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Can Chess, with Hexagons?


7m read
·Nov 7, 2024

Chess, the game of war on 64 squares. But I wondered, can chess be played with hexagons? There have been several attempts, the most successful published in a book in the UK in 1973, which I promptly ordered to investigate.

While waiting for one of the remaining copies to be pulled out of the back of a used bookstore—who knows where—I realized I would need a hexagonal chess board. Something the internet does not make, so I would need to make one myself. While a grid of squares can simply alternate two colors without touching, I mean unless you count the diagonals, a hexagonal grid needs three colors for no touching.

Finding pre-made hex's in three nice matching shades to make my board was a lot harder than I expected. And when I found some, they ended up being a lot bigger than I expected, but I didn't realize that until after I had ordered rather a lot of them. You may be wondering why I didn't just, you know, draw a hex board. That's an excellent question that did not occur to me until after lots of hexagons and chess pieces began arriving at my door.

What can I say? Brains are weird, and this brain needed to finish what it started and build the board. A square chess board has a correct orientation, white on your right, and so too does hex chess have a correct orientation. When building your board, start with black on top, white below, and gray to either side. Then grow the pattern out so no color touches another until you have two edges, each six spaces long. Then complete the pattern until the mega hexagon has six six-sided sides.

Black goes with black and white with white. After completing my board, the book did arrive, which detailed all of the rules and included this delightful pamphlet to join the hex chess association by calling this number with a word in it. The book also came with, it turned out, a hex chess board, but too late! My board was made and I was going to use this board to show you how the pieces move.

Beginning with the most humble, the pawn. In square chess, the pawn moves forward one space at a time and can capture other pieces on the forward diagonals. I've always thought of this as a soldier with a shield protecting his front and a short sword that can jab to either side. The eight pawns, with their diagonal attacks, form self-defending walls that the other pieces can support or push off from. It's these structures that make pawns the soul of chess.

In hex chess, pawn movement is mostly unchanged: move forward one space at a time, capture to the forward sides to keep their soulful nature. This is the pawn's starting arrangement in hex chess. Note there are now nine pawns needed to complete the defensive structure, which is buffed from square chess and buffed again as the pawns begin the game, defending each other.

Pawns also have two special moves. The first: if they make it to the back row, a pawn gets promoted to any piece other than a king. Here we see the first interesting side effect of a hex board. In square chess, every time a pawn captures, it gets one space closer to the back row for promotion. But on a hex board, upon capturing toward the center, it's still the same distance from the back as before. Capturing away from the center, however, brings a pawn closer to promotion.

In chess, controlling the center of the board is vital. But now in hex chess, there's a slight disincentive to pawn capture centerward, and thus a slight incentive to spread the game outward. The next special power of pawns is that the first time a pawn moves, it can move two spaces. This is the same in hex chess, though pawns get another bit of a buff: if the first time a pawn captures, it lands on the starting space of another pawn, it's still allowed to move forward two.

My guess is this rule came about out of play testing. In square chess, it's impossible for a pawn to end up on the starting square of a neighbor; it's forward or nothing. But not so in hex chess, so buffing the pawns this way is just practical; you mostly don't have to keep track of which pawn started where—it doesn't matter.

The last special pawn power is on-pant, aka the top sneaky capture. If an enemy pawn moves forward two spaces past yours, such that you could have captured it if the enemy had only moved forward one, you still can. This rule always trips up noobs in square chess, and it's here to do the same in hex chess in the same way.

Okay, that's pawns—on to the rook! The rook is the most similar piece in both games. In square chess, it can move any number of unblocked spaces horizontally or vertically and can capture anything in its way. Now on the hex board, there is no horizontal, but there are what are called files: straight lines that pass through the neighboring spaces. Rooks can move along any file, which feels pretty buffed from square chess, and I don't mind one bit.

While chess is often symbolized with the knight, my simple pleated heart has always been with the rook. Rook smash! Personal preferences aside, this adaptation to hexagonification makes sense. A square shares sides with four true neighbors; a hexagon shares sides with six neighbors. So horizontal or vertical motion on a hex board translates to a straight line through a series of neighbors, which is exactly what the hex rook does.

Once you think of these lines as being the new horizontal and vertical, the capturing and blocking of pieces in hex chess works exactly the same as square chess. Now on to the knight. Knights are pretty similar to their square versions. Square knights jump forward two spaces over one, and since we now know what straight on a hex board looks like, the hex knight jumps straight too and then over number one.

This jumping motion is unique in the game, allowing knights to skip over any pieces in their way and capture what they land on. Just like the hex rook, the hex knight has more freedom of motion on the hex board: 12 spaces versus 8. But this freedom of motion expansion isn't the case for all pieces, which brings us to the bishop.

The square bishop moves only on the diagonals, forever limiting each to the color they start on. This diagonal motion lets the bishops slide through pieces that seem like they should block it but don't because of diagonals. So how does this translate to hex chess? Well, what diagonal means isn't obvious at first glance.

Going back to the rook as a reminder: while these look like diagonals in hex chess, they aren't. So what's a bishop to do? Well, as we've already seen, diagonal motion on square boards is sort of weird, and one reason to use a hex board like many modern games do is to ditch the diagonals.

But if you really need them, as poor bishops do, hex boards can diagonal too, and the clue is in the colors. This is diagonal motion on a hex board—the hex the bishop is on points the way to the next diagonals, quite literally. Which, when you think about it, is the same as on a square board; it's just less noticeable because diagonal squares share the pointing points, and hex boards don't.

I like this a lot because the hex board makes the strangeness of diagonal motion more apparent in a way square boards can't see. It makes it more like what the bishop lacks in board coverage it gains in diagonal exploitation, sort of teleporting along sight lines. If this is hard to see, I've found it easier to think of the bishop as existing in its own dimension that only partially overlaps with the rest of the game—a monochrome world other pieces move into and out of.

Viewing it this way also makes it really clear a hex board really nerfs each bishop. Yes, it can move in six directions, but there are so few spaces to make up for that. In hex chess, you get one extra bishop to match the extra color, so each covers its third of the board. There are 91 spaces in total: 30 for black, 30 for white, and 31 for gray. You might think this makes the gray bishop slightly more valuable, but this extra space buff comes with the nerf of no ability to attack pieces cornered in the corners, and can make end games trickier.

That's the bishop done, and now that you understand its motion, we can move on to the queen. The queen in square chess moves in straight and diagonal lines, and it's the same with the hex queen—along all the files as the rook would, and along all the diagonals as the bishop. The queen is the most powerful piece in square chess, but it's hilarious how godlike her freedom of motion looks on the hex board, absolutely crushing the king.

Capturing the king is the target of the game, and it is the poor king that is limited to moving just one square in any direction. Simple enough, and you might think that this is how the hex king would move. But don't forget those trixie diagonals. The points point the way to this: one movement in any direction, either to a neighbor or teleporting one space of the same color.

Given all of this, boy does the king really need that extra escape move? In fact, this additional freedom of motion makes him so much slipperier to catch that putting your opponent in stalemate, where the king can't make a non-suicidal move (considered a tie in square chess), counts as a fourth of a win in hex chess—basically winning! There's only one nerf for the king, which is castling doesn't exist because of how the pieces are set up, which we'll get to now.

So you've got the board, you've got the pawns, then across the back row going inward—it's rooks, then knights, queen to the left, king to the right, and three bishops in the middle. That's the way hex chess works. And since I made this ridiculous board, I decided I might as well try it out. And since I had no one to play against, I played a game against myself, which turned out to be rather brain-bending.

Not just because trying to remember all the new piece movements and patterns was really hard, but it was even harder to see them on the board and think with them. My game against myself did not go well; I made some truly dumb moves and turned what should have been a stalemate into losing quite badly to myself. But it sure was interesting and answered the question: can chess be played with hexagons? Yes! [Music] Aon

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