new_contents: import random
  import math
  
  """
  According to our calculation:
  the probaility that Q bets as first player should be sqrt(6)/2 - 1
  and the probability that K bets as first player should be 1
  """
  PROB_Q_BET = math.sqrt(6)/2 - 1
  PROB_K_BET = 1
  
  """
  The function decision takes in two parameters:
  1. isFirst: True if the bot is the first player, False otherwise;
  2. hand: 0 if hand is Queen, 1 if hand is King, 2 if hand is Ace,
  and returns True if the bot plays aggressively,
  (bets if first player, or calls if second player)
  or False if otherwise.
  """
  def decision(isFirst, hand):
      randomNum = random.random()
      if (isFirst):  # bot plays the first position
          if (hand == 0):
              return randomNum <= PROB_Q_BET
          elif (hand == 1):
              return randomNum <= PROB_K_BET
          else:
              return True  # Ace always bets in first position
      else:  # bot plays the second position
          if (hand == 0):
              return False  # Queen always folds to a bet
          elif (hand == 1):
              prob = PROB_Q_BET / (1 + PROB_Q_BET)
              return randomNum <= prob
          else:
              return True  # Aces always calls a bet
  
  def testDecision(n):  # Tests the bluff decision of Queen n times
      count = 0
      for i in range(n):
          if (decision(True, 0)):
              count += 1
      print(str(count) + " out of " + str(n) + " times of bluffing.")
  
  testDecision(1000)  # Test for 1000 times
  
subject: add PokerBot.py