fusion festival: probability to get fusion tickets by crew size

calculation.rb

def next_row row
  ([0] + row).zip(row + [0]).collect do |l, r|
     l + r
  end
end

def pascal n
  ([nil] * n).inject([1]) do |row, y|
    y = next_row row
  end
end

class Array
  def sum
    inject(0) { |sum, x| sum+x }
  end
end

max_clique_size = 15

puts ".---------------------------------------------------------."
puts "|             |        combinations         |             |"
puts "| clique size | overall |  we win | we lose | probability |"
puts "+---------------------------------------------------------+"

(1..max_clique_size).to_a.each do |clique_size|
  pascal_array = pascal(clique_size)

  overall_combinations = 2 ** clique_size
  overall_wins = pascal_array[0..pascal_array.size/2 - (clique_size % 2)].sum # odd
  overall_loses = overall_combinations - overall_wins

  prob = (overall_wins.to_f/overall_combinations.to_f) * 100

  puts "| %11s | %7s | %7s | %7s | %11s |" % [clique_size, overall_combinations, overall_wins, overall_loses, "%.2f %" % prob]
end

puts "`---------------------------------------------------------´"

output.txt

.---------------------------------------------------------.
|             |        combinations         |             |
| clique size | overall |  we win | we lose | probability |
+---------------------------------------------------------+
|           1 |       2 |       1 |       1 |     50.00 % |
|           2 |       4 |       3 |       1 |     75.00 % |
|           3 |       8 |       4 |       4 |     50.00 % |
|           4 |      16 |      11 |       5 |     68.75 % |
|           5 |      32 |      16 |      16 |     50.00 % |
|           6 |      64 |      42 |      22 |     65.63 % |
|           7 |     128 |      64 |      64 |     50.00 % |
|           8 |     256 |     163 |      93 |     63.67 % |
|           9 |     512 |     256 |     256 |     50.00 % |
|          10 |    1024 |     638 |     386 |     62.30 % |
|          11 |    2048 |    1024 |    1024 |     50.00 % |
|          12 |    4096 |    2510 |    1586 |     61.28 % |
|          13 |    8192 |    4096 |    4096 |     50.00 % |
|          14 |   16384 |    9908 |    6476 |     60.47 % |
|          15 |   32768 |   16384 |   16384 |     50.00 % |
`---------------------------------------------------------´