Benefit on EV of taking max of multiple rolls

gistfile1.rb

def roll
  Random.rand(10) + 1
end

# Monte Carlo-in it
(1...10000000).inject(0){ |avg,i| avg += (roll - avg).to_f/i }

(1...10000000).inject(0){ |avg,i| avg += ([roll, roll, roll, roll].max - avg).to_f/i }

# Closed form thx http://math.stackexchange.com/questions/150586/expected-value-of-max-of-iid-variables
def ev a, b, n
  a + (n.to_f/(n+1)) * (b - a)
end