### Re: Rolling a biased die

by ViceRaid (Chaplain)
 on Apr 12, 2002 at 10:26 UTC ( #158539=note: print w/replies, xml ) Need Help??

in reply to Rolling a biased die

Hi

This one's bugged me before, but I think you can do it with full accuracy by creating a hash where the keys represent the bounds between different probabilities. For speed, I'm checking the most likely results first in the second iteration:

```
sub weightedprob {
my %bias = @_;
my (\$total, %boundaries);

# prepare the boundary map
foreach ( sort { \$bias{\$b} <=> \$bias{\$a} } keys %bias ) {
\$total              += \$bias{\$_};
\$boundaries{\$total} = \$_;
}

# get a random place on the boundary map, look it up
my \$random = rand(\$total);
foreach ( sort { \$a <=> \$b } keys %boundaries ) {
return \$boundaries{\$_} if \$random < \$_;
}
}

my \$result = weightedprob(
1 => 3.1,
2 => 2.0234,
3 => 1.7,
4 => 1.542232,
5 => 1.321249563,
6 => 1.0142,
);

I'm not sure if there's a neater way of doing it without having to iterate the hash twice; maybe not, as you need to know the aggregate value of all the values of the weighted die first.

Update: yep, there is a way, as IO ably demonstrated above. I didn't quite see how his/her algorithm was intended. It's shorter, and faster (by about three times, by my Benchmark). I'll doze off again.

//=\\

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