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Hexagonal chess. Chess on a board, made out of hexes. Variant of Dave McCooey. (Cells: 91) (Recognized!)[All Comments] [Add Comment or Rating]
Tim O'Lena wrote on Thu, May 27, 2021 02:25 PM UTC:

McCooey's Hexagonal Chess

Reviewed by Tim O'Lena

Dave McCooey's Hexagonal Chess variant is my favorite chess variant.

Dave's variant is designed to be as equivalent to orthodox chess as possible. In my experience, this variant is the closest to orthodox chess of any hexagonal variant. It is not a large chess variant and does not use any unorthodox pieces. The games use about the same number of moves and take the same time as a standard Chess game, given the relative strengths of the players.

Dave McCooey invented his variant along with Richard Honeycutt around 1978. After some trial and error, they concluded that the 91 hexagon board, with six hexagons on a side, was the most workable. Richard originally tried the 196 hexagon board, with eight hexagons on a side.

The initial setup in McCooey's Hexagonal Chess was designed by Richard Honeycutt. Richard and Dave each designed an initial setup, independent of each other. They independently arrived at the same overall diamond shape with 7 pawns, but after comparing the two setups, they agreed that Richard's was better. The main difference in Dave's setup was that the Bishops were in an oblique line instead of centered, and the King was in the corner. The result was Richard's setup on Dave's board.

Dave says that his variant is less drawish than orthodox Chess. My experience leads me to concur. Attacking seems more likely to succeed. Timid play can lose quickly and neither side can afford to pull punches. Black can quickly steal White’s opening initiative and even win quickly if White tries to be coy, stall, play for a draw, or play conservatively.

The hexagonal geometry provides some interesting differences between Hexagonal Chess and orthodox Chess. The ability to move diagonally is not as important for a piece, because each color only covers a third of the board. The result is that the Rooks are slightly increased in value relative to the other pieces. A King can “tunnel” through a Rook’s line of influence, unlike orthodox Chess where a King cannot cross a Rook's line of influence. This ability is not as annoying to the attacking player as one might expect, because it is easily managed. I encourage players to study the checkmate positions involving (K+R vs. K) and (K+Q vs. K) then play these endgames from both sides, to observe the mechanics.

Here are Dave's estimates of the relative piece values: Pawn=1 Bishop =3 Knight=3 Rook=6 Queen=9

In reality, there is an evaluation dilemma between Knight and Bishop, and it seems even more complex than the equivalent question in orthodox chess. For example, the value of a Bishop depends heavily on how many other friendly Bishops are still on the board. In my experience, Zillions of Games seems to favor the Bishops. Dave and I have observed that there are positions where Bishops are better than Knights, but these seem to be less common. The Scatha program seems very adept at managing the Knights and Bishops, and the decisions it makes are often surprising. I have found that a single Knight does indeed seem stronger against a single Bishop, but trying to prove an advantage with NBB versus BBB is tough. Experience has suggested that one does not want to part with the Bishop triple early in the game, but when the piece count is low and the Bishop triples are gone, the Knights show superiority to the Bishops. Like standard Chess, there may be positional issues that determine what exchanges need to occur.

The Hexagonal geometry allows all of the pieces to triangulate. Knights can hop to a new hex without necessarily losing control of a target hex. Bishops and Rooks gain the ability of moving along a given line while maintaining control of a certain hex that is NOT on that line. This concept does not exist for orthodox Bishops and Rooks. In fact, Dave believes it is this ability that makes the Hex Chess Rook closer in power to the Queen. In orthodox Chess, only the Queen has this ability, and that's what makes it reign supreme.

The Hex Chess King can "catch up to" a Pawn from behind, by moving diagonally. It appears that endgame play will be altered in the sense that a player can not depend on certain truths from orthodox chess. However, there are also many new endgame truths to be learned.

There are some sample games on the Variants page:

Game Courier Logs:

You can find a Zillions of Games implementation of McCooey chess on the Chess Variants page. Various hexagonal chess variants by Jens Markmann:

App for iOS devices that plays numerous Chess variants, including McCooey’s:

Dave has a program online based on the Scatha engine:

Kevin Pacey wrote on Fri, Jul 31, 2020 02:32 AM UTC:

Okay, thanks for the winning stats Dave!

The figures P=1, B=3, N=4, R=5, Q=9 for Glinski's were ones I saw that came on a paper inside a tube for Glinski's, when I used to own a set. It also had a picture of several tables of players playing Glinski's (on physical boards). I discussed the values a bit in an old email to Tim O'Lena, as I tend to agree with them - they also avoid situations where a Q plus piece is worth less than 2 Rs, which seems to make sense.

These days I'm an aging Canadian national chess master (title, no longer rating), with only a Candidate Master FIDE rating nowadays. I had 2400 Canadian ratings briefly about 10 years ago, and a provisional USCF rating of 2400+ back in 1981 after a 9 round Pan Am college team event in NYC - for some reason a team mate registered me as Kev Pacey, perhaps to try to be kind in case I were to play in USCF events later, but I would have thought an organizer there would put 2 and 2 together in that case.

Dave McCooey wrote on Thu, Jul 30, 2020 03:43 AM UTC in reply to Kevin Pacey from Mon Sep 10 2018 04:56 AM:
Hi Kevin.  The 91-hex board endgame databases that I generated take into account colorbound pieces, including the distinction between "central" and "non-central" colorbound pieces.  The results are available on these pages, with a link from this page.  For the KNBvK endgame, I use the suffix "(xc)" for the central-B case and "(xn)" for the non-central-B case.  The central-B case has a slightly higher winning percentage (0.98% vs 0.25%), but both of these percentages are quite small.  Over 99% of all positions in both endgames are drawn.

Kevin Pacey wrote on Mon, Sep 10, 2018 04:56 AM UTC:

Regarding N+B being unable to mate lone K except in rare positions according to McCooey's database, long ago I thought I convinced myself to some degree that a N plus a B on the colour of the centre hex could normally perform the task. To clarify, I'm wondering if such 91-hex board endgame database(s) have taken into account whether the B runs on the same colour as the centre hex, or else the other case for colour being different than that of the centre hex, in case the difference is very or even slightly significant to the statistical result for win percentage expected.

Greg Strong wrote on Thu, Jun 30, 2016 12:32 AM UTC:

Hello and welcome!

Unfortunately, we can't see your image.  You've loaded a link to your local C: drive ("C:/Users/Pat/hexChess.png")

[email protected] wrote on Tue, Jun 28, 2016 08:34 PM UTC:

I like all the work and thought you have put into this!  I created a couple of boards to be set up more like regular chess.  Both boards are set up with a row of pawns in front; the king, queen, bishops, knights, and castles/rooks from each side mirror each other; and castling functions in both directions.  Both have an extra bishop so that there is one on each color. 

The first board's ends bow towards each other while the middle parts are futhest away, and the wide spread causes extra pawns (11 total) to be required to keep the rooks from being able to automatically get out.  It also has the effect of allowing the bishops to all be able to line up against opposing bishops or a rook immediately after blocking pawns are moved.  

The second board also has a row of pawns in front, but it is straight across, and this ends up leaving one blank spot that only the king or a knight could move into.  The bishops are more centrally located so, like your original, none of them or the queen diagonlly line up with any opposing pieces.  Also, the rooks are much more hampered in moving "sideways" than in the first board, which more closely reflects regular chess.

I have attached a picture of the boards.  I am interested to hear what you think!

Carlos Cetina wrote on Fri, Nov 27, 2015 03:40 PM UTC:
Very accurate your analysis, Kevin. I am definitely more practical than theoretical and would be happy playing with you any hexagonal variant that you like.

Kevin Pacey wrote on Wed, Nov 25, 2015 11:11 PM UTC:
Hi Carlos

Your variant is interesting, especially in that there is an extra queen per side, which is an extra sweetener for a hexagonal game, as far as tactical players would be concerned, I'd think. It's nice any pawn can make an initial double step without instantly depriving the opponent's pawn on the same file of an initial double step with such a move. I don't know if castling would often be especially beneficial in such a hexagonal variant (presumably it's not always a poor idea), but at least that rule emulates the one in chess, if that's a positive thing (it might be in the eyes of at least some chess players).  Hypothetically, what might make for a more (at times) strategic-maneuvering hexagonal variant than those I've looked at would be using McCooey's pawn capture rules (as your variant does), and the sort of almost boardwide setup for pawns as in either Glinski's variant or yours, except to try to find a way to add 2 extra pawns per side to the 2 remaining pawnless files in the start position (i.e. on the 'a' and 'k' files, presumably on each side's rearmost hexes on those files). 

Otherwise, I would suppose those 2 extra pawnless outer files might nearly always eventually make for a considerably less blocked (or duller) struggle in the middlegame or opening than can arise at times (and go on for many, many moves) in chess middlegames or openings, if only because major pieces (particularly rooks) might tend to be traded on the open files in such hexagonal variants, at least in games between evenly matched players. Adding 2 extra outside file pawns would seem a more natural modification with your variant than Glinski's. Doing so for either game might result in a start position that's not so pretty in either case, however. That's especially since the extra outside file pawns could well be unprotected to start with. There would not be this drawback if Glinski's pawn capture rules were used instead, but then there would be no blocked pawn chains possible as in chess, as previously mentioned, and I'd think that wouldn't be helpful for stategic manuevering. Nevertheless, note that in such tri-coloured hexagonal variants, diagonal-moving pieces can get through a mutual pawn chain situation, if they can move on the third colour the mutual chain situation does not affect, something that does not happen in chess.

Still hypothetically, in the case of your variant's start position, having all of each side's rearmost pawns (i.e. those on red hexes in your diagram) 1 hex forward on their respective files would allow the rooks to guard such additional 'a' and 'k' pawns, satisfying my desire of having them protected at the start, and such a start position might not be so ugly. I need to note that, in this hypothetical setup, even though I think I might not mind allowing an initial double-step by any pawn, I suppose there would be pros & cons whatever the initial pawn step rule(s) might be. I kind of like having the bishops start on 3 different colour hexes, as in Glinski's or McCooey's variants, but perhaps one can't always have everything one wishes for. If I get very keen on the idea of hexagonal variant(s) again, I may want to think about how to arrange that for the 3 bishops, which could include my adding in some extra (perhaps even fairy) chess pieces to help fill in the resulting empty hexes in each player's camp in the tentative hypothetical start position. This could also help make for a more strategic-manuevering game at times, with more existing pieces in search of thus more scarce good/adequate hexes in the opening/middlegame - in fact there would then be less than 50% of the cells empty (39/91) at the start, less than in chess. Alternatively, I might go back to using just 1 queen to make more room/symmetry (if necessary) for 3 different coloured bishops, if I still prefer having the latter. Still, I haven't by any means researched all known hexagonal variants, and someone may have already thought of all these considerations & more.

Carlos Cetina wrote on Wed, Nov 25, 2015 01:25 PM UTC:
What about this setup?

Could it fit, satisfy the lovers of strategic maneuvering taste?

I'm naming it Hexajedrez.

Kevin Pacey wrote on Wed, Nov 25, 2015 03:32 AM UTC:Excellent ★★★★★

One thing I like about Glinski's game in comparison to the present game is that there is quite a bit less distance on a given file (in terms of hexes) between pawns (especially for edge-ish ones) in Glinski's start position than is the case for the present game. Another thing I like about Glinski's game is that a pawn capture moves the pawn by just one hex 'forward' (in a sense) on the file the pawn finishes its move on, like in chess in that sense. Similar to how a pawn only advances one hex forward on a file when making a non-capturing move in Glinski's game (or the present one, for that matter).

A pawn capture in the present game can advance a pawn by as much as two hexes towards promotion, which doesn't happen in chess - but nor can a diagonal pawn capture fail to advance a pawn towards promotion at all, as often happens with Glinski's game (which is one thing I like about the present game's rules). That is, in both games pawn captures away from more central files are 'rewarded' in terms of being closer to a promotion hex to some degree. Capturing towards a more central file is at least 'rewarded' (to any extent) in the present game (by putting a pawn one hex closer to promoting), I would note. The present game also answers my wish for having similar pawn chains to like in chess, which Glinski's game fails to allow.

Decades ago I saw values given for the pieces in Glinski's that would seem to apply to McCooey's too: P=1; B=3; N=4; R=5; Q=9. I'd add that I estimate the fighting value of K=4 approximately (though naturally it cannot be traded).

[edit: Note that except for a pawn making an initial 2-step move, in McCooey's game it seems it would often take at least 2 moves to make a pawn chain consisting of only just 2 pawns, perhaps more often than is the case in chess.] However, either hexagonal game does not seem to really allow lengthy periods of very locked up ('closed') positions (due to virtually boardwide pawn chains), as can happen in chess, anyway, due to the board's roomy geometry and ratio of pawns & pieces to hexes for both hexagonal games in question. My guess is that lovers of strategic maneuvering might want to look at another sort of variant altogether for that. So far the pros & cons I've mentioned for Glinski's game & the present one tend to balance themselves out in my mind, although I've only played Glinski's game (occasionally), and that was decades ago before my one opponent (my brother) stopped playing. Glinski's game might have a considerably larger over-the board following worldwide, for all I know, though, which could count for something, if only for its having a leg up on the present game. Somehow I received a tube set for Glinski's game a long time ago, but finally discarded it some years ago due to lack of over-the-board opponents locally. In games with my brother, endgames often arose where I'd win with extra pawn(s) - though I'd let him take back gross mistakes earlier in the games since I had more skill at chess-like games than he did. {P.S.: After playing a number of games with an expert in this (McCooey) variant, I've found the game is rather tactical and it's easy to get creamed right from the start! Both sides have a number of tactical weaknesses in the setup, and it seems the number of playable openings may be somewhat limited, at least for the early part of the game. especially from Black's perspective.}

Jean-Louis Cazaux wrote on Sun, Feb 23, 2014 07:09 PM UTC:Excellent ★★★★★
Answer to Charles Gilman: Yes, me, I tried. See Echexs for 3, or 6, players with McCooey's arrangement.

Kirby wrote on Tue, Dec 27, 2011 02:19 AM UTC:
I recently uploaded to YouTube a series of 9 short videos showing the board and moves of a six-player hybrid Square/hexagonal chess game I created about 25 years ago. Thought your readers might be interested:

GiViT wrote on Thu, Aug 25, 2011 10:59 AM UTC:Poor ★
Trop bidon !

Charles Gilman wrote on Wed, Jul 8, 2009 06:23 AM UTC:
I mentioned that this variant's camps are compact enough to extend to 3 players, but has anyone ever done that and if so with what Checkmate rules?

Dave McCooey wrote on Sun, May 20, 2007 10:37 PM UTC:
Your proposal of making pawns attack diagonally toward the center and orthogonally toward the outside would solve the rank advancement problem, but it would not solve the pawn chain problem. If a pawn chain protects itself toward the outside (for example, White pawns on g4, h4, i4), then opposing pawns that block that chain (Black pawns on g5, h5, i5) would be able to capture some of the original pawns (g5xh4 or h5xg4 or h5xi4 or i5xh4). It would be possible to make blocked chains where the pawns can't capture each other, but one of the sides (White or Black) would not form a protection chain. For example, White pawns on g4, h5, i6; Black pawns on g5, h6, i7. All pawns are blocked, and no captures are possible, but the White pawns would not form a protection chain.

Cleatus wrote on Sun, May 20, 2007 09:14 PM UTC:
Might you rectify both these problems (rank advancement and pawn chains) by forcing pawns to attack diagnally toward the center and orthonogonally toward the outside?

Dave McCooey wrote on Fri, May 26, 2006 11:40 AM UTC:
To clarify, Glinski's pawn capture does not advance the pawn one step
closer to promotion as in regular chess.  It advances the pawn 1/2 of a
step closer.  In my variant, a pawn capture advances the pawn 3/2 of a
step closer, so neither variant emulates regular chess perfectly in this

The diagonal pawn capture used in my variant allows pawn chains to behave
as they do in regular chess, which is not true of Glinski's pawn chains.

For example, it is impossible in Glinski's chess to have interlocking
head-to-head (blocked) pawn chains where the pawns can't capture each
other.  Try creating something equivalent to the following regular chess
pawn chain:  White pawns on f3, e4, d5; Black pawns on f4, e5, d6.  All 6
pawns are immobile, they cannot capture each other, and each side forms a
protection chain starting at an unprotected base pawn.  In my variant,
equivalent would be White pawns on g4, f6, e7; Black pawns on g5, f7, e8.

In Glinski's variant, it can't be done:  Either the pawns can capture
each other, or the pawns on each side don't form a protection chain. 
(Note:  I am labeling hexes using the bent-rank notation where the 1st
rank consists of the 11 hexes on White's edge of the board.  The hex in
the center of the board is f6.)

Gary Gifford wrote on Fri, May 26, 2006 10:29 AM UTC:
I think Glinski chose his pawn movements such that pawn chains would more closely resemble Fide Chess pawn chains. I chose the same movement for that reason in my Hexagonal Hole Chess. In the rules for that game I discuss both types of Hexagonal Pawn movements. Jonathan's logic also seems very probable.

Jonathan wrote on Fri, May 26, 2006 07:41 AM UTC:Excellent ★★★★★
I only have a theory, but I think I know the reason why Glinski had his form of pawn capture. I suspect it was to avoid getting pawns close the the far rank too quickly. In regular chess, a pawn capture only advances the pawn one step closer to promotion, just as a regular pawn step would have. In Glinski's version, a capture only advances a pawn one step closer as well, while in McCooey's, it actually advances the pawn the equivelant of two spaces closer than it already was. Does that make sense? Glisnki was better emulating the difficulty of pawn promotion, while McCooey was better emulating the movement. I guess it just depends on your preference in that case.

Dave S. wrote on Sat, Mar 5, 2005 08:22 AM UTC:Excellent ★★★★★
I've never understood Glinski's pawn taking manoeuvre. Dave McCooey's version makes much more sense. Great article!

Charles Burns wrote on Thu, Sep 16, 2004 02:27 PM UTC:Excellent ★★★★★
Very good rules. I agree this is a better game than Glinski's, especially your reasoning behind the pawn moves. I also 'discovered' these moves while experimenting with hex's for a three handed game, before I read about Glinski's game, so I agree they are the most natural rendering of conventional chess into hex's. Look forward to it gaining in popularity!

Will McCooey wrote on Sun, Mar 2, 2003 05:29 PM UTC:
From one McCooey to another,this looks excellent.Can't wait to find the time to tyr it!

Charles Gilman wrote on Sun, Feb 16, 2003 10:06 AM UTC:Good ★★★★
One advantage of this version over Glinski's is that, as it is more compact, it adapts better into a three-handed game.

(optional) wrote on Sat, Oct 26, 2002 03:42 PM UTC:Excellent ★★★★★
My kids and I made a hex chess board and we found this to be a lot of fun! The game is quite faithful to conventional chess and the moves were similar enough that my five-year-old son learned them on his own, just from studying this site; thanks for the great diagrams.

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