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Representation of data in the computer---a 7-card 
poker hand could be represented by:

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\disleft 25pt:
(1):One string:

\smallskip\halign{\qquad\qquad\lft{\tt #}\cr
	S = AD QH ... 2C\cr
\qq	   \hbox{(Ace of diamonds, Queen of Hearts, etc.)}\cr}

\smallskip
\disleft 25pt:
(2):An array of seven strings:

\smallskip\halign{\qquad\qquad\lft{\tt #}\cr
	S[1]=AD\cr
	S[2]=QH\cr
\qq	  \hbox{etc.}\cr}

\smallskip
\disleft 25pt:
(3):Two arrays of numbers, where the rank is 11 for Jacks, 12~for Queens, etc., 
    and the suits are 1~for clubs, 2~for diamonds, etc.

\smallskip\halign{\qquad\qquad\lft{\tt #}\cr
	RANK[1]=14 SUIT[1]=2\cr
	RANK[2]=12 SUIT[2]=3\cr}

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(4):Two such arrays, but with the cards arranged in increasing order of rank.

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(5):A two-dimensional array of integers, with the first subscript being the rank,
    the second the suit.  A~one in the array indicates the presence of the card;
    a zero its absence.

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(6):The same, except that an extra row and column contain the sums of the cards in
    each row and column; that is, the number of cards of each suit, and the
    number of each rank.

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To find out what kind of a poker hand you have may be easy or hard, depending on
which of these representations you use.  To tell if you have a flush (*****: define)
in the first representation requires going through the string counting occurrences
of {\tt C}, {\tt D}, {\tt H}, and~{\tt S}; 
to find the high card in the flush is even messier.  To do the
same in the sixth representation, one can look at the four row sums and see if
any one is at least five; if so, the last~1 in that row is the high card of a
flush.

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{\bf Exercise:} 
Test in one or more of these representations, whether the hand contains a
          full house (three cards of one rank, two of another).

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A final project in a programming course was to test which of two such poker hands
was the better.

Similarly, to represent the relative strength of one flush (as best) relative to
another, one approach is to rank the cards, then pack the ranks into a number, like

\smallskip\halign{\qquad\qquad\lft{\tt #}\cr
	11 08 06 03 02\qquad\hbox{(for }J 8 6 3 2\hbox{).}\cr}

\smallskip\noindent
Another is to have positions in each number, which are set to 1 if a card is 
present, 0~if absent, with more significant positions for higher cards, eg:

\smallskip\halign{\qquad\qquad\lft{\tt #}\cr
	14  13  12  11  10  9  8  7  6  5  4  3  2  1\cr
	\phantom{0}0 \phantom{0}0 \phantom{0}0 \phantom{0}1 \phantom{0}0  
0  1  0  1  0  0  1  1  0\cr}

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Once obtaining the numbers for two hands, the larger number is from the better hand.








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\copyright 1984 Robert W. Floyd

First draft March 28, 1984

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