Re: Re: Rolling a biased die

[ferrency]

Update:I'm totally wrong! Please ignore me! And take my advice: try the code before you claim it's broken :) Sorry, IO.

I don't think you want to put the rand() inside the loop. I think to get the correct results, you need to choose one random number outside the loop, and test it vs. the sum as you go along.

Try out a simple case by hand:

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

Assuming your first iteration picks up (1 => 1), you have:

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

What you really want is something like this:

my $sum = 0;
$sum += $_ foreach (values %bias);
my $target = rand($sum);
$sum = 0;
while (my ($k, $v) = each %bias) {
    if ($target <= ($sum += $v)) {
        $rand = $k;
        last;
    }
}

I'm sure there's a golfier way to do it, but this demonstrates the basic idea.

Update: Okay, after actually trying the code, I believe I'm totally wrong. I think that what I thought was a combination of two bugs may actually be a clever solution. Though I'm still not sure I believe it produces the correct result distribution. IO, would you care to describe how it works? Sorry about that.

Alan