Wednesday, June 4, 2014

Behind the cards -- mathematics

A couple of weeks ago at an MAA math lecture by Alissa Crans on the Catalan numbers, I sat near card-trick mathematician Colm Mulcahy.  And I asked him if he knew any poems about card tricks and their mathematics.
   Though he at first said "no," Mulcahy turned out to have a couple of connections up his sleeve.  From Matthew Wright he learned of "The Card Players" -- a colorful sonnet from Philip Larkin's 1974 collection High Windows and available here with selections of Adriaen Brouwer's art.  
     And Bruce Reznick reminded him of the lyrics for "The Gambler" by Kenny Rogers.  The complete lyrics may be found here; I include below a stanza that offers some instruction about counting.

       You've got to know when to hold 'em
       Know when to fold 'em
       Know when to walk away
       And know when to run
       You never count your money
       When you're sittin' at the table
       There'll be time enough for countin'
       When the dealin's done

Also from Reznick (Thanks, Bruce!) an alert  to the most fun of them all -- "Politics and Poker" -- from the 1959 Broadway Musical, "Fiorello."  The entire song is available here on YouTube -- and a bit of the song's flavor is shown in these excerpted passages.  And of course, the mathematical probabilities are present and powerful (although hidden between the lines).

    from  Politics and Poker    (lyrics by Sheldon Harnick)

     Gentlemen, here we are, and one thing is clear
     We gotta pick a candidate for Congress this year

     ("Big ace" "Ace bets" "You'll pay through the nose")
     ("I'm in" "So am I" "Likewise" "Here goes")
     ("Possible straight" "Possible flush" "Nothing")

     Gentlemen, how about some names we can use
     Some qualified Republican who's willing to lose
     How's about we should make Jack Riley the guy ?
     Which Riley are you thinkin' of - Jack P. or Jack Y?
          . . .
     I say, "Neither one - I never even met 'em"
     I say, "When you got a pair of Jacks, bet 'em!"
     Politics and poker, politics and poker
     Shuffle up the cards and find the joker
     Neither game's for children; either game is rough
     Decisions, decisions, like
     Who to pick, how to play, what to bet, when to call a bluff
          . . .
    Politics and Poker, Politics and Poker
    Playing for a pot that's mediocre
    Politics and Poker running neck and neck
    If politics seems more predictable..
    That's because usually
    You can stack the deck!
          . . .

Thanks, Colm Mulcahy, for connections to all of this.

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