slightly revised elo simulation.

elo.py

#!/usr/bin/python
import random

def simulate():
  start = 1200
  elo = start
  elo40 = elo
  elo100 = elo
  elo500 = elo
  k = 80
  r = random.Random()
  wins = 0
  # moderately lucky at starting matches
  winrate = 55

  def delta(): return k / 2
  def wr(): return 100 - winrate

  for i in range(0,1000):
    wl = 1 if (r.randint(1, 100) > wr()) else 0
    wins = wins + wl

    if i > 100: k = 20
    elif i > 50: k = 25
    elif i > 20: k = 30

    if i > 20:
      # anything in elo hell is a gamble, your edge contributes 1%
      if elo < 1000: winrate = 51
      if elo > 1200: winrate = 55
      if elo > 1600: winrate = 50
      if elo > 2000: winrate = 40

    if i == 40: elo40 = elo
    if i == 100: elo100 = elo
    if i == 500: elo500 = elo
    # lets say the player does well dramatically after the first 30 matches
    # for 10 matches
    if i in range(30,40):
      winrate = 75

    elo = elo + (delta() if wl == 1 else (-1 * delta()))

  if elo40 < 1000:
    print "%d: %4d => %4d => %4d => %4d" % (wins,elo40,elo100,elo500,elo)

for i in range(0,1000): simulate()

"""
[pfnguyen@galactica0 ~]$ ./elo.py 
527:  995 =>  908 => 1050 => 1550
529:  905 => 1106 => 1348 => 1608
530:  955 =>  958 => 1016 => 1636
497:  975 => 1104 => 1066 =>  946
523:  995 => 1112 => 1610 => 1510
534:  965 => 1046 => 1188 => 1708
522:  995 =>  968 =>  930 => 1450
529:  935 => 1058 => 1220 => 1600
537:  985 =>  976 => 1354 => 1774
536:  995 => 1058 => 1620 => 1740
505:  995 => 1046 =>  824 => 1124
500:  915 =>  864 => 1046 =>  946
507:  965 => 1034 => 1012 => 1172
541:  995 => 1124 => 1522 => 1862
534:  935 => 1010 => 1448 => 1688
484:  975 =>  786 =>  664 =>  704
531:  905 =>  896 => 1138 => 1598
491:  965 =>  854 =>  772 =>  792
499:  965 => 1088 => 1030 => 1010
491:  965 =>  704 =>  426 =>  766
496:  985 => 1096 =>  894 =>  974
497:  895 =>  796 => 1014 =>  934
478:  915 =>  936 =>  794 =>  514
524:  985 => 1168 => 1530 => 1570
514:  775 =>  862 =>  824 => 1184
534:  965 => 1058 => 1196 => 1716
493:  865 =>  886 =>  944 =>  764
488:  935 => 1034 =>  576 =>  776
528:  965 =>  926 => 1428 => 1548
484:  945 =>  960 =>  842 =>  642
529:  955 => 1126 => 1468 => 1648
496:  935 =>  788 =>  686 =>  886
"""