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 Changing aces (Posted on 2005-01-31)

Four different aces are dealt, face up, one apiece, to you and three other players. They are shuffled and redealt, this time face down.

Before looking, the chance is 75% that you have an ace different from your original card.

Question 1) But what if the first player looks at his card and, without showing the card, truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that one player's card is known to be different?

Question 2) And what if the second player also looks at his card and, without showing the card, also truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that two players' cards are known to be different?

Question 3) Finally, what if the third player also looks at his card and, without showing the card, also truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that all three other players' cards are known to be different?

 See The Solution Submitted by Steve Herman Rating: 3.5000 (4 votes)

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 posting my sol'n - then checking mine against yours | Comment 5 of 9 |

There are 24 permutations possible:

C D H S
C D S H
C H D S
C H S D
C S D H
C S H D
D C H S
D C S H
D H C S
D H S C
D S C H
D S H C
H C D S
H C S D
H D C S
H D S C
H S C D
H S D C
S C D H
S C H D
S D C H
S D H C
S H C D
S H D C

Question 1 eliminates 6 of these.  Of the 18 remaining, 4 of them involve you having the same card as before.  4/18 = 22.22...%

Question 2 eliminates another 4 of the 18.  Of the 14 possible distributions remaining, 3 involve you having your original card.  3/14 = 21.43%.

Question 3 knocks off another 3 permutations.  Of the 11 remamining, you get your original card in 2 of them, or 18.18...%

Interestingly, this would imply that your odds are not improved at all, and can in fact be decreased, by the above intelligence.  Seems counterintuitive!

(Edited by the Department of Redundancy Department.)

Edited on February 2, 2005, 11:07 pm
 Posted by John on 2005-02-02 22:20:08

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