use strict;
use warnings;

# We'd like to see the likelihood that by running a given number
# of trials that one of these trials gives a result in some top X%
# of all the possible results.
#
# As an example, suppose we need to generate a solution in the top
# 10% of all possible solutions, i.e. we want to exceed a "clip
# level" of 0.90.  How many trials would we need to run to have an
# X% chance that one of those solutions out of all those trials is
# in that top 10%?
#
# Generating a simple little table shows us the percentage chance
# that one of those trials will be in that bracket.  For a 95.8%
# chance that one of our trials is in the top 10%, our little
# table shows us that we'd need to run 30 trials.
#
# Running 31 trials would boost our likelihood of being in that
# top 10% by about 0.4%.
#
# Changing the clip level to 0.95 and upping our upper bound to
# 65 shows that running 62 trials would give us that 95.8%
# confidence of one of our trials being in that set of solutions
# in the 95-100% range of best solutions.  By running only 30
# trials, we'd only be 78.5% sure that one of our solutions is
# superior to 95% of all possible solutions.

my $want_soln_above_this_clip_level = 0.90;
my $min_no_trials = 15;
my $max_no_trials = 35;
	
my $value;
my $prev_value = 0;

foreach ( $min_no_trials .. $max_no_trials ) {
	print "$_\t";
	#printf("%.1f%%",100*(1-.9**$_));
	$value = 100*(1-$want_soln_above_this_clip_level**$_);
	printf("%.1f%%", $value);
	print "\t";
	printf("%.1f%%", $value - $prev_value);
	print "\n";
	$prev_value = $value;
}

__DATA__
15	79.4%	79.4%
16	81.5%	2.1%
17	83.3%	1.9%
18	85.0%	1.7%
19	86.5%	1.5%
20	87.8%	1.4%
21	89.1%	1.2%
22	90.2%	1.1%
23	91.1%	1.0%
24	92.0%	0.9%
25	92.8%	0.8%
26	93.5%	0.7%
27	94.2%	0.6%
28	94.8%	0.6%
29	95.3%	0.5%
30	95.8%	0.5%
31	96.2%	0.4%
32	96.6%	0.4%
33	96.9%	0.3%
34	97.2%	0.3%
35	97.5%	0.3%