Chestonia and the other hexagonal games

People have been putting chess on hexagons for well over a century, and there are more attempts than most players realise. The one that took hold is Gliński’s, published in 1936 and popular enough in central and eastern Europe to be reported at half a million players, with tournaments, books and a body of opening theory behind it. If somebody says "hexagonal chess" without qualifying it, they almost always mean Gliński’s.

The rest of the family is a long argument about the same handful of problems. How big should the board be. What does a pawn do when "forward" is two directions rather than one. What is a diagonal on a hexagon, and how many bishops does it take to cover it. Every variant below answers those differently, and Chestonia is one more set of answers rather than a departure from the idea.

What follows is where those answers differ, in the places the difference is actually felt over a board.

Gliński’s board is 91 cells. Chestonia’s is 169, seven rings out from the centre instead of five. That is the single decision everything else follows from, and it is not a decision Chestonia made alone: Hofstadter’s Chesh and the Catalan variant C’escacs both use 169 too.

What is unusual is what was done about it. Most variants put broadly classical moves on a bigger board and accept that the game gets slower. Chestonia scaled the pieces up instead. A pawn runs four cells on its first move and three afterwards, where Gliński’s steps one, or two from the start. The knight has two leaps rather than one — two cells and a turn, or three cells and a turn — which gives it twenty-four destinations against Gliński’s twelve. A queen standing in the middle of an empty board has sixty squares to choose from.

The effect is that the armies are in contact almost immediately. On a 169-cell board with classical ranges, two sides would spend twenty moves walking toward each other before anything was in danger. Here the first exchanges happen in the opening, which is what makes the extra space worth having rather than merely large.

The pawn is the piece that changes most, and the games played here bear it out: pawn moves are about forty-four per cent of all moves, and pawns are about seventy-three per cent of everything captured. A Chestonian pawn takes one cell away in any direction it may move — sideways included — which makes it a short-range attacking piece rather than the slow wall it is in orthodox chess. Gliński’s and McCooey’s pawns capture along a diagonal only.

A hexagonal board splits into three colour classes rather than two, and a bishop travelling the hex-diagonals never leaves the class it started on. Gliński’s answer was to give each player three bishops, one per class, so nothing is unreachable. Most variants that followed did the same.

Chestonia gives each player two. The back row is rook, knight, bishop, king, queen, knight, bishop, rook — sixteen pieces and a king between the two rooks — and the two bishops start on two of the three classes. The third class has no bishop in it at all, for either side.

That is a real asymmetry and it is worth knowing about before you rely on a bishop. It also makes the alternating-colours board more than decoration: on that board the left knight and bishop swap places, which changes which classes your bishops are bound to and therefore which third of the board they can never touch.

Hexagonal chess for three is not new — Wellisch published a three-handed version in 1912, twenty-four years before Gliński — and there have been others since, including Hofstadter’s Chesh and the three-player variant on Green Chess. But almost every hexagonal game is designed for one number of players and only that number. Wellisch’s is three-handed; Gliński’s, McCooey’s and Shafran’s are two-handed.

Chestonia is meant to be either. Three players sit at alternating edges and two sit opposite each other, on the same board with the same armies, and the board turns so that whichever seat you took is nearest you.

The interesting consequence is what happens when somebody is checkmated. The three-player variants generally end the game there: on Green Chess the player who gave the mate scores a point, the mated player none, and the third player takes a half. Chexs goes the other way and hands the defeated player’s pieces to whoever beat them.

Chestonia does neither. A checkmated player is out of the game, but their army stays exactly where it is and goes on attacking — nobody inherits it and nobody removes it. The two survivors now have to fight each other across a board still full of a dead player’s pieces, which frequently decides the game. A player who is stalemated rather than mated is skipped instead of eliminated, because the position may free them again later.

Hexagonal draughts already has a good implementation: Christian Freeling’s Hexdame, from 1979, which is international draughts moved faithfully onto a 61-cell hexagon. Sixteen men a side, a man steps forward into one of three directions, captures by hopping into any of six, and a king flies along all six lines.

Chestonia’s checkers is played on the same 169-cell boards as its chess, with fifteen men a side, or twenty-seven in the long game. The differences from Hexdame are in the geometry rather than the piece count.

A Chestonian man moves one or two cells, and it may turn a corner on the way — forward and then sideways — which no Hexdame man can do. It moves in four of the six directions rather than three: everything except straight backwards. And it captures along twelve lines, not six: the six straight hops, and six diagonal ones that land four cells out. A crowned man flies all twelve.

The two-cell move brings a rule that has no counterpart in square draughts at all. A two-cell move needs a way through, and on a hexagon a cell two away can often be reached by more than one route — so the move is blocked only when every route is blocked. That single rule accounts for most of the positions where Chestonian draughts stops feeling like draughts.

Somewhere between three and ten rounds into a game, play stops and every player still in it owes one throw at the board. You aim at a cell; the server decides where the dart actually lands, scattering around your aim. Where it lands is scored by ring: the centre earns a rook or a bishop, the second circle a knight, the third a pawn, the outer rings nothing, and a throw that leaves the board costs you a pawn. Anything the dart lands on is knocked off, whoever owns it, kings excepted.

Chess variants with a luck element are not new — dice chess, where the roll decides which piece you may move, goes back a long way. But a recurring round that both removes pieces and hands out reinforcements, aimed by the player and scattered by the game, is something I could not find in any other hexagonal chess variant. If it exists elsewhere, it is well hidden.

It is worth saying that this makes Chestonia a less pure game than Gliński’s, and deliberately so. A dart round means a position can be changed by something you did not calculate. What the numbers from real games say is that it is not as arbitrary as it sounds: about three throws in four earn a piece, only one in forty is an actual bullseye, one in five knocks something off — and close to a third of those hit the thrower’s own piece. Aiming is a real decision, and greed is punished.

Darts can be switched off entirely, on any board. Two of the four boards are drawn for them and two are not.

There are good online implementations of Gliński’s chess to play against a computer, and their engines are conventional: they know the rules because somebody wrote the rules into them.

Chestonia can seat a language model instead — Claude, GPT, Gemini, Grok and a hundred others — against each other, against the built-in bots, or against you. None of them has ever seen this game. There is no training data for it and there never will be, so the model is handed the rulebook and the position on every single turn and has to work out a hexagon from prose.

They are not very good at it, which is the interesting part. Every turn is checked against the same rules a person’s click goes through, an illegal move is refused with the reason, and the model is asked again; the mistakes it keeps making are counted and read back to it in its next game. When a model cannot find a legal move at all, the built-in bot plays the turn so the table is never held up.

This costs real money and the game does not hide it: the whole rulebook goes out on every call, so a fifty-move game runs from a few cents against the cheapest models to well over ten euros against the dearest. The seat picker prices each model before you choose it. Watching two bots play is free and needs no account.

Gliński’s hexagonal chess has had ninety years, a reported half-million players, printed opening theory and tournament play. Chestonia has a few dozen recorded games and no theory whatsoever. If you want a hexagonal chess with a body of knowledge behind it, a community that can tell you why your opening is bad, and an established answer to almost every position, that is not this.

Hexdame is a cleaner piece of design than Chestonia’s draughts. Freeling took international draughts and moved it onto a hexagon changing as little as possible, and the result is coherent in a way that a game carrying two-cell moves, corner turns, twelve capture lines and an optional dart round is not trying to be.

Chestonia is also considerably more complicated than any of them. Four boards, two games, an optional giveaway mode where the aim is to lose everything, an optional dart round, two or three players and a clock. That is a lot to hold at once, and the honest recommendation is to start with two players on the plain board with darts off, which is very nearly Gliński’s game on a larger board with longer pieces.

What Chestonia has that the others do not is that it is free, needs no account, runs in a browser, plays two-handed or three-handed on the same board, and will seat a language model opposite you. Whether the dart round is a good idea is a matter of taste. It is certainly not an accident.

Every claim about another game comes from one of these. Chestonia’s own figures were measured from the code and from the archive of games played here.

• Hexagonal chess — Wikipedia
• Hexdame — Wikipedia
• Three-player chess — Wikipedia
• Dice chess — Wikipedia
• Gliński’s Hexagonal Chess — The Chess Variant Pages
• Shafran’s Hexagonal Chess — The Chess Variant Pages
• Three Hexagonal Chess — Green Chess
• Hexagonal variants in draughts — MindSports
• Chess Variants/Hexagonal Chess — Wikibooks