aqueval builds chess and poker engines and publishes every change with its statistical test result, including the ones that fail. Two programmes are running: a chess engine in Rust with its own neural evaluation, and a poker AI that runs only in simulation.
No single game decides anything. aqueval studies decisions under uncertainty through verified engines, reproducible experiments and statistical evidence.
What has been built so far, the evidence for each piece, and the methods behind it. Each entry links to the page where it is measured.
Chess is a game of perfect information, poker one of hidden information. Both use the same discipline: a verified engine first, then measured improvements.
A UCI chess engine in Rust with neural evaluation trained only on its own games. Version 1.0 is released as Quant; further search experiments are paused after three consecutive rejections.
No-Limit Texas Hold'em: an equilibrium baseline from counterfactual regret minimisation, a model of human decisions, and both compared in simulation.
The same four steps apply to a pruning margin in chess and to a new strategy in poker.
aqueval is an independent research project on engines for games of perfect and hidden information. Code is written and tested in isolated environments; long runs execute on a single workstation. Results appear here once a milestone has been measured. The poker engine runs only in simulation and never on a live poker site.
Explore the chess-engine source and releases, or contact Deniz about methods and results. Poker results are documented in the supplied milestone reports.
Chess-engine source code, test history and documentation in the Quant repository.
Open the repositoryVersioned chess-engine releases and their documented changes.
View releasesA question about the method, a result that looks wrong, or an idea for working together. contact@aqueval.com
Write an emailaqueval is a UCI chess engine written in Rust, with a neural network evaluation trained only on its own games. Every change is tested against the current main branch with a sequential probability ratio test before it is merged.
aqueval is a UCI chess engine written from scratch in Rust, using bitboards, a strictly legal move generator and an alpha-beta search. Since 26 October it evaluates positions with an efficiently updatable neural network (NNUE) [4], trained only on positions from its own games; the handcrafted evaluation it replaced remains as a fallback build. Each change is tested against the current main branch with a sequential probability ratio test (SPRT); changes that fail are not merged.
Each change plays against the current main branch until the SPRT accepts or rejects it at fixed error rates. Elo is measured in self-play at 8+0.08 s and given with the error margin of each test.
Bars are truncated at +140 Elo; the tapered evaluation (+501) and the network (+711) are drawn with a break. Where a change needed a retest or a second design, the row shows the run that decided it; rejected changes show the better of two designs. Time management was tested at 20+0.2 s. Self-play gains overstate gains against other engines; playing strength is therefore measured separately in a gauntlet (Table 2).
| Date | Build | Stockfish levels | Score | Implied Elo | Estimate |
|---|---|---|---|---|---|
| 17 Oct | Handcrafted evaluation, search steps 1 to 4 | 2000 / 2300 | 55.3% / 43.3% | 2036 / 2252 | ≈2150 |
| 19 Oct | Handcrafted evaluation with pruning and reductions | 2300 / 2600 | 65.3% / 29.5% | 2409 / 2448 | ≈2430 |
| 23 Oct | Handcrafted evaluation, end of phase 1 | 2300 / 2600 | 78.5% / 49.5% | 2524 / 2596 | ≈2560 |
| 26 Oct | First network (NNUE) | 2600 / 2900 | 81.5% / 48.8% | 2857 / 2891 | ≈2875 |
| 5 Nov | Quant 1.0 · NNUE gen-0 | 2900 | 61.4% | 2980 ± 18 | ≈2980 |
October: 200 games per level at 10+0.1 s. November: 1,000 games at 60+0.6 s against UCI_Elo 2900 on a cloud server with 16 dedicated vCPUs. These estimates use different time controls and are not directly comparable or official ratings. All 1,800 games of the November gauntlet and Hash checks ended without crashes, illegal moves or time losses.
Each estimate combines the previous estimate with the new measurement, weighted by the gain K; the band is the 95% confidence interval. The slider sets the assumed process noise and with it K. The filter illustrates estimation under uncertainty; it is a browser demonstration, not the engine’s search algorithm.
Changes follow a fixed test protocol. Dedicated hardware is the target; the latest LMR test shared its machine with training and recorded time losses on both sides. The package was rejected.
| Type of change | Bounds | Time control | Hypothesis |
|---|---|---|---|
| Gainer | [0, 10] nElo | 8 + 0.08 s | The change gains Elo |
| Simplification or speedup | [−8, 0] nElo | 8 + 0.08 s | The change loses no Elo |
| Time management | [0, 10] nElo | 20 + 0.2 s | The new time allocation gains Elo |
| Network against network | [0, 10] nElo | 8 + 0.08 s | The new network is stronger than the previous one |
nElo denotes normalised Elo; [0, 10] nElo corresponds to roughly [0, 5.8] Elo at this time control. After three consecutive failed or inconclusive tests, the queue is halted for review. Before 22 October, gainers used [0, 5] nElo with lower game limits; Table 1 records each test with the bounds it ran under.
The work is organised in five phases, each concluded by a measurement. Forecasts were made in advance; measured values are the sum of the accepted SPRT gains or, where stated, the gauntlet.
Status as of 5 November 2026.
aqueval’s chess engine is available as Quant 1.0 in the source repository and release downloads. It supports UCI on Linux, Windows and macOS (Apple Silicon). The engine and its bundled network are licensed under GPL-3.0-or-later.
Works referred to on this page.
A research programme on No-Limit Texas Hold'em: an equilibrium baseline from counterfactual regret minimisation, a model of human decisions, and both compared under reproducible conditions.
The programme builds three things on one verified engine. First, a game-theoretic baseline: CFR, validated against OpenSpiel on Kuhn and Leduc poker, then a heads-up blueprint computed by Monte Carlo CFR on an abstracted game. Second, a model of human decisions in the spirit of Maia Chess, trained on 21.6 million hands of online play from 2009 and conditioned on stake level. Third, a study of which observable features separate human from automated play, kept in its own package and never used to train the agent. All work runs in simulation.
Three layers are measured: the engine against PokerKit, a reference implementation of the rules; the CFR code against OpenSpiel on games with a known solution; and the heads-up blueprint in duplicate matches against rule-based agents.
| Check | Mismatches | Cases | What is compared |
|---|---|---|---|
| Decisions | 0 | 914,873 | Legal actions, stacks and bets before every decision |
| Pots | 0 | 164,897 | Final pot sizes and payouts |
| Showdowns | 0 | 94,922 | Winner and hand ranking |
| Side pots | 0 | 46,798 | Pots created by all-in players |
| Short all-in raises | 0 | 18,888 | Raises below the minimum and the betting they reopen |
| Split pots | 0 | 9,185 | Pots shared between equal hands |
| Odd chips | 0 | 3,433 | The remainder chip in a split pot |
The engine is checked against PokerKit, a reference implementation of the rules. Every decision of 100,000 random hands with 2 to 9 players is compared: legal actions, stacks and bets before each decision, pots and payouts at the end.
To confirm that the comparison can fail, rule faults were injected on purpose. Each was found in 12 to 2,930 of 3,000 hands, except one that removed a redundant check and left behaviour unchanged. The same seed produced identical hands on the cloud sandbox and on the workstation.
| Configuration | Heads-up | Six players |
|---|---|---|
| Plain Python, workstation | 4,000 | 1,367 |
| Numba, cloud sandbox | ≈465,000 | 277,000 to 306,000 |
| Numba, workstation | 558,803 | 309,642 |
| Decisions per hand | 4.58 | 9.85 |
Random-action playouts. CFR also reads and writes regret tables at every node, so these figures are an upper bound for training speed, not a forecast. Numba is about 140 times faster than plain Python heads-up and about 226 times faster with six players.
| Algorithm | Iterations, Kuhn / Leduc | Kuhn | Leduc | Leduc, OpenSpiel |
|---|---|---|---|---|
| CFR | 10⁴ / 10³ | 1.13 × 10⁻⁴ | 1.18 × 10⁻² | 1.18 × 10⁻² |
| CFR+ | 10⁴ / 10³ | 9.6 × 10⁻⁶ | 2.56 × 10⁻⁴ | 2.57 × 10⁻⁴ |
| Discounted CFR | 10⁴ / 10³ | 2.4 × 10⁻⁵ | 1.74 × 10⁻⁴ | 1.44 × 10⁻⁴ |
| External sampling | 10⁶ | 7.2 × 10⁻⁴ | 1.90 × 10⁻² | 2.16 × 10⁻² |
| Outcome sampling | 10⁶ | 2.9 × 10⁻³ | 0.20 | – |
Sampling methods are means of 10 seeds. On Kuhn the full-width variants match OpenSpiel to 10⁻¹³ at every checkpoint, and the value for the first player is −0.055556 (−1/18). On Leduc [13] they agree to 10⁻¹³ for about 100 iterations and then drift apart; perturbing the project's own regrets once by a factor of 1 + 10⁻¹⁵ produces differences of the same size, so the drift is floating-point chaos, not a different algorithm. External sampling here draws all chance events once per traversal, OpenSpiel once per branch; with OpenSpiel's scheme the result is 0.0219 against 0.0216. Outcome sampling: 0.515 against 0.523 at 10⁵ iterations, 40 seeds.
| Opponent | Final blueprint | 95% CI | Best-LBR blueprint | 95% CI |
|---|---|---|---|---|
| Calling station | +2,258 | 2,070–2,446 | +2,606 | 2,392–2,820 |
| Pot raiser | +4,880 | 4,324–5,437 | +4,897 | 4,333–5,462 |
| Random | +2,045 | 1,773–2,318 | +2,428 | 2,145–2,710 |
| Equity threshold | +1,571 | 1,333–1,810 | +1,822 | 1,568–2,076 |
Each opponent plays 20,000 duplicate pairs, 40,000 hands: every deal is replayed with the seats swapped. The blueprint is the average strategy of external-sampling Monte Carlo CFR [9] on 19.5 million infosets: 169 lossless preflop classes, 500 buckets per later street from k-medians clustering of equity histograms under the earth mover's distance [11], 39,096 betting nodes and stacks of 200 big blinds. The run took 644 million iterations in 8.2 hours on 10 threads, with 8.9 GB peak memory. The best-LBR blueprint is the checkpoint with the lowest local best response.
The opponents always check or call, raise the pot whenever allowed, choose fold, call or a pot raise at random, or act on Monte Carlo equity against a random hand. They are weak, so the table shows that the blueprint plays sound poker, not that it is strong. Local best response [5] stayed between 822 ± 180 and 1,247 ± 177 mbb/hand at all eleven checkpoints without a downward trend, so the exit criterion of M4 is only partly met. Bets outside the abstraction are the main weakness: against the pot raiser the blueprint left its betting tree 1,345 times in 40,000 hands and fell back to check or call. Depth-limited subgame solving (M5) is meant to close that gap.
HandHQ hand histories from July 2009 in the PHH format: 21,782 files, 16 GB unpacked, stakes from 25NL to 1000NL. The full run parsed all 21,606,087 hands without an error and extracted 174,164,978 decisions in 49 minutes; the tables below cover all of them.
Show and muck are logged as actions in the raw files but are not decisions; they are dropped from the decision table. Only 15.8% of hands reach showdown, so hole cards are visible for a small and biased subset. They are kept for filtering and analysis but never used as a model input: visible cards almost always mean the player did not fold (3,191 of 91.5 million folds show cards), so they would leak the label.
Each player is assigned to training, validation or test by a hash of the player ID, 90, 5 and 5%, so no player appears in two splits: 250,238, 13,856 and 13,889 acting players. The most active 1% of players make about a third of the decisions in every split. Stacks are unknown for the iPoker network, 27.8% of all hands; those fields stay empty instead of being filled with guesses.
Kuhn poker [4] uses three cards and one betting round, so it can be solved exactly. It was the first test for the project's own CFR code (M2): the value for the first player converges to −1/18 and every variant matches OpenSpiel (Table 3). This figure runs both algorithms in your browser and is a demonstration, not the project's code. Exploitability is what a best response wins against the average strategy, in chips per hand.
Every milestone ends with a measurement that decides whether the next one starts. Nothing is accepted on the strength of a small positive sample.
| Milestone | Status | Measure | Criterion |
|---|---|---|---|
| M1 Engine | Met | Mismatches | Identical to PokerKit on 100,000 random hands |
| M2 CFR foundation | Met | Exploitability | Kuhn value converges to −1/18; exploitability falls towards zero and matches OpenSpiel |
| M4 Heads-up blueprint | Partly met | mbb/hand, LBR | Beats every rule-based agent; local best response falls over training |
| M6 Imitation model | Data ready | Log-likelihood | Better than a frequency baseline at every stake level, on held-out players |
| M9 Human plausibility | Planned | Strength vs likelihood | Stronger than the imitation model while staying close to it on human data |
M4: the blueprint beats every rule-based agent (Table 4), but local best response did not fall over the 8-hour run.
mbb/hand is milli-big-blinds won per hand. Local best response (LBR) estimates how exploitable a strategy is when the game is too large to solve exactly. Duplicate matches replay the same cards with seats swapped to cancel out card luck.
Twelve milestones in five phases. Code is written and tested in a cloud sandbox; long training runs execute overnight on the workstation.
The engine and every experiment run only in simulation. The detection study lives in its own package, and a test fails if training code imports it.
Works referred to on this page.