C'escacs' Corner

Github pages

• https://cescacs.github.io

Github repository

• https://github.com/cescacs/cescacs.github.io
• https://github.com/cescacs/cescacs.typescript

Hexagonal board for printing

Hexagonal board to print.

Some hexagonal boards and special pieces

Bobby Fischer about chess variants and chess openings

Well, I have to start by saying that I am sure that Bobby Fischer knows the Capablanca variant perfectly well, even though it may seem that he does not in the references he makes, but he probably does this consciously, since his intention is to refer in general to chess variants.

But yes, it is absolutely true that anyone who knows how complex chess can be can be intimidated by a variant like C'escacs. The advice, if someone feels intimidated by hexagonal chess variants, is to start by trying the Mini Hexchess, a small toy that allows you to lose your fear of hexagonal geometry.

Mini Hexchess

Dave McCooey Mini Hexchess.

• Board to print.
• Rules (english, español and català)..

Hexagonal Grids

• Hexagonal Grids.
• Hexagonal Coordinate Systems.
• Programmer implementation references.

Endgames analysis, by Dave McCooey

Endgames on 91 hexes boards (Gliński/McCooey)

Hexagonal chess endgames were first studied by Władysław Gliński, and have subsequently been studied in depth by Dave McCooey with a computer. The results apply to both Gliński's and McCooey's chess.

• The King and a Rook can mate a lone King.
• The King and two Knights can mate a lone King.
• The King, a Knight and a Bishop cannot checkmate a lone King, except in a few and very rare positions (0.5%).
• The King and two Bishops cannot checkmate a lone King, except in a few and very rare positions (0.17 %).
• The King and a Rook beat a King and a Bishop (without exception).
• The King and a Rook beat a King and a Knight (except in a very few cases (0.0019 %) in which a draw is produced by perpetual check).
• The King and a Queen do not beat a King and a Rook: 4.3% of the positions are stalemate by perpetual check, and 37.2 % are stalemate by exceeding the number of moves (checkmate is not achieved).

Enlargement for endgames on 169 hexes board (C'escacs)

For the new pieces incorporated in C'escacs (Dragon and Pegasus)

javascript for playing C'escacs

There is a javascript C'escacs game display. It does only display moves on the screen, allowing only valid moves. It is also a place for saving and loading the game moves.

The Grand C'escacs variant available in the game play

There is a variant Grand C'escacs, also named there as Grand Hunigcamb Chess, which is an experimental variant I've used for doing some proves, but it has not been real game proved.

• Introduces the Almogavar piece, which also can be named as Archer. It moves orthogonally two steps on any of the six orthogonal directions, but always two steps. There are four of them.
• Each player has four knights and fiveteen pawns, one pawn on each column.
  • Initial position of pawns on columns B, C, K, I are one step forward (two lines); they retain the triple step capability on those new initial positions.
  • Pawns on colums A and L are the most advanced.
  • The flank pawns from the A-column on one side, and L-column on the other, have no option for triple movement from those initial positions.
• En passant captures has been extended; Pawns, Almogavars and Elephants can do En passant captures each other.
• There is also an extension for the capture of the scornful pawn, which allows the capture of the pawn also when the scornful move has been done to capture a piece. On such situation, the special capture is done by the oponent pawn backwards.

From Minimax using Alfa-Beta pruning to Montecarlo search with neural networks

Sorry, this article is not yet translated.

Deepmind: AlphaZero and MuZero

Some AlphaZero against Stockfish matches:

• AlphaZero vs Stockfish match selection (spanish comments)
• blog zugzwang (spanish comments)
• December 2018 match (spanish comments)
• July 2022: Stockfish 15 (3880) Vs Alphazero (3872) 2022 new Game
• Setember 2022: Includes explanation about DeepMind Google bindings with the new alpha-zero code: Better than Alphazero: 4000 Elo Performance of Alfazero vs Stockfish 15.
• 2023: New AlphaZero (4050 Elo) Played Perfect Chess Against Stockfish 15.1

Some other references

1. How Computers Play Chess, 1990, D.N.L. Levy, Monty Newborn. Ed W.H.Freeman & Co Ltd.
2. Chess Programming Wiki
3. Desarrollo de un motor de ajedrez. Algoritmos y heurísticas para la reducción del espacio de búsqueda. Bachelor Thesis. Omar Edgardo, L. S. 2010
4. https://stockfishchess.org/
5. Stockfish: configuración, descarga y secretos
6. Stockfish 15.1: nueva versión todavía más fuerte
7. AlphaZero: Analizamos sus mejores jugadas de ajedrez en el match contra Stockfish
8. Minimax and Monte Carlo Tree Search
9. Wikipedia: Monte Carlo tree search
10. AlphaZero Resources (DeepMind)
11. Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm
12. Monte Carlo Tree Search: An Introduction
13. AlphaZero Chess: How It Works, What Sets It Apart, and What It Can Tell Us
14. A Simple Alpha(Go) Zero Tutorial
15. MuZero: The Walkthrough (Part 1/3)
16. MuZero: The Walkthrough (Part 2/3)
17. MuZero: The Walkthrough (Part 3/3)