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A Game of Probabilities


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18 replies to this topic

#1 Yoruichi-san

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Posted 22 June 2012 - 07:22 AM

You and I are playing a little game (that is in no way whatsoever related to any game played on this site *cough*). There are 12 objects, 4 of which have the property M. The goal is to choose an object with the property M.

However, you and I are playing by different rules. For each round, first there is the N phase, in which you secretly choose an object (write down its number or something), then there is the D phase, during which I pick an object and it is revealed whether or not the object has property M.

If the object I pick has the property M, I win, if not we keep going. During any N phase, after you choose an object, you can call 'STOP' and the game will end. Then you reveal your choices, and if at least one has the property M, you win. If none have the property M, I win.

What is your play?

Bonus: Generalize to a case of n objects, k of which have the property M.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

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#2 Yodell

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Posted 22 June 2012 - 09:59 AM

Spoiler for

edit... added spoiler

Edited by Yodell, 22 June 2012 - 10:01 AM.

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____________
CARPE DIEM !!

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#3 CaptainEd

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Posted 22 June 2012 - 03:45 PM

I guess neither of us knows which objects have property M, and we rely on a third party to give us a determination at the end of each N phase or the STOP event?
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#4 Yoruichi-san

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Posted 22 June 2012 - 04:20 PM

I guess neither of us knows which objects have property M, and we rely on a third party to give us a determination at the end of each N phase or the STOP event?


Yes, or they could be, like, upside down cards or mahjong tiles or something like that that we shuffled.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#5 Yoruichi-san

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Posted 22 June 2012 - 05:41 PM

Or beakers of acid/base we test with litmus paper...or glasses of pepsi/coke we taste test...but not beakers of acid/base that we taste test...

(sorry, couldn't resist ;P)
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#6 phil1882

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Posted 22 June 2012 - 07:20 PM

let me see if i have the riddle correct with an example.
let's say i have 12 playing cards, 4 of which are spades. all cards are over turned, so no one knows which is which.
player 1 chooses 1 card, and keeps it down turned.
then player 2 chooses 1 card. player 2's card is revealed. if it's a spade, he wins, else keep playing.
player 1 picks another card (assuming player 2 didn't win.) player 1 can call stop. if either of the two cards are spade, player 1 wins.
else, player 2 wins.
sound good?
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#7 CaptainEd

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Posted 22 June 2012 - 07:27 PM

I think the second player could choose one of the cards chosen by the first player, as the first player's choices are secret.
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#8 bonanova

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Posted 22 June 2012 - 07:34 PM

Spoiler for my guess



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#9 bonanova

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Posted 22 June 2012 - 07:38 PM

let me see if i have the riddle correct with an example.
let's say i have 12 playing cards, 4 of which are spades. all cards are over turned, so no one knows which is which.
player 1 chooses 1 card, and keeps it down turned.
then player 2 chooses 1 card. player 2's card is revealed. if it's a spade, he wins, else keep playing.
player 1 picks another card (assuming player 2 didn't win.) player 1 can call stop. if either of the two cards are spade, player 1 wins.
else, player 2 wins.
sound good?


Only possible difference is that player 2 [I think] doesn't know which card[s] player 1 has chosen.
E.g. P2 might choose one of them herself, and thus can 'steal' some of p1's chances.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 Yoruichi-san

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Posted 22 June 2012 - 08:29 PM

Yes, your choice is secret, and the object (beaker/tile/card) is not removed from the selection process.

And if I choose your card, your chances for stopping the second round aren't as good. ;)
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.





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