Neither did I reveal the spoiler, nor did look at the Youtube post.

The arrangement of the prisoners' numbers in the boxes is a permutation of 100 numbers. Every permutation consists of a number of cycles. I believe that chances are not too high that any given permutation has a cycle that is larger than half of the number of its elements. When every prisoner follows the cycle starting with his own number, they will stay in prison only if there is a cycle larger than 50 in the given permutation.

I don't want to claim this strategy would be optimal, but it looks like chances of getting free are around 0.31 with this approach. 

#!/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

[download]

Greetings,
🐻

$gryYup$d0ylprbpriprrYpkJl2xyl~rzg??P~5lp2hyl0p$

In reply to Re: Proving Veritasiums riddle using Perl by jo37
in thread Proving Veritasiums riddle using Perl by cavac

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.