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Author Topic:   Three Curtains
rstrats
Member (Idle past 182 days)
Posts: 114
Joined: 04-08-2004


Message 31 of 48 (729323)
06-09-2014 6:50 AM
Reply to: Message 30 by PaulK
06-09-2014 1:35 AM


Re: exploiting strategies
What would you do if after your initial pick of curtain #1, and before any curtain was opened, the host told you that you could stay with #1 or switch to BOTH #2 and #3?
This message is a reply to:
 Message 30 by PaulK, posted 06-09-2014 1:35 AM PaulK has responded

Replies to this message:
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PaulK
Member
Posts: 14489
Joined: 01-10-2003
Member Rating: 1.6


Message 32 of 48 (729324)
06-09-2014 7:13 AM
Reply to: Message 31 by rstrats
06-09-2014 6:50 AM


Re: exploiting strategies
That's just another variation that makes no difference.
This message is a reply to:
 Message 31 by rstrats, posted 06-09-2014 6:50 AM rstrats has responded

Replies to this message:
 Message 33 by rstrats, posted 06-09-2014 8:30 AM PaulK has responded

    
rstrats
Member (Idle past 182 days)
Posts: 114
Joined: 04-08-2004


Message 33 of 48 (729328)
06-09-2014 8:30 AM
Reply to: Message 32 by PaulK
06-09-2014 7:13 AM


Re: exploiting strategies
PaulK,

re: "That's just another variation that makes no difference."

Why do you think that having 2 curtains to look behind isn't better than having only 1?


This message is a reply to:
 Message 32 by PaulK, posted 06-09-2014 7:13 AM PaulK has responded

Replies to this message:
 Message 36 by PaulK, posted 06-09-2014 8:48 AM rstrats has responded

  
Modulous
Member (Idle past 54 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 34 of 48 (729329)
06-09-2014 8:36 AM
Reply to: Message 30 by PaulK
06-09-2014 1:35 AM


Re: exploiting strategies
Switching has to be better or worse or the same as not switching. If it's the same (worst case for the contestant) then it's still a 50-50 guess.

Actually depending on the strategy in play, switching can be worse than 50/50 for the contestant. At the extreme and boring end, imagine the host only ever offers the switch in the cases where you picked the car. Now switching is a losing proposition every time.

If the host is randomly opening one of the three doors, then the strategy becomes:
1/9 host opens the door you picked AND its a winner (stick)
2/9 he opens your door and its a loser (switch)
1/9 he opens door 2 AND it's a winner (switch)
2/9 he opens door 2 AND it's a loser (odds go up, but switching is irrelevant.)
1/9 he opens 3 AND winner (switch)
2/9 he opens 3 and loser (doesnt matter)

here, you win 1/9 (x3) of the time = 1/3 of the time outright. And you win 50% of the time the remaining. Your general odds going in are better than 50/50.

If he randomly opens the two non picked doors
1/3 he opens a door and it is a winner (1/6 for each door)
2/3 he opens a door and it is a loser.

So in this example your odds go up because 1/3 of the time you win outright and 2/3 you have a 50/50 shot, meaning your odds are better than 50/50

And we know if he deliberately selects one of the remaining losing doors each time - you win 2/3 of the time by switching 100% of the time.

Therefore, if you adopt the correct strategy you do a bit better than 50/50 if any switch is offered.

Unless the host can choose to not offer a switch. In the cases where he does this, you lose 2/3 of the time if he chooses at random. If he selects to do this at whim he can make you lose 2/3 of the time or less (ie the times he offers a switch he improves your odds).

We also note, that in complete random selections - switching is sometimes worse than 50/50 (1/9 of possibilities where he opens your door and it is a winner).


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Replies to this message:
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PaulK
Member
Posts: 14489
Joined: 01-10-2003
Member Rating: 1.6


Message 35 of 48 (729330)
06-09-2014 8:45 AM
Reply to: Message 34 by Modulous
06-09-2014 8:36 AM


Re: exploiting strategies
quote:

Actually depending on the strategy in play, switching can be worse than 50/50 for the contestant.

That's what I said. And that is why I've been saying that you need to know the strategy.

Simply by choosing when to offer the chance to switch the host can trivially guarantee that a switch will always win or always lose.


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 Message 34 by Modulous, posted 06-09-2014 8:36 AM Modulous has responded

Replies to this message:
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PaulK
Member
Posts: 14489
Joined: 01-10-2003
Member Rating: 1.6


Message 36 of 48 (729331)
06-09-2014 8:48 AM
Reply to: Message 33 by rstrats
06-09-2014 8:30 AM


Re: exploiting strategies
Oh dear. The point is that offering the chance to choose the other two is no different from revealing one of the other two as losing and offering the chance to switch to the remaining one. So it doesn't change the analysis at all.
This message is a reply to:
 Message 33 by rstrats, posted 06-09-2014 8:30 AM rstrats has responded

Replies to this message:
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rstrats
Member (Idle past 182 days)
Posts: 114
Joined: 04-08-2004


Message 37 of 48 (729334)
06-09-2014 9:02 AM
Reply to: Message 36 by PaulK
06-09-2014 8:48 AM


Re: exploiting strategies
PaulK,

re: "... offering the chance to choose the other two is no different from revealing one of the other two as losing and offering the chance to switch to the remaining one. So it doesn't change the analysis at all."

And the analysis says that it is better to have 2 curtains to look behind than to having only 1.


This message is a reply to:
 Message 36 by PaulK, posted 06-09-2014 8:48 AM PaulK has responded

Replies to this message:
 Message 38 by PaulK, posted 06-09-2014 9:18 AM rstrats has not yet responded

  
PaulK
Member
Posts: 14489
Joined: 01-10-2003
Member Rating: 1.6


Message 38 of 48 (729335)
06-09-2014 9:18 AM
Reply to: Message 37 by rstrats
06-09-2014 9:02 AM


Re: exploiting strategies
No, it depends on the host's strategy as I keep telling you.
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 Message 37 by rstrats, posted 06-09-2014 9:02 AM rstrats has not yet responded

    
Modulous
Member (Idle past 54 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 39 of 48 (729345)
06-09-2014 6:14 PM
Reply to: Message 35 by PaulK
06-09-2014 8:45 AM


Re: exploiting strategies
Actually depending on the strategy in play, switching can be worse than 50/50 for the contestant.

That's what I said.

I'm also trying to put the different strategies out there and in numbers, just to make it more interesting than a standard Monty Hall discussion.

1/3 of the time you pick right first time.
But Monty offers you to switch 2/3 of the time (2/9) in this case and you auto win the rest (1/9) of the time

2/3 of the time you pick wrong. Monty offers to switch 2/9 of these times, but not the other 4/9ths.

Switch option: 2/9 + 2/9 = 4/9ths.
No switch: 5/9ths.

If you always switch then 50% of the time you picked right first time and lose.
If you never switch then 50% of the time you picked wrong first time and you lose.

That is to say, switching makes no difference,
you win 2/9ths
you lose 2/9ths

When you don't get a choice, you win 1/9, and lose 4/9ths.

Thus you win 3/9ths (1/3), and you lose 6/9ths (2/3).

I think that's the best strategy for the host which involves occasional revelation of non-chosen losing options coupled with the choice to switch(which is no different than just picking a random curtain/door) .


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Larni
Member
Posts: 3964
From: Liverpool
Joined: 09-16-2005
Member Rating: 2.6


Message 40 of 48 (729356)
06-10-2014 9:18 AM
Reply to: Message 6 by Modulous
06-07-2014 1:56 PM


Oh, I see now.

The above ontological example models the zero premise to BB theory. It does so by applying the relative uniformity assumption that the alleged zero event eventually ontologically progressed from the compressed alleged sub-microscopic chaos to bloom/expand into all of the present observable order, more than it models the Biblical record evidence for the existence of Jehovah, the maximal Biblical god designer.
-Attributed to Buzsaw Message 53

The explain to them any scientific investigation that explains the existence of things qualifies as science and as an explanation
-Attributed to Dawn Bertot Message 286

Does a query (thats a question Stile) that uses this physical reality, to look for an answer to its existence and properties become theoretical, considering its deductive conclusions are based against objective verifiable realities.
-Attributed to Dawn Bertot Message 134


This message is a reply to:
 Message 6 by Modulous, posted 06-07-2014 1:56 PM Modulous has acknowledged this reply

    
Larni
Member
Posts: 3964
From: Liverpool
Joined: 09-16-2005
Member Rating: 2.6


Message 41 of 48 (729357)
06-10-2014 9:20 AM
Reply to: Message 24 by rstrats
06-08-2014 4:01 PM


Re: Three Curtains
That game uses doors, whereas the OP game uses curtains.

Pure genius.

You made my day with that.


The above ontological example models the zero premise to BB theory. It does so by applying the relative uniformity assumption that the alleged zero event eventually ontologically progressed from the compressed alleged sub-microscopic chaos to bloom/expand into all of the present observable order, more than it models the Biblical record evidence for the existence of Jehovah, the maximal Biblical god designer.
-Attributed to Buzsaw Message 53

The explain to them any scientific investigation that explains the existence of things qualifies as science and as an explanation
-Attributed to Dawn Bertot Message 286

Does a query (thats a question Stile) that uses this physical reality, to look for an answer to its existence and properties become theoretical, considering its deductive conclusions are based against objective verifiable realities.
-Attributed to Dawn Bertot Message 134


This message is a reply to:
 Message 24 by rstrats, posted 06-08-2014 4:01 PM rstrats has not yet responded

    
PurpleYouko
Member
Posts: 713
From: Columbia Missouri
Joined: 11-11-2004


(3)
Message 42 of 48 (729360)
06-10-2014 11:02 AM


a coder's perspective
Ok so somebody further up the thread said that I could replace the host with a computer program so I just did that.

The rules I used are these.
1) car is placed randomly in one of three places
2) The first guess is made as 1, 2 or 3
3) Host chooses one of the unchosen places and eliminates it
4) contestant either sticks or changes
5) results are evaluated and spit out as count rates

Once put into code form it becomes pretty obvious what the result will be without even running the simulation.
The logic is inescapable.
First of all there is one thing to check

1) Was my guess correct? (remember there are only 2 choices now since the host already opened a curtain/door that wasn't the car)
YES (1 in 3 chance) --> Sticking wins, changing loses so add 1 to StickCount
NO (2 in 3 chance) --> Sticking loses, changing wins so add 1 to ChangeCount

The results of 1 million games comes out as follows
StickCount = 332654
ChangeCount = 667346

Until putting this into code form I would have sworn that the chances were 50:50 but as soon as I wrote the problem in code form it's obvious that changing is going to win twice as often as sticking


Replies to this message:
 Message 43 by rstrats, posted 06-10-2014 1:40 PM PurpleYouko has responded

  
rstrats
Member (Idle past 182 days)
Posts: 114
Joined: 04-08-2004


Message 43 of 48 (729372)
06-10-2014 1:40 PM
Reply to: Message 42 by PurpleYouko
06-10-2014 11:02 AM


Re: a coder's perspective
PurpleYouko wins a cigar.
This message is a reply to:
 Message 42 by PurpleYouko, posted 06-10-2014 11:02 AM PurpleYouko has responded

Replies to this message:
 Message 44 by PurpleYouko, posted 06-10-2014 1:50 PM rstrats has not yet responded

  
PurpleYouko
Member
Posts: 713
From: Columbia Missouri
Joined: 11-11-2004


Message 44 of 48 (729373)
06-10-2014 1:50 PM
Reply to: Message 43 by rstrats
06-10-2014 1:40 PM


Re: a coder's perspective
meh.. I don't smoke.
How about you make it a nice pina collada that i can sip while sitting in a swimming pool
This message is a reply to:
 Message 43 by rstrats, posted 06-10-2014 1:40 PM rstrats has not yet responded

  
Minnemooseus
Member
Posts: 3668
From: Duluth, Minnesota, U.S. (West end of Lake Superior)
Joined: 11-11-2001


Message 45 of 48 (732803)
07-10-2014 11:40 PM


The 2 children puzzler
From Car Talk:

http://www.cartalk.com/content/lets-hear-it-boys-0?question

RAY: Here’s the first half of the puzzler: If a mother has two kids and the older one is a boy, what are the chances the younger is a boy?

TOM: I know this puzzler. This is a killer.

RAY: And the answer is 50-50. So I'll give you that part. Now, suppose a different mother has two kids and one of them is a boy. What are the chances that the other one is a boy? Well, it's got to be 50-50, right?

TOM: You would think.

RAY: Wrong.

TOM: Of course.

RAY: So, what are those chances?

-----

http://www.cartalk.com/content/lets-hear-it-boys-0?answer (hidden in white block, drag mouse cursor over to see)

RAY: There are four possible scenarios: Older boy, younger boy. Older boy, younger girl. Older girl, younger boy. And older girl, younger girl. Now, in the first case, when I say the older one is a boy, that immediately leaves out the last two possibilities. It can only be boy-boy or boy-girl. So, in order for the other one to be a boy, it's a 50-50 chance.

TOM: That's right.

RAY: Now,when I say that one of them is a boy, it becomes harder for the other one to become a boy. And the chances are one in three. If you look at the scenarios, you have boy-boy, boy-girl and girl-boy. For the other one to be a boy, it's gotta be choice #1 which is boy-boy. There's one chance in three. Do we have a winner this week?

Moose


Replies to this message:
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