Learning to play the Chess Variant Crazyhouse above World Champion Level with Deep Neural Networks and Human Data

Alena Beyer; Johannes Czech; Johannes F\"urnkranz; Kristian Kersting; Moritz Willig

REVIEW 4 major objections 4 minor 51 references

Learning to play the Chess Variant Crazyhouse above World Champion Level with Deep Neural Networks and Human Data

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A supervised-only neural engine beat the 2017 crazyhouse world champion 4-1.

desk verdict Solid systems paper with real MCTS and representation contributions; the 'above World Champion Level' title rests on five informal games and is statistically weak, but the rest of the evidence and the released code make it worth a serious referee. read the letter →

arxiv 1908.06660 v2 pith:EPO6CWDF submitted 2019-08-19 cs.AI cs.LG

Johannes Czech , Moritz Willig , Alena Beyer , Kristian Kersting , Johannes Fürnkranz This is my paper · ORCID

classification cs.AIcs.LG

keywords DeepLearningChessCrazyhouseSupervisedMonte-CarloTreeSearchNeuralnetworkenginevariant

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish that a neural-network engine called CrazyAra can play the chess variant crazyhouse above the level of the human world champion even though it is trained solely by supervised learning on human games, with no reinforcement learning and no self-play. Its most direct evidence is a 4-1 win in informal games against the 2017 crazyhouse world champion, together with wins against twelve of thirteen engines from the 2017 crazyhouse computer championship while running on CPU hardware. If true, this matters because it would show that the very large computation budgets associated with self-play systems are not the only path to elite play in a complex, high-branching game: a compact architecture, a fully Markovian board encoding, input normalization, and sample-efficient search can turn a modest set of noisy human games into a world-class engine.

What carries the argument

The load-bearing machinery is a dual-head deep convolutional network whose shared residual tower feeds a policy head over all legal-sounding moves and a value head returning a win/loss estimate in $[-1,1]$, coupled with PUCT, an upper-confidence-bound tree search guided by the learned policy prior. The input is a fully Markovian 34-plane $8\times 8$ encoding of the current position only, covering pieces, pocket contents, promoted pieces, en-passant, castling, repetition, and move counters, with each non-binary plane divided by a maximum value. The search is made sample-efficient by Q-value-aware final move selection, principal-variation Q updates, a transposition table, time-dependent search, and a prior-enhancement step that raises the probability of checking moves; these modifications are what let a low node budget compete against engines searching thousands of times more nodes.

What would settle it

Run a controlled match between CrazyAra 0.6.0 and a top human crazyhouse player at a slow time control (for example 30 minutes plus 30 seconds increment) from balanced openings and check whether the 4-1 result survives; separately, compute the value head's accuracy on positions from bullet games where the winner flagged in a materially losing position.

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Extended reading notes

Core claim

On its own terms, the paper's claim is that a single shared neural network predicting both a move policy and a position value, combined with an adapted Monte-Carlo tree search, reaches world-champion-level crazyhouse after supervised training on 569,537 human games. The network reaches 60.4% move-prediction accuracy after 1.5 days of training, and the engine's strength is demonstrated in two ways: a 4-1 informal match win over the 2017 human world champion and a 12-1 record against the field of the 2017 crazyhouse computer championship on CPU hardware. A later version, fine-tuned on engine-generated games, wins three and draws one of ten long-time-control games against a strong alpha-beta engine, which the paper presents as supporting the same underlying approach rather than as evidence that reinforcement learning is required.

Load-bearing premise

The value labels are taken from each game's final outcome and assigned to every position, on the assumption that a player with a large advantage will almost surely win; the paper states this is heavily violated because many games are low-time-control bullet games decided by blunders or time forfeits.

Editorial extensions

If this is right

A supervised-only training pipeline can produce an elite engine in a tactic-heavy game with a higher branching factor than chess, so massive self-play computation is not the only route to top strength.
The search modifications that add Q-values, principal-variation information, transposition reuse, and check-move priors each raise playing strength at low node counts, which suggests they are transferable improvements for other neural-guided MCTS engines.
Beginning with human games and then continuing training on engine-generated games yields a model that takes 3.5 of 10 points from a strong alpha-beta engine at long time control, indicating the human-data model is a viable base for further refinement.
At roughly 330 nodes per second on CPU, the engine beat most opponents despite their searching roughly 3,000 to 14,000 times more nodes, so node count alone is not a reliable proxy for playing strength in this setting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the final-outcome value labels are as noisy as the paper admits, then much of CrazyAra's playing strength may come from the policy head and search priors rather than from the value head; an ablation that feeds a constant value to the search would isolate the value head's contribution.
The 4-1 human result is informal and short-time-controlled; a slower, controlled match against the same champion from balanced openings would be the sharper test of 'above world champion level.'
The same recipe, supervised training on human games, a compact Markovian encoding, and sample-efficient search, could be applied to other games with sparse human data and large branching factors, such as bughouse or shogi variants with drops.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is better than its title. The real contributions are concrete and useful: a compact fully Markovian board representation for crazyhouse, a normalization step that clearly helps training, the RISEv2-mobile architecture that cuts inference cost substantially, and several MCTS sample-efficiency tricks—Q-value-based final move selection, a transposition table, a parameterized U-value divisor, and check-prior boosting. These are evaluated with self-play Elo comparisons and a nice worked example showing how the search adaptations rescue a move the policy assigns near-zero probability. The code and data preprocessing are public, which makes the work independently checkable. The soft spot is exactly where the reader and stress-test put it: the 'above World Champion Level' claim rests on a 4-1 informal match against Justin Tan, whose lichess handle is in the top-20 training-data players. Under a null of equal strength, 4-1 has p approximately 0.19, so it is not statistically significant. And because the opponent is partly in-distribution, the result is even weaker as evidence of generalization beyond the training population. The authors themselves call the games informal, and the conclusion uses the more modest phrase 'level of the strongest human players'—the title and abstract oversell. The engine match results against twelve of thirteen CCVA 2017 engines are credible but those engines are mostly far below Stockfish, and CrazyAra lost all ten to Stockfish. CrazyAraFish's 3-1-6 showing against Stockfish 10 is a legitimate data point but does not rescue the human-champion claim. One more caveat worth flagging: the value labels are final game outcomes assigned to every position, and Section 3.1 admits this assumption is 'heavily violated' because of bullet games. That means the value head, and therefore MCTS guidance, is trained on noisy targets. The policy accuracy and mate-finding metrics are solid, but the value signal should be treated as a known weakness, not an afterthought. Who is this for? Researchers working on supervised game learning with limited, noisy data, and anyone interested in MCTS improvements that transfer beyond crazyhouse. It deserves serious peer review, but with a required major revision: rephrase the central claim with an error bar or more games, release model weights so the in-distribution concern can be quantified, and acknowledge the value-label issue in the evaluation. I would bring it to a reading group and would cite it for the MCTS sample-efficiency mechanisms.

Referee Report

4 major / 4 minor

Summary. The paper presents CrazyAra, a deep neural network engine for the chess variant crazyhouse, trained purely by supervised learning on 569,537 human games from lichess.org. The authors introduce a compact Markovian board representation, an input normalization scheme, a mobile-friendly residual network architecture, and several Monte-Carlo Tree Search (MCTS) modifications (Q-value-based move selection, principal-variation adjustment, transposition table, dynamic exploration parameters, and check-move boosting). They report a move-prediction accuracy of 60.4% on the validation set, a 4-1 win over 2017 crazyhouse world champion Justin Tan in an informal match, victories against twelve of thirteen participants of the 2017 CCVA Computer Championships on CPU hardware, and, after continued training on Stockfish self-play games (CrazyAraFish), three wins and one draw in ten long-time-control games against Stockfish 10. The central claim, stated in the title and abstract, is that CrazyAra plays 'above World Champion Level'.

Significance. If the strength claims are accepted, the paper would be a notable demonstration that supervised learning from modest amounts of human data, combined with a carefully engineered MCTS variant, can produce an engine competitive with strong human and computer crazyhouse players. The work is also useful for its engineering contributions: the compact input representation, the normalization study, the efficient network design, and the detailed ablation of MCTS components are clearly presented and empirically evaluated. The authors provide open-source code, data-processing scripts, and supplementary match records, which is a strength for reproducibility. The move-prediction and mate-finding metrics give concrete, falsifiable performance numbers. However, the headline 'above World Champion Level' claim rests on evidence that is not statistically robust and is partially in-distribution, so the significance of the paper as a claim about super-human play is not established by the current analysis.

major comments (4)

[Title and Section 11.1, Table 12] The central claim that CrazyAra plays 'above World Champion Level' is supported only by a 4-1 result in five informal games against Justin Tan. Under the null hypothesis of equal strength (win probability 0.5 per game), the probability of winning four or five of five games is 6/32 = 0.1875, which is not statistically significant evidence of superiority. The match is explicitly described as 'informal games', and the opponent (LM JannLee) is one of the most active players in the training data, appearing in Figure 6 and contributing to the 46.03% of games played by the top-20 players. This means the evaluation is partly in-distribution for the network. To support the title claim, the authors need either a larger and more formal match, a statistical analysis with confidence intervals or a Bayes factor, or a revised claim that accurately reflects the evidence, e.g., 'wins an informal match against the 2017 world champion' rather than 'above World Champion Level'.
[Section 3.1] The value labels are assigned from final game outcomes to every board position, based on the assumption that a large advantage almost surely leads to a win. The paper itself states this assumption 'is, however, heavily violated in our data set partly due to the popularity of low time control games' (Section 3.1), and Section 7 reports that 45.15% of games are one-minute bullet games. Since the value head directly guides the MCTS search, noisy value labels can systematically bias move selection. The paper does not quantify the impact of this label noise or test whether filtering or reweighting low-time-control games changes the results. Please provide an analysis of the value-label reliability (e.g., accuracy as a function of game length or time control) or discuss why the observed engine strength is not substantially affected.
[Section 11.2, Table 13] The engine evaluation, while showing strong results against twelve of thirteen CCVA participants, does not provide a bound on human world-champion level. Most of the defeated engines have Elo ratings well below 3,000 (and several are over 1,000 Elo below Stockfish), and CrazyAra lost all ten games to Stockfish 10. The abstract and conclusion use these results in a way that suggests they corroborate the human-match claim, but they are not evidence about the human champion level. The paper should separate more carefully the claims 'wins against most CCVA participants on CPU' from 'plays above human world-champion level', and the latter should be supported by the human-match evidence, which is currently insufficient.
[Section 11.2 and Table 14] The CrazyAraFish results against Stockfish 10 are presented as 'wins three games and draws one out of ten', but the paper does not report the statistical significance of this match either. With 3 wins, 1 draw, and 6 losses, the result is consistent with Stockfish being stronger over the match; the three wins are notable but do not demonstrate overall superiority. The discussion of these results in Section 10 should be phrased with appropriate uncertainty, and the abstract's emphasis on this result should be tempered accordingly.

minor comments (4)

[Throughout] There are several typographical errors: 'soley' should be 'solely', 'Neterov' should be 'Nesterov', 'Consquently' should be 'Consequently', 'mis-leading' should be 'misleading', and 'crazhouse' (Section 3.1) should be 'crazyhouse'.
[Section 7, Figure 6] The caption of Figure 6 says 'matches≥2,000 Elo', but the text says the training data consists of games with 'Elo≥2,000 for both players'. Please clarify the exact filtering criterion and ensure the caption is consistent.
[Section 9.2.1] In Equation (5), the notation Q'(s0,a) is used for the thresholded Q-values, but the definition says 'we set all Q-values with a visit count < Qthresh * max_a(N(s0,a)) to 0'; it would be clearer to write the formula for Q'(s0,a) explicitly, including the re-scaling to [0,1].
[Section 11.1] The text says the match was played by 'CrazyAra 0.3.1' but Table 12 lists 'CrazyAra 0.3.0'. Please correct this inconsistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation chain is empirical and benchmarked externally; the small-match caveats do not reduce any prediction to its training input.

full rationale

The paper's training pipeline (Sections 3-8) fits a policy and value network to final game outcomes (Eq. 1) and validates it on held-out positions; no parameter is fitted to the quantity later advertised as a prediction. The headline strength claim is an empirical match result (Section 11.1, 4-1 against Justin Tan) and a tournament sweep on CPU (Section 11.2), both evaluated against external opponents. Justin Tan's lichess handle appears among the top-20 players in Figure 6, so the match is partly in-distribution; however, beating a player represented in the training set is not a construction-level equivalence, and the match result is never used as a training label or optimization target. Similarly, MCTS hyperparameters were tuned through self-play comparisons (Section 9.2), which is standard engineering iteration, not a claim that the search improvement follows by definition from the network. The paper explicitly flags the noisy value-label assumption (Section 3.1: 'This assumption is, however, heavily violated in our data set partly due to the popularity of low time control games'), a data-quality limitation that weakens the value signal but does not make the evaluation circular. No load-bearing self-citation chain, imported uniqueness theorem, or ansatz-by-citation carries the derivation. The five-game match is too small to establish superiority statistically, but that is an evidentiary weakness, not circularity.

Assumptions & free parameters 12 free parameters · 4 assumptions · 0 invented entities

Free parameters dominate: the engine's strength is the product of many hand-set hyperparameters (network shape, search constants, normalization maxima) and a data filter. No new entities are introduced. The axioms are mostly domain assumptions that the paper itself partly flags as violated. This is normal for an empirical systems paper, but it means the 'above world champion level' claim inherits all of these choices.

free parameters (12)

alpha (value loss weight) = 0.01
Equation 1; set to 0.01 to avoid value overfitting, following Silver et al. 2016.
cpuct-init = 2.5
MCTS exploration constant in U(s,a), set in Section 9.1; affects exploration-exploitation balance.
cpuct-base = 19652
Scaling constant in cpuct(s) (Eq. 3); hand-chosen.
Qfactor = 0.7
Weight for Q-values in final move selection (Eq. 5); fixed during search.
Qthresh schedule = init=0.5, max=0.9, base=1965
Dynamic threshold parameters (Eq. 7) for pruning low-visit Q-values.
udivisor schedule = umin=0.25, uinit=1, ubase=1965
Parameters of the U-value exploration divisor (Eq. 11).
checkfactor = 0.5
Prior boost for checking moves (Eq. 12), with checktresh=0.1.
max learning rate = 0.35
One-cycle learning rate maximum (Section 8), found via LR range test; min 1e-5.
weight decay = 1e-4
L2 regularization constant in Eq. 1 (Section 8).
input normalization maxima = pocket=32, moves=500, no-progress=40
Hand-set soft maxima in Section 4.1.
network depth and width = 13-19 blocks, 256 channels; heads 8/8
Architecture variants in Tables 3-5; chosen by validation performance.
data quality filter = Elo >= 2000
Training set filter (Section 7); excludes weaker players and shapes the style learned.

assumptions (4)

domain assumption Game outcome labels are usable training targets for every position despite blunders and time forfeits.
Section 3.1: 'This assumption is, however, heavily violated in our data set partly due to the popularity of low time control games.'
domain assumption A history-free Markovian board representation is sufficient for strong crazyhouse play.
Section 4 removes the 7-step history, arguing crazyhouse is full-information and the repetition/no-progress channels encode the needed state.
domain assumption Self-play Elo gains of MCTS variants transfer to strength against external engines and humans.
Section 9.2 tunes and validates Q-value move selection via matches of CrazyAra against itself (Table 11), without independent external baselines for the tuning protocol.
standard math Standard deep learning and tree-search background results hold as used.
Residual networks, batch normalization, PUCT, and backpropagation are taken as given.

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Cite this review

Pith. "Pith review of Learning to play the Chess Variant Crazyhouse above World Champion Level with Deep Neural Networks and Human Data." pith.science (2026). https://pith.science/paper/EPO6CWDF

@misc{pith2026190806660,
  author       = {Pith},
  title        = {Pith review of: Learning to play the Chess Variant Crazyhouse above World Champion Level with Deep Neural Networks and Human Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPO6CWDF}},
  note         = {Machine review of arXiv:1908.06660}
}

read the original abstract

Deep neural networks have been successfully applied in learning the board games Go, chess and shogi without prior knowledge by making use of reinforcement learning. Although starting from zero knowledge has been shown to yield impressive results, it is associated with high computationally costs especially for complex games. With this paper, we present CrazyAra which is a neural network based engine solely trained in supervised manner for the chess variant crazyhouse. Crazyhouse is a game with a higher branching factor than chess and there is only limited data of lower quality available compared to AlphaGo. Therefore, we focus on improving efficiency in multiple aspects while relying on low computational resources. These improvements include modifications in the neural network design and training configuration, the introduction of a data normalization step and a more sample efficient Monte-Carlo tree search which has a lower chance to blunder. After training on 569,537 human games for 1.5 days we achieve a move prediction accuracy of 60.4%. During development, versions of CrazyAra played professional human players. Most notably, CrazyAra achieved a four to one win over 2017 crazyhouse world champion Justin Tan (aka LM Jann Lee) who is more than 400 Elo higher rated compared to the average player in our training set. Furthermore, we test the playing strength of CrazyAra on CPU against all participants of the second Crazyhouse Computer Championships 2017, winning against twelve of the thirteen participants. Finally, for CrazyAraFish we continue training our model on generated engine games. In ten long-time control matches playing Stockfish 10, CrazyAraFish wins three games and draws one out of ten matches.

Figures

Figures reproduced from arXiv: 1908.06660 by the authors.

**Figure 1.** Compilation pipeline of the CrazyAra engine was started with the goal to replicate AlphaZero in a collaborative effort using distributed computing from the crowd. Several other engines 6 built up on Leela or are partly based on the source code of the Leela project. Our work on crazyhouse started as an independent project. Generally, only little work exists on machine learning for crazyhouse chess. One exception is t… view at source ↗

**Figure 2.** We trained a small AlphaZero like network , see Table 3, with seven residual blocks on a subset of our training [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Plane representation of an exemplary game position of our test data set, [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (15 more)

**Figure 4.** Figure 4: Activation maps of model 4-value-8-policy when processing input sample ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 6.** Figure 6: Top 20 most active crazyhouse players with matches [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Game outcomes of the lichess data set (569,537 games) and Stockfish self play data set (121,571 games) 7 Training Data Now that the architectures are in place, let us turn towards the data used for training. As training data we mainly used 569,537 human games 18 played…

**Figure 8.** Figure 8: Statistics of the lichess data set 0.0 0.5 1.0 1.5 2.0 Number of Training Samples processed ×108 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Learning Rate (a) Learning rate schedule 0.0 0.5 1.0 1.5 2.0 Number of Training Samples processed ×108 0.80 0.82 0.84 0.86 0.88 0.90…

**Figure 9.** Figure 9: Schedules used for modifying the parameters of Nesterov’s stochastic gradient descent optimizer [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: Learning progress of training for seven epochs on the lichess.org crazyhouse data set for different model [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

**Figure 11.** Figure 11: Detailed view on the last iterations of training for different model architectures [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

**Figure 12.** Figure 12: Self Elo increase with respect to nodes [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

**Figure 13.** Figure 13: Search tree statistics over time for the Move [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]

**Figure 14.** Figure 14: Chosen opening positions validating the playing strength of [PITH_FULL_IMAGE:figures/full_fig_p027_14.png]

**Figure 15.** Figure 15: Chosen opening positions between CrazyAraFish 0.6.0 on GPU and Stockfish 10 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png]

**Figure 16.** Figure 16: Game 4 / 10 29 [PITH_FULL_IMAGE:figures/full_fig_p029_16.png]

**Figure 17.** Figure 17: Game 8 / 10 30 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png]

**Figure 18.** Figure 18: Game 9 / 10 31 [PITH_FULL_IMAGE:figures/full_fig_p031_18.png]

**Figure 19.** Figure 19: Game 10 / 10 32 [PITH_FULL_IMAGE:figures/full_fig_p032_19.png]

Discussion (0). Continue with ORCID to comment.

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