Trying to code a simple paper, scissors, stone game

I have got as far as being able to input 'paper', 'scissors' or 'stone'. It's then that I get an error message saying that whatever I have inputed is "undefined". Here's my code:

[#the computer will select a random number from 1 to 3
#first the draws ...
#then the player wins ...
#then the computer wins ...
#then invalid entries
#then use up one round

while rounds != rounds_required:
    mighty = random.randint(1, 3)
    choice = input("What'sss your choisssce? ")
    if choice == "paper" and mighty == 1 or choice == "scissors" and mighty == 2 or choice == "stone" and mighty == 3:
        print "Amazzzingly you and the Mighty Python think alike ... "
        rounds = rounds + 1
    elif choice == "scissors" and mighty == 1:
        print "Aaah, your scissorsss cut my Mighty paper !!"
        player = player + 1
        rounds = rounds + 1
    elif choice == "stone" and mighty == 2:
        print "Youch, your pesssky ssstone blunted my Mighty ssscissorsss !!"
        player = player + 1
        rounds = rounds + 1
    elif choice == "paper" and mighty == 3:
        print "Hisss ... my Mighty ssstone wasss wrapped by your creepy paper !!"
        player = player + 1
        rounds = rounds + 1
    elif choice == "scissors" and mighty == 3 or choice == "paper" and mighty == 1 or choice == "stone" and mighty == 2:
        print "Hah! The Mighty Python triumphsss!!!"
        python = python + 1
        rounds = rounds + 1
    else:
        print "Invalid attempt ... please type all lower cassse and check your ssspelling."

#announce the final scores

if player == python:
    print "You were a worthy challenger we both scored", player," the true winner wasss the game."
elif player > python:
    print "I sssalute your random cunning you beat me by", player, " pointsss to", python, "."
else:
    print "The Mighty Python triumphsss by", python, " points to a mere", player, "pointsss!"]

I thought it might be the way I have herded together all those "and" and "or" commands but I rewrote it as 9 different elifs and got the same outcome. Of course that doesn't necessarily mean that the "and"s and "or"s are any good themselves does it?