cut_the_knot_coin_toss_intuition.rb

class Array
        def sum
                inject(0.0) { |result, el| result + el }
        end

        def mean
                sum / size
        end

end

def flip
        if (rand * 2).ceil == 1
                'heads'
        else
                'tails'
        end
end


def simulate_alice
        alice_tries = []
        alice_not_found = true
        while alice_not_found
                alice_tries << flip
                if alice_tries.count >= 2 && alice_tries[-2] == 'heads' && alice_tries[-1] == 'tails'
                        alice_not_found = false
                end
        end
        alice_tries.count
end

def simulate_bob
        bob_tries = []
        bob_not_found = true
        while bob_not_found
                bob_tries << flip
                if bob_tries.count >= 2 && bob_tries[-2] == 'heads' && bob_tries[-1] == 'heads'
                        bob_not_found = false
                end
        end
        bob_tries.count
end

puts 10000.times.map { simulate_alice }.mean

puts 10000.times.map { simulate_bob }.mean