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Perfect Pairs (Posted on 2009-02-11) Difficulty: 4 of 5
Suppose the local casino introduces a card game named "Perfect Pairs". The game involves a player making a bet followed by a dealer dealing out two cards to every player who has made a bet. If the player has a pair, the player wins 11 times his initial bet as well as keeping his initial bet. If the player does not get a pair, the player loses all the money he has bet in that round to the casino.

Additionally, suppose that six full decks of cards are initially shuffled and used and the dealer does not re-shuffle the cards until 5 decks of cards are used up. For the sake of terminology we will call a set of rounds that are played without the cards being shuffled a "match".

If there are n players always playing the game, what is the expected percentage of "matches" that will have at least one round in which a player who has memorized the previous cards dealt in that "match" could calculate that he has an edge over the dealer (ie, expected percentage of matches in which there is at least one round in the match when the chance of making a pair exceeds 1/12)?

No Solution Yet Submitted by Chris, PhD    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Ho ho, or Ho hum? | Comment 3 of 6 |
(In reply to Ho ho, or Ho hum? by ed bottemiller)

A session can time out. This does not happen if you have checked the "remember me" box (I think that's what it's called; it doesn't still show up when you're logged on). It's safest to compose your message in a text editor, such as Notepad. (avoid using a word processor, as internal markup can foul up posts). Then copy and paste to a fresh comment box.

But if you ask to be remembered, you should not be logged out by time.

  Posted by Charlie on 2009-02-11 18:26:57
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