Probability distribution of continuous stream of random numbers vs probability distribution of sporadic picks of a continuous stream of random numbers

probability_distribution_test.rb

EXPERIMENTS_COUNT = 100000
PICKED_MATCH_COUNT = 5
DISREGARD_PICK_PROBABILITY = 0.26

pg = ProviderSelection::PriorityGroup.new(0)
pg.matches << ProviderSelection::Match.new(nil, -100)
pg.matches << ProviderSelection::Match.new(nil, 0)

# Continuous stream of random numbers
result_continuous = []
1.upto(EXPERIMENTS_COUNT) do

  result = Hash.new(0)

  while(result.values.sum < PICKED_MATCH_COUNT)
    result[pg.matches.find_index(pg.get_random_match)] += 1
  end

  result_continuous << result
end

# Sporadic picks of the continuous stream of random numbers
result_sporadic = []
1.upto(EXPERIMENTS_COUNT) do

  result = Hash.new(0)

  while(result.values.sum < PICKED_MATCH_COUNT)
    # We are disregarding at least every other output of rand() since we are calling it in the condition
    # How many of the remaining rand() calls we disregard is defined by DISREGARD_PICK_PROBABILITY
    result[pg.matches.find_index(pg.get_random_match)] += 1 if rand > DISREGARD_PICK_PROBABILITY
  end

  result_sporadic << result
end

# Display the result
complete_prob_of_0 = result_continuous.sum{ |result| result[0] }.to_f / EXPERIMENTS_COUNT
complete_prob_of_1 = result_continuous.sum{ |result| result[1] }.to_f / EXPERIMENTS_COUNT

sporadic_prob_of_0 = result_sporadic.sum{ |result| result[0] }.to_f / EXPERIMENTS_COUNT
sporadic_prob_of_1 = result_sporadic.sum{ |result| result[1] }.to_f / EXPERIMENTS_COUNT

puts "Probability of picking the 1st in continuous: #{complete_prob_of_0}"
puts "Probability of picking the 2nd in continuous: #{complete_prob_of_1}"
puts "The ratio of the 2 pick: #{complete_prob_of_0.to_f / complete_prob_of_1}"

puts "Probability of picking the 1st in sporadic: #{sporadic_prob_of_0}"
puts "Probability of picking the 2nd in sporadic: #{sporadic_prob_of_1}"
puts "The ratio of the 2 pick: #{sporadic_prob_of_0.to_f / sporadic_prob_of_1}"