Interactive · Rock paper scissors
Can you beat Blank Sheet?
Blank Sheet is the bot from our video that starts with an empty notebook. Every round, it writes down what you did after a win, a tie or a loss, and bets you'll do it again. Play 100 rounds. Can you stay unpredictable?
Pick a throw.
Blank Sheet's notebook
| After | Same throw | Switched up | Switched down |
|---|---|---|---|
| After you won | |||
| After a tie | |||
| After you lost |
Up means switching to the throw that beats your last one (rock → paper → scissors → rock). Down is the other way.
Round 1: nothing written down yet, so it throws at random.
What a million matches say
We ran Blank Sheet against two opponents, a million matches each, a thousand rounds per match.
of matches against our human model, Blank Sheet was ahead after 100 rounds. After 300 rounds: 94.3%.
wins to losses per 100 rounds against the human model, over a whole match. It starts near 34 : 33 and gets better as the notebook fills up.
against a truly random player. After 100 rounds it was ahead in only 47.5% of matches. Random has no habits to write down.
Our human model comes from one experiment (Wang, Xu & Zhou 2014, 360 students in China), with habits read off the paper's charts. Real people vary. You might be harder to read, or easier.
How Blank Sheet thinks
This is the whole idea, the same snippet as in the video. The full version, with every simulation in the video, is on GitHub.
class BlankSheet:
# tally[outcome][change]: what you did
# after a win, a tie, a loss
def move(self):
change = argmax(self.tally[self.your_last_outcome])
guess = (self.your_last + change) % 3
return (guess + 1) % 3 # beat itTwo moves to try on your friends
Based on how people played in that experiment. They only kick in after the first throw, so save them for best-of-three or longer. In our model, they win about 41 rounds for every 27 they lose. Real people are messier, so it's a nudge, not a guarantee.
They just won or tied
Throw whatever beats what they just threw.
They just lost
Throw the same thing they just threw.
See the whole story
Pure luck, a bot with the answers, a bot that learns, and a 1999 tournament where playing at random finished 27th out of 55.