#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my %special = ( ... ); # copy from the OP

my %reachable = ( 0 => undef );

my $turn = 0;
while (not exists $reachable{100}) {
    my %next;
    for my $square (keys %reachable) {
        for my $spin (1 .. 6) {
            my $target = $square + $spin;
            next if $target > 100;
            undef $next{$target};
            undef $next{ $special{$target}{end} } if $special{$target};
        }
    }
    undef @reachable{ keys %next };
    say ++$turn, ': ', join ' ', sort { $a <=> $b } keys %reachable;
}
say "$turn";