"""
Copyright 2018 ContentsMayBeHot

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""

import random

tiers = ["bronze", "silver", "gold", "diamond"]
pts_win = [20, 20, 20, 15]
pts_loss = [10, 10, 10, 15]
soft_floor_losses = 3
soft_floor_derank_percent = 0.5
trials = 10000

win_percent = 0.55
start_tier = "bronze"
start_subtier = 3
start_pts = 0

def sim_season():
  cur_tier = start_tier
  cur_subtier = start_subtier
  cur_pts = start_pts
  games = 0
  grace_losses = soft_floor_losses
  deranks = 0

  while True:
    games += 1
    did_win = random.random() < win_percent
    tier_idx = tiers.index(cur_tier)
    #print '%s at %s %d @ %d pts' % ('win' if did_win else 'loss',
    #                                cur_tier, cur_subtier, cur_pts)
    if did_win:
      # Reset derank counter
      grace_losses = soft_floor_losses
      # Add points and see if we rank up
      cur_pts += pts_win[tier_idx]
      if (cur_pts >= 100):
        # rank up
        cur_pts = 0
        cur_subtier -= 1
        # maybe go up a tier
        if cur_subtier == 0:
          if cur_tier == "diamond":
            break
          else:
            cur_tier = tiers[tier_idx+1]
            cur_subtier = 3
    else:
      if cur_pts != 0 or cur_subtier == 3:
        cur_pts -= pts_loss[tier_idx]
        if (cur_pts < 0):
          cur_pts = 0
      else:
        # maybe de-rank
        grace_losses -= 1
        if grace_losses <= 0:
          derank = random.random() < soft_floor_derank_percent
          if derank:
            deranks += 1
            cur_subtier += 1
            cur_pts = 100 - pts_loss[tier_idx]


  return (games, deranks)

for percent in range(48, 66, 1):
  games = 0.0
  deranks = 0.0
  win_percent = percent / 100.0
  for i in range(0, trials):
    (g, d) = sim_season()
    games += g
    deranks += d

  print '%2.2f%% games: %1.2f deranks: %1.2f' % (percent, games/trials, deranks/trials)