Winning ratios

n-win-m-match.rb

#!/usr/bin/env ruby

# n-win-m-match.rb : じゃんけんをm回やって，そのうちn回以上勝つ確率
#   by takehikom

require "rational"

class NWinMMatch
  def initialize(opt = {})
    @choose = {}  # 2項係数
    @rate_eq = {} # match試合でちょうどwin勝する確率
    @rate_ge = {} # match試合でwin勝以上する確率
    @rate_one = opt[:p] || Rational(1, 2) # 1回の勝率
    @match_max = opt[:match] || 5 # matchの最大値
    @flag_noprint = opt[:noprint] # 各値を出力しないなら真
  end
  attr_reader :choose, :rate_eq, :rate_ge
  attr_reader :rate_one, :match_max, :flag_noprint

  def start
    p = @rate_one; q = 1 - p
    puts "p=#{p}=#{p.to_f}"

    1.upto(@match_max) do |match|
      rate2 = Rational(1)
      0.upto(match) do |win|
        if win == 0 || win == match
          @choose[s(match, win)] = 1
        else
          @choose[s(match, win)] =
            @choose[s(match - 1, win - 1)] +
            @choose[s(match - 1, win)]
        end
        rate1 = p ** win * q ** (match - win) * @choose[s(match, win)]
        @rate_eq[s(match, win)] = rate1
        @rate_ge[s(match, win)] = rate2
        rate2 -= rate1

        puts "win=#{win}, match=#{match} : choose(#{match},#{win})=#{@choose[s(match, win)]} : rate1=#{@rate_eq[s(match, win)]} : rate2=#{@rate_ge[s(match, win)]}=#{@rate_ge[s(match, win)].to_f}" unless @flag_noprint
      end
    end

    self
  end

  def s(a, b)
    [a, b].join(":")
  end
end

if __FILE__ == $0
  NWinMMatch.new.start
=begin
  n = NWinMMatch.new(:p => Rational(1, 3), :match => 100, :noprint => false).start
  h = n.rate_ge
  nearhalf_key = h.keys.sort_by {|item| (0.5 - h[item].to_f).abs}.first
  nearhalf = h[nearhalf_key]
  puts "#{nearhalf_key} : #{nearhalf.to_f}"
=end
end