door, knowing it is the wrong door.
2 door = 1 in 2 or 50:50 (from the perspective of the player)
Hypothetically, what if the quiz master opens the last remaining wrong door. What are the odds then? If its 'evens' because the player is now going to open the right door. Then by adding 1 wrong door (and the player doesn't know which is right and which wrong) then the odds go back to 50:50. So going back to the 3 door, 2 door thing.... If there are 3 doors and 1 is removed the odds are 50:50.
I think.
If you have 3 doors and the quizmaster first opens a door with a goat behind it, then says 'pick a door' then sure, 50/50.
Picking a door, then having someone give you the benefit of their knowledge will change the game completely.
As UE said, make it 20 doors.
You pick one door
Quizmaster opens 18 doors with goats behind.
Quizmaster asks if you want to change.
You still sure it's 50/50 that the first door you picked had a car behind it? Remember, the quizmaster didn't open 18 doors at random, he chose 18 that he knew for certain had goats behind.0 -
OK I get your point.Food Chain number = 4
A true scalp is not only overtaking someone but leaving them stopped at a set of lights. As you, who have clearly beaten the lights, pummels nothing but the open air ahead. ~ 'DondaddyD'. Player of the Unspoken Game0 -
DonDaddyD wrote:OK I get your point.
Explain it to the class
Not that I don't get it, I just want to make sure you do.
*ahem“New York has the haircuts, London has the trousers, but Belfast has the reason!0 -
DonDaddyD wrote:3 doors = 1 in three chance
Quiz master opens a door, knowing it is the wrong door.
2 door = 1 in 2 or 50:50 (from the perspective of the player)
Bad Sketchley. Very bad Sketchley.
Perhaps this will help.
Step 1: 3 doors = 1 in three chance. Tick.
You choose Door #1. You have a 1/3 chance of bagging the car. That means there is a 2/3 chance that the car is behind Doors #2 and #3.
Step 2: Quiz master opens Door #3, revealing curry fodder.
Now, there is still a chance of precisely 1/3 that the car is behind Door #1. The fact that a door has been opened hasn't increased the probability of a car being behind Door #1 - there were always 3 doors, and always one car.
There still therefore remains a 2/3 chance that the car is behind Doors #2 and #3.
Step 3: What are the chances of the car being behind Door #2? Well, the chances that the car was behind Door #2 or Door #3 were 2/3 - see steps 1 and 2. And now we know it is not behind Door #3, so the chances it is behind Door #2 must be 2/3.
If that's making your head spin, try this.
You choose Door #1. You are then asked: "would you like to be able to choose Doors #2 AND #3? And to sweeten the deal, I'll guarantee that there's a goat behind Door #3".
Doors #2 and #3 gives you a 2/3 chance of winning. Those are much better odds that sticking with Door #1, right? And if you know Door #3 is a dead end, you'd be a mug not to take Door #2, right?0 -
I can't accept that the game doesn't change after the goat is revealed. (There's a sentence I never thought I'd type)
Put it this way
I have a gun with 3 chambers and 1 bullet
I hand it to G66, he puts it to his head and pulls the trigger - he lives
G66 hands the gun to DDD.
You telling me that DDD has a 1 in 3 chance now?“New York has the haircuts, London has the trousers, but Belfast has the reason!0 -
TailWindHome wrote:I can't accept that the game doesn't change after the goat is revealed. (There's a sentence I never thought I'd type)
Put it this way
I have a gun with 3 chambers and 1 bullet
I hand it to G66, he puts it to his head and pulls the trigger - he lives
G66 hands the gun to DDD.
You telling me that DDD has a 1 in 3 chance now?
Different game, different maffs. In that example, DDD would have a 50:50 chance of getting dead.0 -
dhope wrote:DonDaddyD wrote:dhope wrote:DonDaddyD wrote:Nah, there are two remaining doors. So assuming one has the prize and the other contains the got the actual real term odds are 50:50.
From the quizmasters perspective the odds may apper to be 5% because he knows the answer and he hasn't given an answer.
The contestant is just being dicked with so doesn't know what to think.
For the outsider looking in there is now only 1 right answer and 1 wrong answer so it's 50:50.
Yep, that's what most assume at first, myself included.
having 2 remaining doors doesn't mean the odds are 50/50. If you started with 2 doors then yes, but you started with 3 and the quizmaster has opened a door based on his knowledge of the winning door, which is what skews the odds.
3 doors = 1 in three chance
Quiz master opens a door, knowing it is the wrong door.
2 door = 1 in 2 or 50:50 (from the perspective of the player)
Hypothetically, what if the quiz master opens the last remaining wrong door. What are the odds then? If its 'evens' because the player is now going to open the right door. Then by adding 1 wrong door (and the player doesn't know which is right and which wrong) then the odds go back to 50:50. So going back to the 3 door, 2 door thing.... If there are 3 doors and 1 is removed the odds are 50:50.
I think.
If you have 3 doors and the quizmaster first opens a door with a goat behind it, then says 'pick a door' then sure, 50/50.
Picking a door, then having someone give you the benefit of their knowledge will change the game completely.
As UE said, make it 20 doors.
You pick one door
Quizmaster opens 18 doors with goats behind.
Quizmaster asks if you want to change.
You still sure it's 50/50 that the first door you picked had a car behind it? Remember, the quizmaster didn't open 18 doors at random, he chose 18 that he knew for certain had goats behind.
OK, I'll bite... Maybe this is about gaming the quizmaster, rather than playing the odds, in which case I've missed the point completely!
The quizmaster's removal of goat-doors doesn't change the game, unless you assume that he's giving you a clue.
With twenty doors you choose number one. He removes eighteen, without letting on whether your choice was correct or not. You are given the chance to change but have no more information about the current situation than you did before. You can change your selection but you still don't know which door is correct, so there's no advantage to doing so.
Your odds are better than they were, because the quizmaster has reduced them from one in twenty to one in two, but you still don't know whether you were right the first time or not.
If we assume, for example, that he wants you to win a goat, so they can run the show the following week with the same car, then he's just trying to con you into changing from the correct door to the last wrong one. If he wants you to win the car, because they need winners to improve their viewing figures, then he's trying to help you win instead. You don't know which... do you?
The quizmaster can open any wrong door. Unless you have some way of knowing which door he won't open he's not telling you anything... and he always has the choice of your selected door and at least one wrong one.
From a statistical point of view, though, there's no advantage to changing your original choice... the odds are the same for both doors. (50/50).
[edit]: So- most of the above (and specifically the conclusion I drew) is flat wrong. Fascinating... thanks for the education, guys :-)
Cheers,
W.0 -
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TailWindHome wrote:I can't accept that the game doesn't change after the goat is revealed. (There's a sentence I never thought I'd type)
Put it this way
I have a gun with 3 chambers and 1 bullet
I hand it to G66, he puts it to his head and pulls the trigger - he lives, because the good guy always makes it to the final scene of the movie.
G66 hands the gun to DDD.
You telling me that DDD has a 1 in 3 chance now?
Indeed, different game.
Take you game. DDD says "I want the third chamber" [he chooses Door #3]
I take the gun, and fire it, disclosing that the first chamber is empty. [I disclose the goat behind Door #1]
The chance that the third chamber had the bullet was 1/3.
The chance that the bullet was in chamber 1 and 2 was 2/3.
I've shown it is not in chamber 1.
So the chance of the bullet being in chamber 2 is 2/3.
DDD would choose poorly were he to say "I want chamber 2, now I've seen G66 dodge the bullet". He should stick to chamber 3.
If he survives, you can have the last go though. Remember, there's a chance the bullet will bounce off the outside of his head. You never know...0 -
I'm not trying to sound patronising here by quoting repeatedly, seriously.
It changes the odds dramatically.WGWarburton wrote:The quizmaster's removal of goat-doors doesn't change the game
Yep.WGWarburton wrote:With twenty doors you choose number one. He removes eighteen, without letting on whether your choice was correct or not. You are given the chance to change but have no more information about the current situation than you did before.
You don't know for certain but you now have a very good idea.WGWarburton wrote:You can change your selection but you still don't know which door is correct, so there's no advantage to doing so.
Precisely. There was a 1 in 20 chance of you being right. The quizmaster tailored the doors he opened according to your initial pick. He doesn't actually have a choice of which door he opens. If you choose the wrong one then he has to open 18 other wrong ones, leaving only the one you picked at the right one. If you chose the right one then okay, he can pick 18 other random wrong doors, leaving your correct one and a random wrong one.WGWarburton wrote:Your odds are better than they were, because the quizmaster has reduced them from one in twenty to one in two, but you still don't know whether you were right the first time or not.
In 19 of 20 initial situations the only remaining door he doesn't open will be the winner. In 1 of 20 the only remaining door he doesn't open will be a loser. That's why the odds become hugely in your favour to switch.
The quizmaster doesn't care if you win a goat or a car, there is no motivation and no trick. He As above, he doesn't really have a choice which doors he opens, he's just following the rules.WGWarburton wrote:If we assume, for example, that he wants you to win a goat, so they can run the show the following week with the same car, then he's just trying to con you into changing from the correct door to the last wrong one. If he wants you to win the car, because they need winners to improve their viewing figures, then he's trying to help you win instead. You don't know which... do you?
The odds are 95/5, not 50/50.WGWarburton wrote:The quizmaster can open any wrong door. Unless you have some way of knowing which door he won't open he's not telling you anything... and he always has the choice of your selected door and at least one wrong one.
From a statistical point of view, though, there's no advantage to changing your original choice... the odds are the same for both doors. (50/50).0 -
Ok, what I don't understand about this is why you wouldn't change the odds [on your initial choice being correct] after having new information about the potential number of goats in the remaining selection?0
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DonDaddyD wrote:MrChuck,
Do you form an opinion of people based on how good there grammar is. There isn't enough oxygen to sustain two people up there, I reckon.
I mean based on the serious discussions but grammar on a forum, really?
What do you do:
'Used one 'o' instead of two for the word 'too'. Therefore must be a chav?'
Seems a tad judgemental to me.
Not quite. But if you think that YOU don't form some idea of the person behind a post based on what's in that post then you are deluding yourself. Seriously. We all do it, for better or worse. What you say and how you say it says something about you. You can imply that I'm some sort of snob if you like but there it is.0 -
You've chosen your door.
Without opening any of the doors, the quizmaster then says you can stick with your one door, or change to have both the other two. Do you change? Of course you do, even 'though you know there's a goat behind one of the doors you now have.0 -
This goat and door thingy is dragging on too long....
For all you non-statisticians out there, think about all the paths to successfully getting the car:
Ok, there are 20 doors. Behind one is a car.
Choose a door. 18 other doors are revealed to have goats.
Now either change your door, or stick with the same one.
Let's consider the change door policy.
If we chose the incorrect door at the first decision (19/20 chance) this yields a win.
Let's consider the stick with same door policy
If we chose the correct door at the first decision (1/20 chance) this yields a win.
Lo and behold we're 19x more likely to win if we change door.
THis problem has been done and dusted from the year X... yawn yawn.
With only 3 initial doors a la the original conundrum, it's a bit more subtle but we're still 2x likely to win with the change door policy.0 -
# 1 competitors first choice
# 2-19 host opens
# 20 remaining unopened door
The logic that it is better to switch to #20 is based on the 19/20 probability that the car is behind #20.
Surely there is also a 19/20 probability that the car is behind #1-19, you know it's not behind #2-19 so so wouldn't pick them.
It makes no difference picking #1 or #20“New York has the haircuts, London has the trousers, but Belfast has the reason!0 -
“New York has the haircuts, London has the trousers, but Belfast has the reason!0
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notsoblue wrote:Ok, what I don't understand about this is why you wouldn't change the odds [on your initial choice being correct] after having new information about the potential number of goats in the remaining selection?
Consider this.
You pick a card from a deck. You don't look at it. What are the chances it is the ace of spades? 1/52. Obvious.
The dealer throws 50 of the 51 cards he is holding away. What is the chance you are holding the ace of spades? Still 1/52.
The dealer now asks you what are the chances that the card he has is the ace of spades. You're smart though. So you ask him "when you threw the other cards away, did you do so randomly?". He says yes. So the chance the dealer is holding the ace of spades is also 1/52.
But what if the dealer were to say "No. Each time I threw one away, I made sure it was not the ace of spades". What's the chance he is holding the ace of spades now? 51/52 - the only way he cannot be holding the ace is if you are.
But what is the chance you are holding the ace? Your chance remains 1/52. You picked from a pack of 52 cards, entirely at random. The dealer didn't pick his card at random - he went through the deck, discarding cards that weren't the ace until he had one card left. That's why his chances are so much higher than yours.
When the host opens the door, he does so knowing that he will reveal a goat. His is a non-random selection. Your choice of Door #1 is random.
Geddit?0 -
Greg66 wrote:Someone else recently wrote:Hence we get people like you, who, either by good timing or fortunate schooling, feel that they are superior to those who can't correctly place a comma.
Fixed that for you....2010 Lynskey R230
2013 Yeti SB660 -
TailWindHome wrote:
The initial thread was boring too.0 -
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TailWindHome wrote:# 1 competitors first choice
# 2-19 host opens
# 20 remaining unopened door
The logic that it is better to switch to #20 is based on the 19/20 probability that the car is behind #20.
Surely there is also a 19/20 probability that the car is behind #1-19, you know it's not behind #2-19 so so wouldn't pick them.
It makes no difference picking #1 or #20
The fact that #1 remains unopened gives you no information. The host couldn't open it. The fact that #20 remains unopened tells you there's a 1 in 2 chance of it being the prize.
Go back to my original post and think it through or are you a logic nazi lol?0 -
“New York has the haircuts, London has the trousers, but Belfast has the reason!0
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TailWindHome wrote:# 1 competitors first choice
# 2-19 host opens
# 20 remaining unopened door
The logic that it is better to switch to #20 is based on the 19/20 probability that the car is behind #20.
Surely there is also a 19/20 probability that the car is behind #1-19, you know it's not behind #2-19 so so wouldn't pick them.
It makes no difference picking #1 or #20
You're almost there
# 1 competitors first choice
There is a 1/20 chance it's behind #1.
There is a 19/20 chance that it's behind #2-#20.
# 2-19 host opens
# 20 remaining unopened door
There is still a 19/20 chance that it's behind #2-#20. This doesn't change
New knowledge is that there is a a 0/20 chance that it's behind #2-#19.
therefor there is a 19/20 chance that it's behind #20.0 -
TailWindHome wrote:
Oh.
In that case
That's you, that is. Putting on your special clever face, for your favourite teacher.0 -
What are the odds of this thread degenerating into name calling and personal insults
Of course if we take this to the quantum level it all depends on the width of the game show host's smile0
