You cannot defeat my dynamically learning rock-paper-scissors bot
Represent your species in the ultimate field of battle.
Mark Henry
Ideal rock-paper-scissors play converges to a 33% winrate given perfectly random play. But humans are not perfectly random. Can we exploit human nonrandomness to beat the 33% baseline?
What you are playing against
A neural net with 1,091 parameters, pretrained on a corpus of human play. It sees the last five rounds (your throw and its throw, one-hot encoded), passes them through a 32-unit hidden layer, and outputs a probability distribution over your next throw. It then plays whatever beats your predicted move.
After you throw, the net takes your move as a training example and does sixteen steps of gradient descent (Adam, learning rate 0.01): one step on the round that just happened, fifteen replaying rounds sampled from the last forty-eight. Then it predicts again.
Gwern thinks that this is how personalized LLMs should work.
Results
In this configuration, a naive, untrained network can download a simple opponent in 20 rounds.
| alogrithmic opponent | margin, first 30 | margin, first 200 |
|---|---|---|
| always rock | +97% | +100% |
| cycle R,P,S | +81% | +97% |
| pattern R,R,P | +86% | +98% |
| pattern R,P,P,S,R | +68% | +95% |
| beat bot’s last | +47% | +92% |
| win-stay, lose-shift | +46% | +92% |
| never repeat | +15% | +25% |
| counter the counter | +79% | +97% |
| random | −0% | +1% |
| markov exploiter | +5% | +16% |
But because the typical website visitor is just going to play a couple rounds, I've decided to give it a head start by pretraining it on a corpus of 266,415 rounds of human play, from 911 players across four published experiments: Brockbank and Vul, Arai et al., and Komai, Kurokawa and Kim.
What does this get us?
| opponent | margin, first 30 rounds | margin, first 200 rounds | ||||
|---|---|---|---|---|---|---|
| untrained | pretrained (self-play) | pretrained (humans) | untrained | pretrained (self-play) | pretrained (humans) | |
| always rock | +97% | +93% | +93% | +100% | +99% | +99% |
| cycle R,P,S | +81% | +80% | +83% | +97% | +97% | +98% |
| pattern R,R,P | +86% | +77% | +74% | +98% | +97% | +96% |
| pattern R,P,P,S,R | +68% | +55% | +63% | +95% | +93% | +95% |
| beat bot’s last | +47% | +50% | +39% | +92% | +92% | +91% |
| win-stay, lose-shift | +46% | +32% | +35% | +92% | +89% | +90% |
| never repeat | +15% | +25% | +30% | +25% | +25% | +27% |
| counter the counter | +79% | +57% | +83% | +97% | +94% | +98% |
| random | −0% | +4% | −6% | +1% | −1% | +1% |
| markov exploiter | +5% | +4% | +6% | +16% | +15% | +12% |
| held-out corpus | margin, first 30 rounds | margin, all rounds | ||
|---|---|---|---|---|
| untrained | pretrained (humans) | untrained | pretrained (humans) | |
| human vs. human (Brockbank v1) | +5% | +10% | +11% | +12% |
| vs. fixed-pattern bots (Brockbank v2) | +15% | +21% | +43% | +44% |
| vs. adaptive bots (Brockbank v3) | +4% | +13% | +13% | +16% |
| vs. online perceptron (Arai 2025) | +7% | +13% | +19% | +22% |
| vs. GP model, 50 rounds (Komai 2022) | +5% | +10% | +8% | +13% |
| all held-out (726 players) | +6% | +11% | +18% | +21% |
How to beat it
If you are in the corpus distribution, you have the following weaknesses:
| tendency | what 1,637 people did | ||
|---|---|---|---|
| any throw | rock 32% | paper 33% | scissors 35% |
| first throw | rock 34% | paper 30% | scissors 35% |
| after a win | stay 28% | up 39% | down 33% |
| after a loss | stay 28% | up 35% | down 37% |
| after a tie | stay 30% | up 34% | down 36% |
| vs. opponent’s last throw | beat it 33% | copy it 33% | lose to it 34% |
The masters say that if you meditate upon the above table and let go your conscious self, you will transcend your biases.
Some also say that you can tick the "cheat" checkbox and see what the bot predicts you will do.
Or reject your human fallacies, and roll a die.