[Tutor] Rock, Paper, Scissors game

[Peter Otten]

Saad Javed wrote:

> I'm trying to understand how this code works. I've commented the line
> that I can't seem to understand. How did the guy come up with this?
> 
> #!/usr/bin/env python
> 
> import random
> 
> #rock > scissor > paper > rock
> 
> WEAPONS = 'Rock', 'Paper', 'Scissors'
> 
> for i in range(0, 3):
>   print "%d %s" % (i + 1, WEAPONS[i])
> 
> player = int(input ("Choose from 1-3: ")) - 1
> cpu = random.choice(range(0, 3))
> 
> print "%s vs %s" % (WEAPONS[player], WEAPONS[cpu])
> if cpu != player:
>   if (player - cpu) % 3 < (cpu - player) % 3: #How does this line work?

I would never have come up with this line, but I think it can be pictured as 
follows:

Given the cycle 

+-->rock-->paper-->scissors--+
|                            |
+---------------<------------+

and only one direction allowed the winning "weapon" is always the one 
farther away from the loser, e. g.

rock vs paper
rock-->paper: 1 step
paper-->scissors-->rock: 2 steps
paper wins

rock vs rock: 
0 steps both
tie

The modulo operator helps with determining this "directed distance" by 
maintaining

-n == N-n

e. g.

-1 % 3 == 3 - 1 == 2

You could anecdotally test the above outline by adding more weapons. For 
four weapons you should get ties between distinct weapons:

+-->rock-->paper-->scissors-->banana--+
|                                     |
+---------------<---------------------+

rock vs scissors:
rock-->paper-->scissors: 2 steps
scissors-->banana-->rock: 2 steps
tie

You can modify the script to work with an arbitrary number of weapons by 
replacing 3 with length(weapons) if you like.

>     print "Player wins"
>   else:
>     print "CPU wins"
> else:
>   print "tie!"
> 
> Thanks.