http://www.perlmonks.org?node_id=158567

in reply to Re: Rolling a biased die
in thread Rolling a biased die

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