I just can't figure out whats wrong with my little game. It gives always same answer printing "That's too high, pick lower." I have no idea what I did wrong.
import random
global number
number = random.randint(1,20)
def start():
    name = raw_input("Welcome, what's your name?")
    print "Hello %s guess the number from 1 to 20!" % (name)
    game()
def game():
    print "Guess a number!"
    guess = int(raw_input(">"))
    if (guess > number):
        print "That's too high, pick lower."
        game()
    if (guess < number):
        print "That's too low, pick higher."
        game()
    if (guess == number):
        print "Yay that's the right one!"
start()
 
    