# from the starting state, select the next state according to the
# transition matrix T
function rungame(T)
  # start at state 140
  current = 140

  # count turns
  turns = 0

  while current != 134
    # get transitions from current state
    A = [(i,j) for (i,j) in enumerate(T[:,current]) if i != 0]

    # separate transitions into states and probabilities
    states = [i[1] for i in A]
    probs = [i[2] for i in A]

    # select the next state from the transitions distribution
    current = sample(states, Weights(probs))
    turns+=1
  end

  return turns

end

# run function rungame on transition matrix T
# and return the average turns over N runs
function getAverageTurns(T,N)
  result=0
  for i=1:N
    result+=rungame(T)/N
  end

  return result
end


println("turns:\t",getAverageTurns(T,1000),"\n")