Figure out how many tengus you have to eat to get both teleportitis and teleport control. Also calculate the probability of getting teleportitis and teleport control using Monte Carlo integration.

tengutins.py

"""
Figure out how many tengus I have to eat to get both teleportitis and teleport control.
Author: Craig Calef <craig@dod.net>
"""

import random, sys, os, pprint

def rn2(i):
  return random.randint(0, i-1)

def debug(s):
  #print s
  pass

POISON = 0
TELEPORT = 1
TELECTRL = 2

chances = [15, 10, 12]

def givit(mlevel, intrinsic):
  """ Model the givit() function in NetHack in a basic way. """
  # Eat.c 662
  chance = chances[intrinsic]
  # Eat.c 676
  outcome = rn2(chance)
  debug("Givit chance: %d mlevel: %d outcome: %d " % (chance, mlevel, outcome))
  return mlevel <= outcome

def eat(mlevel):
  """ Model the 'eat a tengu' process, returning the intrinsic gained or -1 if none. """
  debug("Eating level %d corpse" % mlevel)
  # Eat.c 928
  count = 0
  tmp = 0
  for i in range(0, 3):
    count = count + 1
    if not rn2(count):
      debug("Intrinsic %d replacing %d" % (i, tmp))
      tmp = i
  # if this check fails givit returns early and the intrinsic is not granted
  if not givit(mlevel, tmp):
    return tmp
  return -1 
    
def montecarlo(mlevel, trials, intrin):
  """ Monte Carlo integration of intrinsic granting.  Given more trials will converge on the
      exact probability of being granted an intrinsic """
  a = 0
  for i in range(0, trials):
    got = eat(mlevel)
    if got == intrin:
      debug("Got target intrinsic %d" % intrin)
      a = a + 1
    else:
      debug("Different intrinsic %d target=%d" % (got, intrin))
  debug( "%d positive trials out of %d" % (a, trials))
  return a

def chowdown(mlevel):
  """ Return the number of tengu I had to eat to get teleport and telectrl via random trial """
  telectrl = False
  teleport = False
  i = 0
  while not (telectrl and teleport):
    i = i + 1
    print "--- TRIAL %d --- telectrl:" % i, telectrl, " teleport:", teleport
    grant = eat(mlevel)
    if grant == 1:
      teleport = True
      debug("Got teleport")
    if grant == 2:
      telectrl = True
      debug("Got telectrl")
    if not grant == 1 and not grant == 2:
      debug("Got %d" % grant) 
  return i

def feast(mlevel, trials):
  results = [0, 0, 0]
  for i in range(trials):
    intrin = eat(mlevel)
    print "---"
    if intrin >= 0:
      results[intrin] = results[intrin] + 1
  return results

def gorge(mlevel, trials):
  results = []
  for i in range(trials):
    results.append(chowdown(mlevel))
  return results

def rungorge(mlevel, trials):
  results = gorge(mlevel, trials)
  print "Tengu feast. mlevel: %d trials %d" % (mlevel, trials)
  print "Results:", results
  results.sort()
  print "Min:", results[0], "Max:", results[-1], "Median:", results[len(results) // 2], "Avg:", sum(results) / len(results)

def runmontecarlo(mlevel, trials):
  tpp = float(montecarlo(mlevel, trials, 1))
  tcp = float(montecarlo(mlevel, trials, 2))
  print "Teleport Probability for %d trials: %f" % (trials, tpp / trials)
  print "TeleCtrl Probability for %d trials: %f" % (trials, tcp / trials)

if __name__ == '__main__':
  if len(sys.argv) != 3:
    print "%s <monster level> <number of trials>" % sys.argv[0]
    mlevel = 10
    trials = 100
  else:
    mlevel = int(sys.argv[1])
    trials = int(sys.argv[2])

  #results = feast(mlevel, trials)
  #results = chowdown(mlevel) 
  #rungorge(mlevel, trials)
  runmontecarlo(mlevel, trials)

mlevel for tengu is always 6.