Python if statement always picking same answer [duplicate]

This question already has an answer here:

• Python: Problem with raw_input reading a number 3 answers

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()