Cleaning up/optimizing numerical guessing game

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
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()
• A good start would be not using globals - there is always a better way. In this case, pass more arguments and return more values. – Latty Nov 11 '12 at 23:47
• 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. – Pedro Romano Nov 11 '12 at 23:47
• I believe the phrase is great minds think alike ;) – Latty Nov 11 '12 at 23:48
• 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? – user1790412 Nov 12 '12 at 0:19

• 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.

• 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) – Matt Nov 13 '12 at 14:41
• 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. – raylu Dec 14 '12 at 4:34