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Use rpsrunner.py to play unranked matches on your computer.

Source code:

from hashlib import sha256

# The constant used here came to me in a dream.
state = input and state + input or 'e+4sk5jfPPON3muIQJPM-KBCJPyYHgkkgXgpprL2'
output = 'RPS'[int(sha256(state).hexdigest(),16)%3]