Cleaning up/optimizing numerical guessing game

Question

I'm a Python newbie and I'd like to know how I could clean this up/optimize it (but nothing too advanced, please).

As far as I know, it's working as it should, but if you see any errors then please point it out! This is a numerical guessing game with two symbols in front. You can pretty much see how it works by looking at the print messages.

from random import randint, choice 
import string
maxguesses = 11 # Default number of max guesses
wins = 0 
losses = 0 
points = 0 # Points accumulated
games = 0 # Games played
numguesses = 0 # Number of guesses
flag = True
allowed = list(string.digits + '+' + '*')
guesses = '' # Track wrong guesses, resets every game when formula is regenerated
letters = set() 
partial = '' # Current progress of guesses
def genform(): # Generate secret formula
 global secret, maxguesses 
 sym = choice(['++','**','+*','*+']) # Pick operation symbols
 num = '' 
 max = randint(3,9) # Set max between 3 & 9
 for i in range(max): # Range of max variable
 num = num + str(randint(0,9)) 
 secret = sym + num # Assign secret formula
 maxguesses = len(secret)+2 # Max guesses based on length of formula
 return secret 
def evaluate(formula): 
 evaluated = ''
 s1,s2 = secret[:2]
 for i in range(2,len(secret)-1): # Loop after two symbols
 evaluated = evaluated + secret[i]
 evaluated = (evaluated + s1) if not (i%2) else (evaluated + s2) # Place symbols appropriately
 evaluated = evaluated + secret[-1] # Put together
 return evaluated 
def takeguess(ch):
 global numguesses, wins, points, games, partial, guesses
 numguesses = numguesses + 1 # Add guess
 print 'Remaining Guesses: ' + str(maxguesses-numguesses)
 if (ch in partial) or (ch in guesses): # Check if already guessed
 print "\nYou've already guessed '%s'. Try again: " % ch
 elif ch not in secret:
 guesses = guesses + ch
 print 'Wrong, guess again.'
 elif ch in secret: # If in formula
 letters.add(ch) # Add guess to set
 print "\nGood guess, it's in the secret formula!"
 partial = ''.join([l if l in letters else '-' for l in secret])
 print 'Formula so far: ' + partial
 if partial == secret: # If guesses are complete
 print 'You win!'
 wins = wins + 1
 points = points + 2
 games = games + 1
 bonus = raw_input("Evaluate the formula for 10 bonus points: ") # Ask bonus question
 if bonus == str(eval(evaluate(secret))): # Calculate result
 points = points + 10
 print "That's correct! +10 points."
 print eval(evaluate(secret)) #REMOVE AFTER
 play_again()
 else: # If bonus answer is wrong
 print "That's incorrect. The right answer is", eval(evaluate(secret))
 play_again() 
def play_again(): 
 global numguesses, guesses, partial, letters, flag
 letters = set() # Clear set
 if points < 2: # Check points
 print "\nYou don't have enough points to play again.\nGames Played: " + str(games) + '\nPoints: ' + str(points)
 else: # Good to go
 ans = raw_input('Would you like to play again? [y/n] \n')
 if ans in ('yY'):
 numguesses = 0
 guesses = ''
 partial = ''
 play()
 elif ans in ('nN'):
 flag = False
 print '\nOkay, goodbye.\nWins: %s \nLosses: %s \nPoints: %s' % (wins, losses, points)
 else:
 print 'Invalid input.'
 play_again()
def play(): 
 global points, games, losses
 genform() # Generate new formula
 print 'Unsolved formula: ' + ('-'*len(secret))
 print 'You have %s guesses.' % maxguesses
 print secret #REMOVE AFTER
 while (numguesses < maxguesses) and flag: # Enough guesses and run OK
 guess = raw_input('\nEnter a guess: ') # Receive guess
 if guess not in allowed: # Check if valid
 print '\nInvalid guess, please enter a single digit, *, or +. Try again: ' 
 elif partial != secret: # Process guess
 takeguess(guess)
 print guesses # REMOVE AFTER
 if numguesses == maxguesses: # Guess limit reached
 points = points - 2
 games = games + 1
 losses = losses + 1
 print '\nSorry, you lose. The answer is: ' + secret
 play_again() # Ask for replay
 return 
print 'Welcome to Numerical Hangman!\n'
play()

• Latty: A good start would be not using globals - there is always a better way. In this case, pass more arguments and return more values.
• Pedro Romano: My first suggestion is getting rid of the global variables. Is there any reason why you can't pass those as function parameters? If you need to keep more complicated state, then maybe you can create a class to represent it or use a dictionary.
• Latty: I believe the phrase is great minds think alike ;)
• user1790412: I've only learned the very basics of global variables and I don't know about alternatives. Could an example be done for one of my global variables so I can visually see what is meant?

Answer 1

• Not good:

  points = points - 2 # lots of this kind of code
  

  Good:

  points -= 2
  

• Not good:

  allowed = list(string.digits + '+' + '*')
  

  Good:

  allowed = string.digits + '+*' #You don't need list in this case
  

• Not good:

  max = randint(3,9)
  

  Good:

  _max = randint(3,9) # max is a function in standard namespace
  

• Not good:

  print 'Remaining Guesses: ' + str(maxguesses-numguesses)
  

  Good:

  print 'Remaining Guesses: {}'.format(maxguesses-numguesses)
  

• Not good:

  if bonus == str(eval(evaluate(secret))): # what do you mean here?
  

• Not good:

  def evaluate(formula): 
  ...
  

  Your local var formula was not used in this function. Instead of this, you're using global secret.

• Not good:

  genform() 
  ... 
  return secret
  

  You're returning secret in this function, but you don't use it in your app. secret is global anyway.

That's a briefly view. Please read Google’s Python style guide.

• Matt: Some of the information at that link is outdated. For example, they advocate using % for string formatting when people should be using str.format() now. (actually, that is the only problem I saw)
• raylu: string.digits.join creates lots of duplicate copies of '+*' in the allowed string which, while not erroneous, is probably not what you meant. You also probably want it to be a set.