Software:Leela Chess Zero

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Short description: Deep neural network-based chess engine
Leela Chess Zero
Leela Chess Zero logo.svg
Original author(s)Gian-Carlo Pascutto, Gary Linscott
Developer(s)Gary Linscott, Alexander Lyashuk, Folkert Huizinga, others
Initial release9 January 2018; 6 years ago (2018-01-09)
Stable release
v0.30 / 21 July 2023; 15 months ago (2023-07-21)
Written inC++
Operating systemWindows, Mac, Linux, Ubuntu, Android
TypeChess engine
LicenseGPL-3.0-or-later
Websitelczero.org

Leela Chess Zero (abbreviated as LCZero, lc0) is a free, open-source, and deep neural network–based chess engine and volunteer computing project. Development has been spearheaded by programmer Gary Linscott, who is also a developer for the Stockfish chess engine. Leela Chess Zero was adapted from the Leela Zero Go engine,[1] which in turn was based on Google's AlphaGo Zero project.[2] One of the purposes of Leela Chess Zero was to verify the methods in the AlphaZero paper as applied to the game of chess.

Like Leela Zero and AlphaGo Zero, Leela Chess Zero starts with no intrinsic chess-specific knowledge other than the basic rules of the game.[1] Leela Chess Zero then learns how to play chess by reinforcement learning from repeated self-play, using a distributed computing network coordinated at the Leela Chess Zero website.

(As of January 2024), Leela Chess Zero has played over 2.2 billion games against itself, playing around 1 million games every day,[3] and is capable of play at a level that is comparable with Stockfish, the leading conventional chess program.[4][5]

History

The Leela Chess Zero project was first announced on TalkChess.com on January 9, 2018.[1][6] This revealed Leela Chess Zero as the open-source, self-learning chess engine it would come to be known as, with a goal of creating a strong chess engine.[7] Within the first few months of training, Leela Chess Zero had already reached the Grandmaster level, surpassing the strength of early releases of Rybka, Stockfish, and Komodo, despite evaluating orders of magnitude fewer positions due to its deep neural network in its evaluation function and its use of Monte Carlo tree search.

In December 2018, the AlphaZero team published a new paper in Science magazine revealing previously undisclosed details of the architecture and training parameters used for AlphaZero.[8] These changes were soon incorporated into Leela Chess Zero and increased both its strength and training efficiency.[9]

The work on Leela Chess Zero has informed the similar AobaZero project for shogi.[10]

The engine has been rewritten and carefully iterated upon since its inception, and now runs on multiple backends, allowing it to effectively utilize different types of hardware, both CPU and GPU.[11]

The engine supports the Fischer Random Chess variant, and a network is being trained to test the viability of such a network as of May 2020.[11]

Program and use

The method used by its designers to make Leela Chess Zero self-learn and play chess at above human level is reinforcement learning. This is a machine-learning algorithm, mirrored from AlphaZero used by the Leela Chess Zero training executable/binary code (called "binary") to maximize reward through self-play.[1][8] As an open-source distributed computing project, volunteer users run Leela Chess Zero to play hundreds of millions of games which are fed to the reinforcement algorithm.[3] In order to contribute to the advancement of the Leela Chess Zero engine, the latest non-release candidate (non-rc) version of the Engine as well as the Client must be downloaded. The Client is needed to connect to the current server of Leela Chess Zero, where all of the information from the self-play chess games are stored, to obtain the latest network, generate self-play games, and upload the training data back to the server.[12]

In order to play against the Leela Chess Zero engine on a machine, two components are needed: the engine binary and a network. (The engine binary is distinct from the client, in that the client is used as a training platform for the engine). The network contains Leela Chess Zero's evaluation function that is needed to evaluate positions.[12] Older networks can also be downloaded and used by placing those networks in the folder with the Lc0 binary.

Self-play Elo

Self-play Elo is used to gauge relative network strength to look for anomalies and general changes in network strength, and can be used as a diagnostic tool when Lc0 undergoes significant changes. Through test match games that are played with minimal temperature-based variation,[13] Lc0 engine clients test the most recent version against other recent versions of the same network's run, which is then sent to the training server to create an overall Elo assessment.

Standard Elo formulae are used to calculate relative Elo strength between the two players. More recent Self-play Elo calculations use match game results against multiple network versions to calculate a more accurate Elo value.

The Self-play approach has several consequences on gauging Lc0 Elo rating:

  • Initial Cumulative Elo inflation in training runs differ drastically due to a-periodic gains in self-improvement and adversarial play.
  • Measuring Elo relative to previous networks fails to measure general strength since networks are trained to anticipate and beat the predictions made by prior Lc0 networks rather than opponents outside the training domain. This is a type of overfitting measured most drastically when testing smaller networks.
  • There is no direct one-to-one correlation between self-play Elo and the strength against Alpha-Beta engines, and no known correlation to strength against humans.
  • Input training data has a significant effect on how a network will perform elo-wise against the next iteration.
  • Cumulative Self-Play Elo does not have a universal conversion to conventional Human Elo due to inflation issues presented by adversarial play, and the reliance of the measure on time control. This holds true even when the engine runs on a standard set of initial conditions.

Cumulative Self-Play Elo inflation can be compared with other runs to gauge the lack of generality in gauging strength with pure cumulative self-play Elo. The Fischer Random Chess run Test 71.4 (named 714xxx nets), ranks at nearly 4000 cumulative self-play Elo 76 nets into its run (714076). The T60 (6xxxx) run 63000 net has a cumulative self-play Elo of around 2900. Pitting 714076 against net 63000 reveals 63000 clearly beats 714076 in head-to-head matches at most, if not all "fair" time controls. However, net 63000's Elo is significantly lower than its opponent. This supports the claim that Cumulative Self-Play Elo is not an objective measure of strength, nor is it a measure which allows one to linearly compare Lc0 network strength to human strength.

Setting up the engine to play a single node with --minibatch-size=1 and go nodes 1 for each played move creates deterministic play, and Self-Play Elo on such settings will always yield the same result between 2 of the same networks on the same start position—always win, always loss, or always draw. Self-play Elo is not reliable for determining strength in these deterministic circumstances.

Spinoffs

In season 15 of the Top Chess Engine Championship, the engine AllieStein competed alongside Leela. AllieStein is a combination of two different spinoffs from Leela: Allie, which uses the same evaluation network as Leela, but has a unique search algorithm for exploring different lines of play, and Stein, an evaluation network which has been trained using supervised learning based on existing game data featuring other engines (as opposed to the unsupervised learning which Leela uses). While neither of these projects would be admitted to TCEC separately due to their similarity to Leela, the combination of Allie's search algorithm with the Stein network, called AllieStein, is unique enough to warrant it competing alongside mainstream Lc0. (The TCEC rules require that a neural network-based engine has at least two unique components out of three essential features: The code that evaluates a network, the network itself, and the search algorithm. While AllieStein uses the same code to evaluate its network as Lc0, since the other two components are fresh, AllieStein is considered a distinct engine.)[14]

In early 2021, the LcZero blog announced Ceres, a new chess engine that uses LcZero networks. It implements Monte Carlo tree search as well as many novel algorithmic improvement ideas. Initial Elo testing showed that Ceres is stronger than Lc0 with the same network.[15]

Competition results

In April 2018, Leela Chess Zero became the first engine using a deep neural network to enter the Top Chess Engine Championship (TCEC), during season 12 in the lowest division, division 4.[16] Leela did not perform well: in 28 games, it won one, drew two, and lost the remainder; its sole victory came from a position in which its opponent, Scorpio 2.82, crashed in three moves.[17] However, it improved quickly. In July 2018, Leela placed seventh out of eight competitors at the 2018 World Computer Chess Championship.[18] In August 2018, it won division 4 of TCEC season 13 with a record of 14 wins, 12 draws, and 2 losses.[17][19] In Division 3, Leela scored 16/28 points, finishing third behind Ethereal, which scored 22.5/28 points, and Arasan on tiebreak.[20][17]

By September 2018, Leela had become competitive with the strongest engines in the world. In the 2018 Chess.com Computer Chess Championship (CCCC),[21] Leela placed fifth out of 24 entrants. The top eight engines advanced to round 2, where Leela placed fourth.[22][23] Leela then won the 30-game match against Komodo to secure third place in the tournament.[24][25] Leela participated in the "TCEC cup", an event in which engines from different TCEC divisions can play matches against one another. Leela defeated higher-division engines Laser, Ethereal and Fire before finally being eliminated by Stockfish in the semi-finals.[17]

In October and November 2018, Leela participated in the Chess.com Computer Chess Championship Blitz Battle.[26] Leela finished third behind Stockfish and Komodo.[27]

In December 2018, Leela participated in season 14 of the Top Chess Engine Championship. Leela dominated divisions 3, 2, and 1, easily finishing first in all of them. In the premier division, Stockfish dominated while Houdini, Komodo and Leela competed for second place. It came down to a final-round game where Leela needed to hold Stockfish to a draw with black to finish second ahead of Komodo. Leela managed this and therefore met Stockfish in the superfinal. In a back and forth match, first Stockfish and then Leela took three game leads before Stockfish won by the narrowest margin of 50.5–49.5.[17]

In February 2019, Leela scored its first major tournament win when it defeated Houdini in the final of the second TCEC cup. Leela did not lose a game the entire tournament.[17][28] In April 2019, Leela won the Chess.com Computer Chess Championship 7: Blitz Bonanza, becoming the first neural-network project to take the title.[29]

In the season 15 of the Top Chess Engine Championship (May 2019), Leela defended its TCEC cup title, this time defeating Stockfish in the final 5.5–4.5 (+2 =7 −1) after Stockfish blundered a seven-man tablebase draw.[30] Leela also won the Superfinal for the first time, scoring 53.5–46.5 (+14 −7 =79) versus Stockfish, including winning as both white and black in the same predetermined opening in games 61 and 62.[31][32]

Season 16 of TCEC saw Leela finish in third place in premier division, missing qualification for the superfinal to Stockfish and new deep neural network engine AllieStein. Leela did not suffer any losses in the Premier division, the only engine to do so, and defeated Stockfish in one of the six games they played. However, Leela only managed to score nine wins, while AllieStein and Stockfish both scored 14 wins. This inability to defeat weaker engines led to Leela finishing third, half a point behind AllieStein and a point behind Stockfish.[33] In the fourth TCEC cup, Leela was seeded first as the defending champion, which placed it on the opposite half of the brackets as AllieStein and Stockfish. Leela was able to qualify for the finals, where it faced Stockfish. After seven draws, Stockfish won the eighth game to win the match.[34]

In Season 17 of TCEC, held in January–April 2020, Leela regained the championship by defeating Stockfish 52.5–47.5, scoring a remarkable six wins in the final ten games, including winning as both white and black in the same predetermined opening in games 95 and 96.[35] It qualified for the superfinal again in Season 18, but this time was defeated by Stockfish 53.5–46.5.[36] In the TCEC Cup 6 final, Leela lost to AllieStein, finishing second.[37]

Season 19 of TCEC saw Leela qualify for the superfinal again. This time it played against a new Stockfish version with support for NNUE, a shallow neural network–based evaluation function used primarily for the leaf nodes of the search tree. Stockfish NNUE defeated Leela convincingly with a final score of 54.5–45.5 (+18 −9 =73).[38][39] Since then, Leela has qualified four times for the superfinal, only to lose every time to Stockfish: +14 −8 =78 in Season 20, +19 −7 =74 in Season 21, +27 −10 =63 in Season 23 and +20 −16 =64 in Season 24.

Results summary

Top Chess Engine Championship (TCEC)[40]
Season Division 4 Division 3 Division 2 Division 1 Division P Infrafinal Superfinal
12 (2018) 8th – – – – – –
13 (2018) 1st 3rd – – – – –
14 (2018) – 1st 1st 1st 2nd – 2nd
15 (2019) – – – – 2nd – 1st
16 (2019) – – – – 3rd – –
17 (2020) – – – – 1st – 1st
18 (2020) – – – – 2nd – 2nd
19 (2020) – – – – 2nd – 2nd
20 (2020) – – – – 1st – 2nd
21 (2021) – – – – 2nd – 2nd
22 (2022) – – – – 3rd 3rd –
23 (2022) – – – – 2nd – 2nd
24 (2023) – – – – 2nd – 2nd
25 (2023) – – – – 2nd – 2nd
Top Chess Engine Championship Cup (TCEC Cup)[40]
Event Result Opponent Score
Cup 1 (2018) 3rd - –
Cup 2 (2019) 1st Houdini 4.5–3.5
Cup 3 (2019) 1st Stockfish 5.5–4.5
Cup 4 (2019) 2nd Stockfish 3.5–4.5
Cup 5 (2020) 2nd Stockfish 1.5–2.5
Cup 6 (2020) 2nd AllieStein 1.5–2.5
Cup 7 (2020) 2nd Stockfish 1.5–2.5
Cup 8 (2021) 2nd Stockfish 3.5–4.5
Cup 9 (2021) 2nd Stockfish 1.5–2.5
Cup 10 (2022) 2nd Stockfish 4–6
Cup 11 (2023) 1st Stockfish 8.5–7.5
Cup 12 (2023) 2nd Stockfish 13.5–14.5
Chess.com Computer Chess Championship (CCC)
Event Year Time Controls Result Ref
CCC 1: Rapid Rumble 2018 15+5 3rd [41]
CCC 2: Blitz Battle 2018 5+2 3rd [42]
CCC 3: Rapid Redux 2019 30+5 2nd [43]
CCC 4: Bullet Brawl 2019 1+2 2nd [44]
CCC 5: Escalation 2019 10+5 2nd [45]
CCC 6: Winter Classic 2019 10+10 2nd [46]
CCC 7: Blitz Bonanza 2019 5+2 1st [29]
CCC 8: Deep Dive 2019 15+5 2nd [5]
CCC 9: The Gauntlet 2019 5+2, 10+5 3rd [47]
CCC 10: Double Digits 2019 10+3 3rd [48]
CCC 11 2019 30+5 1st [49]
CCC 12: Bullet Madness! 2020 1+1 1st [50]
CCC 13: Shapes 2020 3+2, 5+5, 10+5, 15+5 1st [51][52]
CCC 14 2020 15+5 1st [53]
CCC Blitz 2021 2021 5+5 2nd [54]
CCC Chess 960 Blitz 2021 5+5 3rd [55]
CCC 16: Rapid 2021 15+3 2nd [56]
CCC 16: Bullet 2021 2+1 3rd [57]
CCC 16: Blitz 2022 5+5 3rd [58]
CCC 17: Rapid 2022 15+3 3rd [59]
CCC 17: Bullet 2022 2+1 3rd [60]
CCC 17: Blitz 2022 5+5 2nd [61]
CCC 18: Rapid 2022 15+3 2nd [62]
CCC 19: Blitz 2022 5+5 3rd [63]
CCC 19: Rapid 2022 15+3 2nd [64]
CCC 19: Bullet 2023 1+1 3rd [65]
CCC 20: Blitz 2023 3+2 2nd [66]
CCC 20: Rapid 2023 10+3 2nd [67]
CCC 20: Bullet 2023 1+1 4th [68]
CCC 21: Blitz 2023 3+2 3rd [69]
CCC 21: Rapid 2023 10+3 2nd [70]
CCC 21: Bullet 2023 1+1 5th [71]

Notable games

References

  1. ↑ 1.0 1.1 1.2 1.3 "Leela Chess Zero: Full Elo Graph". 7 March 2019. https://lczero.org/?full_elo=1. Retrieved 7 March 2019. 
  2. ↑ "leela-zero". GitHub. https://github.com/gcp/leela-zero. Retrieved 27 April 2018. 
  3. ↑ 3.0 3.1 "LCZero". https://training.lczero.org/. 
  4. ↑ "Lc0 Wins Computer Chess Championship, Makes History" (in en-US). https://www.chess.com/news/view/lc0-wins-computer-chess-championship-makes-history. 
  5. ↑ 5.0 5.1 Pete (pete) (24 May 2019). "Stockfish Strikes Back, Tops Lc0 In Computer Chess Championship" (in en-US). https://www.chess.com/news/view/computer-chess-championship-9-stockfish-lc0. 
  6. ↑ "Announcing lczero". http://www.talkchess.com/forum3/viewtopic.php?t=66280. Retrieved 11 June 2018. 
  7. ↑ "Announcing lczero - TalkChess.com". http://www.talkchess.com/forum3/viewtopic.php?t=66280. 
  8. ↑ 8.0 8.1 Silver, David; Hubert, Thomas; Schrittwieser, Julian et al. (6 December 2018). "A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play". Science 362 (6419): 1140–1144. doi:10.1126/science.aar6404. PMID 30523106. Bibcode: 2018Sci...362.1140S. http://discovery.ucl.ac.uk/10069050/1/alphazero_preprint.pdf. 
  9. ↑ "AlphaZero paper, and Lc0 v0.19.1". 7 December 2018. https://blog.lczero.org/2018/12/alphazero-paper-and-lc0-v0191.html. Retrieved 14 February 2019. 
  10. ↑ Kobayashi, Yuki (2019-09-15), GitHub – kobanium/aobazero: Aoba Zero., https://github.com/kobanium/aobazero, retrieved 2019-09-25 
  11. ↑ 11.0 11.1 "leela-chess-zero". GitHub. https://github.com/LeelaChessZero/lc0. Retrieved 11 May 2020. 
  12. ↑ 12.0 12.1 The rewritten engine, originally for tensorflow. Now all other backends have been ported here.: LeelaChessZero/lc0, LCZero, 2019-03-20, https://github.com/LeelaChessZero/lc0, retrieved 2019-03-21 
  13. ↑ Temperature is a technical concept that makes Lc0's play more random. High temperature effectively means Lc0 more often makes moves other than what it thinks are the best moves. This is a setting that is only meant to be used during training, to help encounter unfamiliar positions and therefore learn them.
  14. ↑ "Allie+Stein, the new neural network based engine entering TCEC S15". 2 March 2019. http://www.chessdom.com/alliestein-the-new-neural-network-entering-tcec-s15/. 
  15. ↑ "Announcing Ceres". https://lczero.org/blog/2021/01/announcing-ceres/. Retrieved 26 July 2021. 
  16. ↑ "Breaking: Leela Chess Zero enters TCEC Season 12". Chessdom. 18 April 2018. http://www.chessdom.com/breaking-leela-chess-zero-enters-tcec-season-12/. 
  17. ↑ 17.0 17.1 17.2 17.3 17.4 17.5 "Seasons 1-14 and TEC Cup 1-2 database". http://legacy-tcec.chessdom.com:80/archive.php. 
  18. ↑ "World Computer Chess Championship 2018". ICGA. http://icga.org/pairing/wccc2018/. Retrieved 19 July 2018. 
  19. ↑ "Leela Chess Zero wins the gold medal in TCEC Div 4 | Chessdom" (in en-US). 11 August 2018. http://www.chessdom.com/leela-chess-zero-wins-the-gold-medal-in-tcec-div-4/. 
  20. ↑ "Ethereal chess engine wins the gold at TCEC Div 3 | Chessdom" (in en-US). 17 August 2018. http://www.chessdom.com/ethereal-chess-engine-wins-the-gold-at-tcec-div-3/. 
  21. ↑ "Chess.com Computer Chess Championship". https://www.chess.com/computer-chess-championship. 
  22. ↑ "CCCC stage 2 ended. Leela 4th with a good performance! Stockfish undefeated!". 26 September 2018. http://blog.lczero.org/2018/09/cccc-stage-2-ended-leela-4th-with-good.html. Retrieved 26 September 2018. 
  23. ↑ Cilento, Pete (26 September 2018). "Stockfish, Houdini Battle For Computer Chess Championship; Komodo vs Lc0 For 3rd". https://www.chess.com/news/view/stockfish-houdini-to-battle-for-computer-chess-championship-komodo-vs-lc0-for-3rd. Retrieved 9 October 2018. 
  24. ↑ "Leela wins the match series against Komodo and wins a Pawn odds game against Stockfish!". 3 October 2018. http://blog.lczero.org/2018/10/leela-wins-match-series-against-komodo.html. Retrieved 9 October 2018. 
  25. ↑ Cilento, Pete (4 October 2018). "Stockfish Wins Computer Chess Championship Rapid; Lc0 Finishes 3rd". https://www.chess.com/news/view/stockfish-wins-computer-chess-championship-rapid-lc0-finishes-3rd-3887. Retrieved 9 October 2018. 
  26. ↑ Cilento, Pete (11 October 2018). "Computer Chess Championship Returns For Blitz Battle". https://www.chess.com/news/view/computer-chess-championship-returns-for-blitz-battle. Retrieved 22 November 2018. 
  27. ↑ Cilento, Pete (19 November 2018). "Stockfish Wins Computer Chess Championship Blitz". https://www.chess.com/news/view/stockfish-wins-computer-chess-championship-blitz. Retrieved 22 November 2018. 
  28. ↑ "Leela won the TCEC CUP!". 4 February 2019. http://blog.lczero.org/2019/02/leela-won-tcec-cup.html. Retrieved 12 February 2019. 
  29. ↑ 29.0 29.1 Cilento, Pete (17 April 2019). "Lc0 Wins Computer Chess Championship, Makes History". https://www.chess.com/news/view/lc0-wins-computer-chess-championship-makes-history. Retrieved 18 April 2019. 
  30. ↑ "TCEC Cup 3 - Final game statistics". https://www.tcec-chess.com/archive.html?season=cup3&round=fl&game=9. 
  31. ↑ "Lc0 won TCEC 15". 28 May 2019. https://blog.lczero.org/2019/05/lc0-won-tcec-15.html. Retrieved 28 May 2019. 
  32. ↑ Högy, Kevin (2 June 2019). "A new age in computer chess? Lc0 beats Stockfish!". https://chess24.com/en/read/news/a-new-age-in-computer-chess-leela-beats-stockfish. Retrieved 25 June 2019. 
  33. ↑ "Season 16, Div P archive". https://www.tcec-chess.com/archive.html?season=16&div=p&game=1. Retrieved 30 September 2019. 
  34. ↑ "TCEC Cup 4 archive". https://www.tcec-chess.com/archive.html?season=cup4&round=fl&game=1. Retrieved 18 November 2019. 
  35. ↑ "TCEC final report". https://lczero.org/blog/2020/04/tcec-s17-super-final-report/. 
  36. ↑ "TCEC Season 18 archive". https://tcec-chess.com/#div=sf&game=1&season=18. Retrieved 3 July 2020. 
  37. ↑ "TCEC Cup 6 Final". https://tcec-chess.com/#game=7&round=fl&season=cup6. Retrieved 23 July 2020. 
  38. ↑ "Season 19, Div SF archive". https://www.tcec-chess.com/archive.html?season=19&div=sf&game=100. Retrieved 19 October 2020. 
  39. ↑ "Stockfish 12". https://blog.stockfishchess.org/post/628172810852925440/stockfish-12. Retrieved 19 October 2020. 
  40. ↑ 40.0 40.1 "TCEC – Live Chess Broadcast". https://www.tcec-chess.com/archive.html. 
  41. ↑ Cilento, Pete (4 October 2018). "Stockfish Wins Computer Chess Championship Rapid; Lc0 Finishes 3rd" (in en-US). https://www.chess.com/news/view/stockfish-wins-computer-chess-championship-rapid-lc0-finishes-3rd-3887. 
  42. ↑ Cilento, Pete (20 November 2018). "Stockfish Wins Computer Chess Championship Blitz" (in en-US). https://www.chess.com/news/view/stockfish-wins-computer-chess-championship-blitz. 
  43. ↑ Cilento, Pete. "Stockfish Wins Rapid Computer Championship Over Lc0; Bullet Chess Next" (in en-US). https://www.chess.com/news/view/stockfish-wins-rapid-computer-championship-over-lc0-bullet-chess-next. 
  44. ↑ Cilento, Pete (31 January 2019). "Stockfish Wins Computer Chess Championship Bullet; 'Escalation' Next" (in en-US). https://www.chess.com/news/view/stockfish-wins-computer-chess-championship-bullet-escalation-next. 
  45. ↑ https://cccfiles.chess.com/archive/tournament-18208.pgn
  46. ↑ Cilento, Pete. "Computer Chess Championship Plays Blitz After Stockfish Defends Title" (in en-US). https://www.chess.com/news/view/computer-chess-championship-playing-blitz-after-stockfish-defends-title. 
  47. ↑ Cilento, Pete (7 August 2019). "Stockfish Wins Computer Chess Championship As Neural Networks Play Catch-Up" (in en-US). https://www.chess.com/news/view/computer-chess-championship-9-stockfish-10-lc0. 
  48. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc10-semifinals. Retrieved 19 September 2019. 
  49. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc11-finals. Retrieved 23 December 2019. 
  50. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc1217-lc0-vs-leelenstein-finals. Retrieved 23 January 2020. 
  51. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc13-finals. Retrieved 14 April 2020. 
  52. ↑ Doggers, Peter (18 April 2020). "Leela Chess Zero Beats Stockfish 106–94 In 13th Chess.com Computer Chess Championship". Chess.com. https://www.chess.com/news/view/13th-computer-chess-championship-leela-chess-zero-stockfish. Retrieved 24 April 2020. 
  53. ↑ "CCC14 Results". https://docs.google.com/spreadsheets/d/15OO7oyXyliBWa1aWRKWCIBblOP8KN6awsOMdS7yOQs0/edit#gid=390633471. Retrieved 19 August 2020. 
  54. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc-blitz-championship-2021-finals. 
  55. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc-chess-960-blitz-championship-semifinals. 
  56. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc-16-rapid-finals. 
  57. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc-16-bullet-semifinals. 
  58. ↑ "Computer Chess Championship". https://www.chess.com/computer-chess-championship#event=ccc-16-blitz-challenger. 
  59. ↑ "Computer Chess Championship CCC 17: Rapid". https://www.chess.com/computer-chess-championship#event=ccc-17-rapid-challenger. 
  60. ↑ "Computer Chess Championship CCC 17: Bullet". https://www.chess.com/computer-chess-championship#event=ccc-17-bullet-challenger. 
  61. ↑ "Computer Chess Championship CCC 17: Blitz". https://www.chess.com/computer-chess-championship#event=ccc-17-blitz-finals. 
  62. ↑ "Computer Chess Championship CCC 18: Rapid". https://www.chess.com/computer-chess-championship#event=ccc-18-rapid-finals. 
  63. ↑ "Computer Chess Championship CCC 19: Blitz". https://www.chess.com/computer-chess-championship#event=ccc-19-blitz-challenger-match. 
  64. ↑ "Computer Chess Championship CCC 19: Rapid". https://www.chess.com/computer-chess-championship#event=ccc-19-rapid-finals. 
  65. ↑ "Computer Chess Championship CCC 19: Bullet". https://www.chess.com/computer-chess-championship#event=ccc-19-bullet-challenger-event. 
  66. ↑ "Computer Chess Championship CCC 20: Blitz". https://www.chess.com/computer-chess-championship#event=ccc-20-blitz-finals. 
  67. ↑ "Computer Chess Championship CCC 20: Rapid". https://www.chess.com/computer-chess-championship#event=ccc-20-rapid-finals. 
  68. ↑ "Computer Chess Championship CCC 20: Bullet". https://www.chess.com/computer-chess-championship#event=ccc20-bullet-semifinals. 
  69. ↑ "Computer Chess Championship CCC 21: Blitz". https://www.chess.com/computer-chess-championship#event=ccc21-blitz-challenger-match. 
  70. ↑ "Computer Chess Championship CCC 21: Rapid". https://www.chess.com/computer-chess-championship#event=ccc21-rapid-finals. 
  71. ↑ "Computer Chess Championship with Top Engines" (in en-US). https://www.chess.com/computer-chess-championship#event=ccc21-bullet-semifinals. 

External links



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