Simulation of Parrondo's Paradox

parrondo.rb

def coin(win) = rand(1000) > (1000 - win) ? 1 : -1
def a(capital) = coin(495) # 49.5% chance of winning
def b(capital) = (capital % 3 != 0) ? coin(745) : coin(95)

def simulate(strategy, count)
    (strategy * count).reduce(100) do |capital,game| 
        capital + send(game, capital)
    end
end

# Simulate [:a] 100 times 
result = 100.times.map { |i| simulate([:a], 10_000) }.sum / 100
puts "Average remaining capital after playing A: #{result}"

result = 100.times.map { |i| simulate([:b], 10_000) }.sum / 100
puts "Average remaining capital after playing B: #{result}"

result = 100.times.map { |i| simulate([:a, :b], 5_000) }.sum / 100
puts "Average remaining capital after playing A,B: #{result}"

result = 100.times.map { |i| simulate([:a, :a, :b, :b], 2_500) }.sum / 100
puts "Average remaining capital after playing A,A,B,B: #{result}"

result = 100.times.map { |i| simulate([:a, :a, :a, :b, :b, :b], 1667) }.sum / 100
puts "Average remaining capital after playing A,A,A,B,B,B: #{result}"

=begin
Sample run

$ ruby parrondo.rb 
Average remaining capital after playing A: -21
Average remaining capital after playing B: -15
Average remaining capital after playing A,B: 32
Average remaining capital after playing A,A,B,B: 245
Average remaining capital after playing A,A,A,B,B,B: 86
=end

Twitter thread about this: https://twitter.com/nileshtrivedi/status/1345230833431429120