Where Da Vinci learns
In developmentThe Arena
The Arena is a ladder of games and simulations we build, and Da Vinci learns by playing them. Each game is our own rules engine, written in C++. Every run writes a dated result file, and the scores on this page are read from those files.
Where It Trains
On Our Own Server
The Arena is written for the server we run ourselves: eight ARM cores, 16 GB of memory and no graphics card. It needs nothing beyond a C++ compiler, and its own random number generator plays the same games from the same seed on any machine.
In Games and Simulations We Build
Every game is written from scratch, with plain genre names and no outside assets. What the Arena learns from is the games it plays.
On a CPU
Every score on this page came from a run on a CPU. A full run of every game takes about a minute on one core.
The Ladder
Each rung asks for a skill the one below it did not. The first three are built, and property trading is next. Beyond the tenth rung are 3D worlds, which need a graphics card. Alongside the ladder, a strand of game theory teaches Da Vinci to reason about other players.
- 01Sudoku Logic: find the forced move.Built
- 02Bingo Chance: forecasts that know how sure to be.Built
- 03Shedding Cards Chance with choices.Built
- 04Property Trading Money, deals and long-term planning.Next
- 05Chess Deep search and evaluation.Planned
- 06Go Pattern and territory.Planned
- 07Hidden Fleet Reasoning about what cannot be seen.Planned
- 08Civilisation-Style Strategy A whole world over many turns.Planned
- 09Persistent World Many agents in one shared world.Planned
- 10Empire Running everything at once.Planned
What Sits at the Centre
A causal model. Every game reports how well Da Vinci predicts the effect of a change, next to how well it plays.
Bayes
Beliefs are probabilities, updated by evidence. In Bingo, Da Vinci is scored on how well its odds match what happens, not on winning.
Seeing
The first rung of Judea Pearl's ladder of causation: what goes with what, learned by watching games.
Doing
The second rung: what happens if we intervene. Da Vinci predicts the effect of a change, then the engine makes the change and measures it.
Imagining
The third rung: what would have happened. Twin games share the same puzzle and the same luck and differ by one move.
Transport
Elias Bareinboim's question: does an effect learned in one place hold in another? Effects measured on easier puzzles are tested again on harder ones it never trained on.
Next-Concept Modelling
The engines describe play as concepts, not words: a forced move on offer, a rival close to winning, a dead end. A small neural network in plain C++ learns to predict the next concept, and it must beat a model that sees only the previous one.
A Physics Neural Network
In developmentA network held to physical law, to give the causal model a world with mass, motion and time. It comes after the CPU rungs.
How It Improves
Recursive self-improvement, with a gate. Artificial random intelligence, which we also call super stochastic intelligence, is the horizon we are building toward, and the Arena is its first layer: SSI × RSI = ARI.
The Gate
Da Vinci proposes a change to its own policy. The change is kept only if it beats a fixed test it cannot see or edit. Every generation, kept or cut, is written into the result file.
Every Change on Record
Every change to the Arena's code is tested and recorded in git, where it can be audited. When a test shows one of our own models is wrong, we publish it and rebuild the model.
The Robespierre Rule
The rules bind us too. Each result file carries the rule: 'A change is kept only if it beats a fixed test it cannot see or edit, and whatever does not serve the work is cut, however much it cost. The rule binds the makers too: no hand-tuned exceptions and no change outside the gate.'
Latest Scores
The latest run of each game, from the result files of 27 October 2026. When our server publishes newer runs, this list reads them from it.
Sudoku
27 October 2026Logic. A wrong digit ends the game, so it has to find the forced move. Tested on 100 puzzles it never saw.
- Puzzles solved
- 0% to 91%
- Causal accuracy, random play to learned
- 31% to 98%
- Failures rescued by fixing one move
- 100%
- Solved on harder puzzles it never trained on
- 72%
Bingo
27 October 2026Chance. No move changes the result, so it learns to forecast its own odds after each ball. Lower forecast error is better.
- Forecast error (Brier score)
- 0.1020 to 0.0984
- Causal accuracy
- 83%
Shedding Cards
27 October 2026Chance with choices. It picks which card to play and improves by playing copies of itself. A fair share against three players is 25%.
- Wins against three random players
- 27.5% to 30.6%
- Causal accuracy
- 86%
Next-Concept Model on Sudoku
27 October 2026Predicts the next concept in games it has not seen, against a model that sees only the previous concept.
- Next concept predicted
- 71.6% to 79.6%
Next-Concept Model on Shedding Cards
27 October 2026The same network and the same test on a game of chance with choices.
- Next concept predicted
- 47.9% to 64.7%
Causal Model on Sudoku
27 October 2026If the player guesses instead of playing a forced move, how much likelier is a dead end? The engine measures it in 1,500 twin games.
- Measured effect
- +14.9 points
- Naive reading of the same games
- +70.8 points
- Model's prediction
- +8.1 points
- Causal accuracy, naive reading to model
- 0% to 54%
- Causal accuracy on harder puzzles
- 96%
Nash Equilibria in Six Games
27 October 2026It finds every equilibrium exactly, then two learners find them by playing each other. The causal test pays one player more and asks who changes.
- Equilibria found
- 12
- Most either side could gain by deviating
- 4.0000 to 0.0045
- Causal accuracy, naive reading to model
- 0% to 99%
Poker With Hidden Cards
27 October 2026Three cards and one bet, learned by counterfactual regret minimisation in self-play. Nobody told it to bluff.
- Exploitability
- 0.4583 to 0.0016
- Value to the first player
- −0.0556
- Value in theory
- −0.0556
- Bluffs with the jack
- 22%
The Repeated Prisoner's Dilemma
27 October 2026Two hundred rounds with 2% noise. The gated loop evolves a strategy that remembers the last round.
- Points per round
- 2.31 to 2.64
- Causal accuracy
- 99%