This is a rather old, and clever, merlyn (IIRC) recipe.

$/ = "\n\n";
rand($.) < 1 && ($line = $_) while <DATA>;
print $line;

__DATA__
You cannot achieve the impossible without attempting the absurd.

Thinking you know something is a sure way to blind yourself.

The first principle is that you must not fool yourself -- and you are 
+the easiest person to fool.
    -- Richard Feynman
[download]

It's a special case of the Fisher-Yates shuffle, IIRC.
map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

AFAIK does Fisher-Yates start with the highest range in rand not the lowest.

The proof may contain similar elements but I have trouble seeing the obvious analogy...

Cheers Rolf
_{(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery}

Since $. is the number of the record, I'd guess this is a biased choice because only the first is guaranteed to be <1.

Or do I miss a math trick to even the choices?

update

Actually it should work fine.

You have to think it from the end, the n'th line has a 1/n chance which is correct.

The line before is competing with the rest and has a 1/(n-1) chance, which is correct. °

And so on, proof by induction.

Indeed clever! =)

update

°) because the lines before have a combined chance of (n-1)/n and you have to multiply the odds. This leaves line n-1 with a chance of 1/n over all. .. :)

Cheers Rolf
_{(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery}

You’re a *much* better mathematician than I. It’s from the Camel, 8.6. Picking a Random Line from a File. I can’t screenshot it or cut and paste it either because the text contains math images. The trick lies in reselecting lines as it goes and the odds of selection being “fair” across the entire file. As you say, one line is guaranteed to be picked. As subsequent lines are scanned, the odds of choosing them, and replacing the original selection, become proportionate to how many lines have been read.

Update: didn’t see your update before I stubmitted. :P

I think this will sort the whole file which is what the OP may have really wanted.

perl -MList::Util=shuffle -e '$/="\n%\n";print +(shuffle<>)' fortune.t
+xt > randomised.txt
[download]

And Now for Something Completely Different

perl -0x25 -e '$_{$.}=$_ while<>; print join"\n",values%_;'

# cookie number is a bonus:
perl -0x25 -e '$_{$.}=$_ while<>; print join"\n"=>%_;'
[download]

bw,
    --bliako
[download]

some more variations:

# no need to join
perl -0x25 -e '$_{$.}=$_ while<>; print %_'

# dumps one random cookie (not just shuffling):
perl -0x25 -e '$_{$.}=$_ while<>; print ((%_)[$.==$.])'

# and this but slicing it
perl -0x25 -e '@_{<>}=1; print ((%_)[$.-$.]);'

# not sure but this works too (re: looks like slice key is created aft
+er slurping)
perl -0x25 -e '@_{1..$.}=<>; print %_;'
[download]

p.s. I did not know about -0x25, thanks