use 5.010;

use strict;
use warnings;

use List::Util 'sum';

my @props = (0.05, 0.1, 0.2, 0.3);
push @props, 1 - sum @props;     # Make sure we sum to 1.

my @THROWS = (5, 10, 25);
my @values = (1, 5, 7, 13, 17, 23, 31, 43, 59, 91, 119);

my %cache;
sub chance;
sub chance {
    my $throws = shift;
    my $target = shift;

    return $cache{$throws, $target} if defined $cache{$throws, $target};

    return $cache{$throws, $target} = 0 if $throws < 1 || $target < $throws;
    if ($throws == 1) {
        return $cache{$throws, $target} = 0 if $target > @props;
        return $cache{$throws, $target} = $props[$target-1];  
    }
    return $cache{$throws, $target} =
            sum map {$props[$_-1] * chance $throws-1, $target-$_} 1 .. $#props;      
}

my $start = sum times;

foreach my $throws (@THROWS) {
    foreach my $value (@values) {
        say "Chance of hitting $value in $throws throws: ", chance $throws, $value;
    }
} 

my $end = sum times;
say "Running time: ", 1000 * ($end - $start), " milli-seconds";

__END__
Chance of rolling 1 in 5 throws: 0
Chance of rolling 5 in 5 throws: 3.125e-07
Chance of rolling 7 in 5 throws: 1.875e-05
Chance of rolling 13 in 5 throws: 0.00968
Chance of rolling 17 in 5 throws: 0.031295
Chance of rolling 23 in 5 throws: 0
Chance of rolling 31 in 5 throws: 0
Chance of rolling 43 in 5 throws: 0
Chance of rolling 59 in 5 throws: 0
Chance of rolling 91 in 5 throws: 0
Chance of rolling 119 in 5 throws: 0
Chance of rolling 1 in 10 throws: 0
Chance of rolling 5 in 10 throws: 0
Chance of rolling 7 in 10 throws: 0
Chance of rolling 13 in 10 throws: 1.69921875e-10
Chance of rolling 17 in 10 throws: 1.014837890625e-07
Chance of rolling 23 in 10 throws: 5.2156428125e-05
Chance of rolling 31 in 10 throws: 0.00234761235
Chance of rolling 43 in 10 throws: 0
Chance of rolling 59 in 10 throws: 0
Chance of rolling 91 in 10 throws: 0
Chance of rolling 119 in 10 throws: 0
Chance of rolling 1 in 25 throws: 0
Chance of rolling 5 in 25 throws: 0
Chance of rolling 7 in 25 throws: 0
Chance of rolling 13 in 25 throws: 0
Chance of rolling 17 in 25 throws: 0
Chance of rolling 23 in 25 throws: 0
Chance of rolling 31 in 25 throws: 1.08633041381835938e-25
Chance of rolling 43 in 25 throws: 7.92373889330642701e-17
Chance of rolling 59 in 25 throws: 9.08413811215993471e-10
Chance of rolling 91 in 25 throws: 1.16278186292830531e-07
Chance of rolling 119 in 25 throws: 0
Running time: 90 milli-seconds