Comments by Kevin Pacey

Regarding the name "Unicorn", I originally preferred to use it in my 4D variant (rather than "Nun", or any other name), until I saw the wiki link on fairy chess pieces, which didn't appear to me to include the way I was using "Unicorn". Apparently I looked in haste, because it now appears to me that it does. I'll go back and edit my submission to change the name "Nun" to "Unicorn".

Back in the 1980s when I came up with the idea of a 4x4x4x4 4D chess variant, in a different city than I am now, I had borrowed a library book on fairy chess which I recall only a very small number of things about (not including the title or the author's name). One thing the book showed was a diagram for a 5x5x5x5 4D chess variant, with the 4D fairy piece type Balloon included. As an aside, I at once preferred a 4x4x4x4 board concept, to have an equal number of light and dark squares, but later I saw that 5x5x5x5 at least often allows a knight more legal moves depending on location.

The book also mentioned the "Unicorn" as a 3D piece. It likely matched wikipedia's description of its movements. If so, I'd note that nowadays this use of "Unicorn" doesn't quite make so much sense to me, however, since the mythical beast is virtually a horse, and it thus seems desirable to me that any such named piece would have some knight-like property to it (regardless, in the 1980s, not thinking of this, I wanted to use the name "Unicorn" for a piece, since it's charming for a name). In spite of this, I'll drop the use of "Nun", as mentioned.

I've edited a couple of my comments & original submission for 4*Chess, in case anyone hasn't noticed.

You are right Ben that the Black 4*Chess K is not mated (i.e. can escape) in the diagram I made of White having two 4*Chess Unicorns (& his 4*Chess K) vs. a lone Black 4*Chess K (it seems there can be no similar position constructed where there is a mate on the board with this material balance). I'll go back and delete the diagram in question from my submission.

Sorry I already deleted the diagram in question, as my sole idea was to try to show a 'basic' mate with just two 4*Chess Unicorns, which unfortunately now seems an impossible task.

Thought I'd mention that 4*Chess got its rules for 4*Chess Pawn movements (& its last rank promotion rule applying only to the appropriate corner mini-board) partly because of the starting position for it, which was designed to allow any square in 4*Chess to be reached by exactly one of the eight 4*Chess Balloons (aka Dirigibles) one starts a game with. For that to happen, essentially all mini-boards of a single quadrant of four mini-boards had to have two opposite coloured 4*Chess Balloons on the same rank of each mini-board involved, as is the case for both sides in the setup position. That meant that for both sides some pawns were going to be closer to promoting from the setup position than others, even if I chose to allow promotions to occur on the last rank of all 4 mini-boards that were on a player's last row of mini-boards. On top of that, from the start I wished promotions only to occur in a corner quadrant where the enemy 4*Chess King starts the game, and so I was happy enough to make that choice instead.

For anyone who missed it, I made edits to my previous comment.

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.

This year top human Arimaa players (including 2 world champs) were beaten
by a computer program, seemingly ending the hopes of that game of remaining even remotely computer resistant. That is, unless humans come up with fresh strategies for the game, but I suppose it is no longer as easy to do that since Arimaa is not such a novel game anymore. 

Based on what I've seen on the web, Arimaa had many attributes that at
least one of its champions thought might make it computer resistant. IMHO
it lacked being played on a board significantly larger than 8x8, which
might have helped since in the case of Go, so far it seems clearly the
larger the board size, the better. 

In Go, I would note that the number of legal moves is not excessively
large, even in the opening phase. Go has the advantage over chess that
there is no king or more than one type of piece, making it tougher for a
computer to evaluate a given position. I've also read that a good Go player can at times easily assess how important a single stone might be for 100 ply ahead, by contrast. This helps with both evaluation and pruning any search tree of moves not worth looking at very deeply.

My own guess is that for chesslike games board size could be important, and having a larger number of moves available on average than in chess could help too. Having Shogi-like drops would help greatly increase the average number of moves, and such can be visualized more easily in a way IMHO than some complex long range [fairy]chess piece movements. 

A problem with drops is that computers can visualize checkmating sequences
of moves better than humans, but this problem would vanish if a player can
drop a piece only on his own half of the board, assuming a variant that is
similar to Shogi. Shogi programs at the moment are close to top human skill level afaik, but a larger board variant and a suitably modified drop rule (if necessary) might make for one type of variant that may be computer resistant for some years to come, I would guess.

All this assumes that alpha beta or some sort of tree searching with modern computers would be
used, but there could be fresh danger for humans when vs. engines if neural net programming becomes sufficently advanced, or practical quantum
computers become available, especially to the general public.

A while ago I saw a variant on this website that was a cross between chess
and Go, in that some sort of checkmate was possible, and there were example games that
lasted a reasonably short number of moves, like for standard chess. If
someone can find it (whether or not before me), perhaps it can be assessed
as to whether it might possibly be just one chesslike variant that is computer resistant. Meanwhile, I had
some faint hope that some of my invented variants (or anyone else's) might
prove computer resistant, if any ever become popular enough to attract the
attention of serious programmers. All my invented variants to date are now
listed on this website fwiw.

edit: The game I'm thinking of is Gess, where in fact no checkmate ever occurs. Thus, not what I had in mind to be a chesslike game, but it still looks interesting otherwise:

http://www.chessvariants.com/crossover.dir/gess.html

As a teen I tried playing the odd (e.g. WWII-based) Avalon-Hill
board-wargame with my brother, though I found it hard to keep track of all
the rules, board hexes and pieces. Based on looking at the link given, The
Battle of Macysburg doesn't appear quite as highly complex by comparison,
based on my vague memories of playing board-wargames in the 1970s, which
may be a plus for many wargamers that could take it up. Even in the 1970s I
was a serious chess player, and had always liked that the rules of chess
were not overly complicated. That's besides liking the beauty of a chess
set as a child.

Fwiw, I fairly recently came up with 12 criteria I would like personally
for chess variants or other board games of skill; being a chess player, my
criteria were designed to favour chess-like games, and hopefully ones that
could still prove popular. I also hope one day for a chess variant to
replace chess as the new standard version of it, hopefully for at least
many decades, if not centuries, as strong computer engines may diminish
strongly skilled human players in the eyes of at least some of the public,
and also such engines make cheating more possible than before. 

To me personally, the minimum criteria to make for a chess variant would be
my final criteria in the list further below, namely:

"12. Kings that can be checkmated are included."

For me, this could include games that have one (or more) "king" per side,
or games where there are other ways to win besides administering a final
checkmate. This would certainly exclude Arimaa, or Go (which unlike Arimaa
is not listed on the present chess variant website afaik); I've play the
odd game of Go, but not yet any games of Arimaa.

Here are the 12 criteria for chess variants or other board games of skill
that I mentioned; I would note that as of nowadays satisfying all 12 of
them (including computer resistance) may prove to be impossible in the long
run, however:

1. Arguably resistant to computer playing engines (ideally even against
human players that aren't close to being the world's best);
2. Any endgame stage not in significant danger of being compromised e.g.
due to tablebases (adjournments feasible if desired);
3. Significant popularity in North America and elsewhere (ideally played in
clubs and cash prize tournaments);
4. Extensively tested (ideally for centuries);
5. Rules arguably not way too complex or simple;
6. Has significant literature and cultural history (ideally no licensing or
copyright requirements on the game itself);
7. Fixed start position, ideally nice & not same as chess if variant (or at
least empty board, before 1st player moves);
8. Opening phase not in danger of being arguably played out any time soon;
9. Two player game (normally, at least);
10. Not way too many/few pieces or board squares/cells/points, and played
on one board;
11. Pieces look & move nicely & board can be on coffeetable (ideally fixed
start position not same as chess if variant);
12. Kings that can be checkmated are included.

Below is a link to one variant I invented that might be somewhat computer
resistant, and yet still satisfy all 12 criteria I gave to at least some
degree. What I imagined are its main weaknesses include that an average
game may take over 200 ply if reasonably well played (though an average Go
game takes about 150 ply, and Go claims to be a war rather than a battle,
unlike chess), and once a lot of pieces might have been exchanged then the
resulting position might not be very computer resistant (though it may not
matter if one side already stands better or is clearly drawing the game):

http://www.chessvariants.com/index/msdisplay.php?itemid=MSsacchess

Here's another chess variant that I invented that does not resort to using
Shogi-like drops, and which may also be computer-resistant to some degree;
however I have even more doubt than in the case of Sac Chess that this
variant will ever become popular:

http://www.chessvariants.com/index/msdisplay.php?itemid=MS4chessfourdime


Then there could be Crazyhouse (or even Bughouse) versions of the following variant of mine (which is similar to Grand Chess); such a version with drops might prove computer resistant to some degree (drops might be limited to one's own half of the board if necessary, to curtail an engine's ability to forsee mating sequences with drops, if the game would then still prove playable). Such a variant might even have a fair chance of becoming popular someday (pawns could be prohibited from promoting somehow, e.g. like in Australian pawn rules Standard Bughouse, if that helps by removing the need for another set in over-the-board games):

http://www.chessvariants.com/index/msdisplay.php?itemid=MSchess1010

I recall I've read that the best human International Checkers (10x10
variant) still beat a computer program in a recent year. That game has a
larger board size than Arimaa, standard chess or checkers, and like Arimaa
the moves are easier to visualize for humans than say for standard chess.
The issue of board size is one possible computer-resistance factor Juhnke's
Chessbase article didn't go into. However, serious programmers may have not
devoted much attention to International Checkers since it isn't as popular
as standard chess or Arimaa (plus both of those had cash incentives for
programmers to succeed at beating humans).

My own guess at what factors could make for computer resistant games
includes 1) larger board size (than say 8x8) which I suppose generally
favours humans; 2) ease of game piece movements for humans to visualize
(though perhaps this is much overrated, e.g. as was ultimately the case
with Arimaa); 3) difficulty for a computer to evaluate a given position in
any search (I think computers will always outdo humans at this in chesslike
games), and 4) difficulty for a computer to prune its search of unpromising
moves adequately enough to search deep enough to be effective against a
skilled human (a huge branching factor [of legal moves per turn on average]
alone may not be necessary, nor suffice - as shown for Arimaa, as a
programmer may find tricks to prune a huge number of branches at each
turn).

In spite of all the above, I feel that any game or chess variant might only
prove computer resistant for so long before future hardware/sofware
developments help computers end up on top. Does that make looking for
computer resistance futile? Well, perhaps new computer resistant
games/variants can be invented as necessary, to buy humans some time -
hopefully for many decades, if not for centuries. Standard chess itself
went through various rule changes over centuries, after all. I see computer
resistance as perhaps a worthy goal, as I alluded to earlier, that is to
restore some lost glory for highly skilled humans who play chess of some
sort (not to mention lost glory for humanity in general), in the eyes of the public, and
to also reduce the possibility of computer assisted cheating as much as
possible (though modern portable communication devices
still have increased the potential for human assisted cheating).

Fwiw, I once looked at a review for the chess program Houdini (some
version), and the inventor had succeeded in making it very selective as far
as choosing (i.e. pruning for) promising candidate moves to look at more
deeply at a given level. About 5 of the legal moves per turn; the average
is thought to be 35 for chess. With this success, such an engine can see 40
ply ahead in lots of important cases of move sequences. Some pruning done
apparently can risk throwing out some vital sequences once in a while, but
it seems the risk is low enough as to be worth it for such chess engine
programmers.

I was wondering if the above might mean that a program seeing 5/35 deeper
could see a ratio of 1/7 deeper typically for a chess variant, even if it
had significantly more than 35 legal moves available to a side on average.
Note that 5/35 is also not far from (sq. root (35))/35 as a ratio, which
could favour humans less than a flat 1/7 ratio. For example the approx.
(i.e. truncated) value of 100/7 moves examined more deeply would be more than
10 moves (out of 100) examined more deeply. Least favourable of all to
humans would be if an engine could always prune down to exactly 5
continuations to look at more deeply, no matter how many legal moves per
turn on average there are in a given chess variant. So it may be vital what
Houdini pruning to 5/35 means exactly when extrapolating to engines for
chess variants. Sorry if my terminology is not up to snuff.

Also fwiw, as a veteran chess master (Canadian), I have some feeling for
the concern that strong chess engines have caused to players, tournament
directors and organizers over the years, especially due to possible
computer-assisted cheating. Also, on a Canadian chess message board some
years ago, one poster noted that upon hearing chess engines were stronger
than people, some non-chess players he had met immediately lowered their
opinion of chess and chessplayers.