Here is a cute trick that you might want to contemplate.

If you make each card a 4-"digit" octal number, then three cards form a "set" if and only if ($a|$b|$c) equals ($a^$b^$c). You can use octal strings or octal numbers. I use octal strings below:

#!/usr/bin/perl -w
use strict;

my %Desc= qw(
    0001 One
    0002 Two
    0004 Three
    0010 Red
    0020 Blue
    0040 Green
    0100 Hollow
    0200 Striped
    0400 Solid
    1000 Diamond
    2000 Squiggle
    4000 Oval
);

my @deck;
for my $a ( 1,2,4 ) {
    for my $b ( 1,2,4 ) {
        for my $c ( 1,2,4 ) {
            for my $d ( 1,2,4 ) {
                push @deck, "$a$b$c$d";
            }
        }
    }
}

sub isSet {
    my( $a, $b, $c )= @_;
    return ($a|$b|$c) eq ($a^$b^$c);
}

sub showCard {
    my( $card )= @_;
    my @desc;
    for my $bit ( sort keys %Desc ) {
        if( $bit eq ( $bit & $card ) ) {
            push @desc, $Desc{$bit};
        }
    }
    return "@desc";
}

while( 1 ) {
    for my $n ( reverse @deck-2..@deck ) {
        my $r = rand $n;
        @deck[$n-1,$r]= @deck[$r,$n-1];
    }
    if( isSet( @deck[-3..-1] ) ) {
        print showCard( $_ ), $/
            for @deck[-3..-1];
        exit;
    }
}
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Update: Replaced nested maps with clearer, shorter for()s.