#!/usr/bin/perl

use v5.16;
use warnings;
use List::Util 'shuffle';
use constant N => 100000;

sub doit {
    my @box = shuffle 0 .. 99;

    prisoner:
    for my $prisoner (0 .. 99) {
        my $box = $prisoner;
        for (0 .. 49) {
            my $found = $box[$box];
            next prisoner if $prisoner == $found;
            $box = $found;
        }
        return;
    }
    1;
}
my $success;
for (1..N) {
    $success++ if doit();
}

say $success / N;
__DATA__
0.31257