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my %bias = (1 => 1, 2 => 1);

$rand = $k if rand($sum += $v) <= $v; 
# This simplifies to: 
# $rand = 1 if rand(1) <= 1
# this is always true.  That's wrong.

my $sum = 0;
$sum += $_ foreach (values %bias);
...
        last;
    }
}