Comments/Ratings for a Single Item

I'm no expert on this.  My understanding is that what one should look for
are a huge variety of possible legal moves per turn, and natural and easily
visualized strategies, gradually developed over multiple turns.  It might
help to have a large board, many pieces with geographically localized
powers (that cannot cross the board in a single swoop), and multiple moves per turn with separate pieces.

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

Spherical Chess 400
http://www.symmetryperfect.com/shots

There is really only one game left on my Symmetrical Chess website anymore.
 Greg Schmidt (the Axiom programmer) and I have tried in a few ways and
failed to make it computer AI playable at a minimal, decent level.  I think
we now share the opinion that such a goal is not achievable with
state-of-the-art computer hardware technology and programming.  From what
you express, I think this game may interest you more than Go, Arimaa or
Gess.  Feel free to write me for details.

How do you define a chess variant? While this may seem to be a somewhat
silly question, it bears directly on this topic. Over several years I
designed a series of games that got farther and farther away from standard
chess variants, starting with Chieftain Chess, a multi-move shatranj
variant (which for reasons of euphony was not called Chieftain Shatranj.)
During this development, the games crossed the line between chess and
wargames, thus managing to turn off both chess variantists and wargamers.
For each, the games were too much like the "other kind". But I think the
series clearly fits into the category of computer-resistant variants. 

The beginning of the series, which I developed and playtested here (thanks,
Nick Wolff and others) were expansions of Chieftain to larger boards and
more pieces, but still very much large shatranj variants with 1 new idea -
that "kings" could be multiple and would control their armies directly,
requiring the "king" to be within a few squares (command range) for a piece
to activate and move. This part of the series I developed with a friend,
and named it the Warlord games, an unfortunate choice, as that name was
already used by a commercial series of games. 

However, this worked well enough that I took the next step to create a true
chess-wargame fusion by adding terrain. In FIDE chess, "terrain" is totally
abstract, and is represented by the difference between dark and light
squares, because some pieces, bishop-types, can only move on one or the
other colored squares. I expanded from white and black to white and grey,
which all pieces can move upon, and brown and green, which restrict certain
pieces from moving onto them. The brown, green, and grey squares are
scattered across a mostly white board, and conceptually represent hills,
trees, and towns. This last part of the series, the "true wargame" part, I
have called the Command and Maneuver series, which is more  description of
the game than it is a name. My developer, Dave, worked on the first few of
these, but then moved away for a job, so I continued on my own.

The best well-playtested game in the series is The Battle of Macysburg.
It's played on a 32x32 board. Players bring 84 pieces on the board in 4
groups of 20 - 22 pieces each, coming in on Turns 1, 5, 15, and 20. There
are 2 times in the game where 1/3 of the captured pieces are brought back
as rallied troops, after turns 12 and 24. With a little care for
positioning of troops and leaders (activators/"little kings"), players can

move all their units each turn, if they so desire. There are 3 levels of
victory, ranging from driving out opponent pieces and occupying Macysburg
to chasing all the opponent's pieces off the board to destruction of the
opponent's army - reducing it to 20 pieces or less. Players may achieve
more than one level of victory, and players may each achieve some level of
victory in the same game. Yet the mechanics are simple chess moves of 1, 2,
or 3 squares for each piece, movement governed by the availability of
leaders within 2 squares of each moving piece as it starts its move. With
no wargamelike rules at all, just the rules mentioned above, the game
reproduces fairly nicely much of the strategy and tactics of Western
European combat around the 17th and 18th centuries. Mechanically, the game
is a chess variant; organizationally it's a wargame. If you consider it a
chess variant, Macysburg is computer-resistant.

This is a review of Macysburg, written by a wargamer and chess, but not
chess variant, player, complete with 2 "snapshots" of the game that give a
reasonable idea of how it looks:
http://boardgamegeek.com/thread/1178742/some-impressions-after-playing-battle-macysburg-sc

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 didn't mind having mobility a little impaired for a while in Sac Chess,
in terms of available legal move options from the starting position. Humans
might even be able know better than engines for the forseeable future which
pieces to develop faster than much of the rest of the pieces, leaving such
as 'reserves' for a long time into the game. In any case, the average
number of legal moves per turn in a game would still significantly reduce the number
of ply ahead a machine could look, I figured. 

Even a modern off-the-shelf chess engine that prunes moves each turn highly selectively (say
like the engine Houdini) sees 40 ply ahead on average, I seem to recall. In
that case, I've estimated that for Sac Chess such an engine might see only
about 30 ply ahead, and maybe a further 5 ply less than that if any
practical memory use requirements (due to using a larger 10x10 board) also
limit the search depth. If my guesswork was not that far off, that could
make a strong Sac Chess engine only strong international master level
strength at best (e.g. 2450 FIDE). By contrast my guesswork for Grand Chess
puts a strong engine at that at about 2750 FIDE (all this is assuming
Houdini-like prowess of such engines, in terms of evaluating positions). Of
course, something may be wrong with the sort of calculations I made.

Even so, I'd be curious to know how strong an engine might be at Capablanca Chess
(8x10 board variant) - if it's weaker than a strong human than I may have grossly overestimated how good a Grand Chess engine might be, for example. In the case of Seirawan Chess, adding two more pieces
per side in the opening didn't seem to help humans when vs. strong engines, I gather, but that game
is played on the smaller 8x8 board still.

I'm not sure if having two moves per turn could one day make for a popular enough variant. As an analogy, I long ago played some sort of card game where a player could under certain conditions pick up another card from the deck after making a play, thus continuing their turn, and that process could even repeat itself indefinitely. I played that card game with older people (for the first time), introducing them to it, and they never seemed to desire to try it again. It seems there is a strong cultural habit/desire of one person taking one turn at a time, and that's it, at least for card games. To be fair, I liked playing Progressive Chess with a friend who was willing, long ago too.

My own limited understanding might be by way of the following illustration.
 Let's say (only by way of illustration) that a game offers 10 reasonable
move options per turn, and that a computer calculating likely futures has a
calculation limit of 10 billion.  It will reach this limit after 10 moves. 
But if there are 20 reasonable move options per turn, it will reach this
limit before 8 moves; if 40 options, then before 7; if 80, then before 6
moves; if 160 then before 5 moves; if 320, then before 4 moves.

None of this helps the human player unless the human can, in some
significant respects, think ahead and see strategic options, using his
natural or intuitive strategic powers, at a number of moves ahead beyond
which the computer can calculate.

That's what I'm not seeing from your "Sac Chess".  It might be huge fun and
result in beautiful unpredictable chaos; but that's mainly from a human
perspective.  If it offers a human a better chance to see several moves
ahead then a computer, then I am not seeing or understanding the strategy
by which the human could achieve this.  

Which brings me to a suspicion and worry that I cannot fully shake off -
that a computer-resistant chess might also be a boring chess variant.

Why do you think that Chess variants can be computer-resistant at all?
Computers can do the same as human brains, except much faster.

Muller, it's not quite that simple.  Human brains can still do things that
computers cannot.  That's why humans continued to be able to beat chess
programs for many many many years after the raw speed and calculating power
of the computer vastly exceeded that of the human brain.  Those days have
passed, but the computer still depends for its success on that (now
increased) raw calculating power, and it might still in theory be possible
to construct a game that more significantly rewards natural human strategic
thinking, while granting a much lesser benefit to the raw calculating power
of the computer.  Human skill, unlike that of the computer, has never depended on the ability to precisely anticipate millions and billions of positions.

For Chess it just took computers (or rather there programmers) some time to
learn how to do it. It won't be different for other games.

Muller, It is already true that some games are more computer resistant than
others.  Checkers (beaten in 1994) is less computer resistant than Chess
(beaten in 1996), which is less computer resistant than Arimaa (beaten
recently, but still, probably more computer-resistant than standard chess
in relative terms), which is less computer resistant than Go (where humans
still reign supreme).

Also, Computer resistance is a relative quality.  If the top computer can
beat the top human, a game might still be somewhat "computer resistant" if
a top human can still give an affordable computer a run for its money.  If
I play online against someone, chances are he's not getting help from the
top computer in the world.

Humans still have their strengths, and a game can cater to them.  I just worry that it might be a boring game.  I've never been fascinated by Go, for instance.

Of course, if you're just postulating the continued advance of computers until they can do ANYTHING as well as humans can or better ... then I don't necessarily deny it.

There's an interesting article by Fritz Juhnke online about creating
computer resistant variants.

Per the article, the inventor of Arimaa at first considered multi-move
chess, but decided it would end up giving computers an advantage.  That, if
correct, shoots down my idea.

But per the suggestions he gives, I think he'd also frown on any suggestion
that Sac Chess would be computer resistant.

Inventing chess variants strictly to be "computer resistant" is not a
worthy goal.  It is intentionally disruptive.  However, inventing chess
variants to be theoretically deep (i.e., possess a high branching factor)
is a worthy goal (amongst several other, desirable game characteristics). 
Of course, it is probable to also be "computer resistant" incidentally.

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).

I suspect what did in Arimaa in 2015 as far as humans vs. computers was
that besides that a computer could be programmed for tactics no human could
normally see (e.g. bringing a rabbit to the final rank when already
somewhat close to it, securing instant victory, as done within even a small
number of ply), programming effective heuristics to take advantage of by
now well-known advice (to Arimaa players) on strategies used by humans must
have finally been achieved.

In Go I understand there are many rules of thumb, or heuristics, about what
constitutes best play in local (e.g. corner) situations, at least in the
opening phase of the game. Though I am a duffer at Go (as opposed to chess,
at least some might say), I understand that for tactical considerations
'liberties' is a vital concept (i.e. how many empty points are next to the
whole perimeter of a group of stones). That would be something to strive to
optimize. Then for Go strategy there are also at least a handful of really
grand concepts that are more difficult to program for computers, I would
imagine; in short, a skilled human can at times see the strong influence
exerted on territory and group(s) of stones by one or more stones for a
long time to come. Also, good Go players can get a rough count during the
middlegame phase of how much territory each player can expect to end up
with, if neither side sooner or later tries to initiate a risky tactical
melee, it seems.

For those who may think that Go is rather dull, I wondered that too. In
talking to a friend who spent some time in Japan and became somewhat
skilled at Go (and Shogi), he told me that these days the top country at Go
is South Korea. Apparently there are at least two fundamental styles at Go,
similar to in standard chess. In Go one can play to win quietly by mostly
winning on territory (like strategically played chess) or one can play to kill one or
more large groups of stones, taking many prisoners and territory if
successful, and likely inducing the opponent to resign earlier than near
the endgame phase (like tactical attacking chess). The South Koreans apparently all
like to play in such an aggressive attacking style.

Speaking of strategy, I can mention that for Sac Chess there could still be
weak pawns that appear, as well as players being left with just one bishop
at some stage (and perhaps then weak on squares of the opposite colour), so
there are at least these elements of strategy that may carry over from
standard chess to some degree. I would also note that in Sac Chess if a
player would avoid making an early big mistake, his king may be well
defended by all the extra pieces near it, even if they are doing little
else for a long time to come. This is one important difference that there
may be between Sac Chess and (say) Alekhine Chess, even though the latter
may also apparently have a little too much piece firepower for some folks
to like too.

Muller, your use of the phrase "proper evaluation criteria" seems
arbitrary.  Obviously, evaluation criteria exist, or some Go players would
not be better than others.  To label such criteria improper, merely because
humans can assess them better, would sound like computer sour grapes, if
not for my conviction (inspired by my reluctance to accept that computers
can already do anything humans can) that you are probably human.

Go also has short-term goals and short-term captures.  But computers
cannot foresee long term, and even the relative short-term might not be short enough.  The branching factor, as
well as the number of moves involved in even relatively short-term victories, is a part of this.

In Chess, gaining material is indeed "a way to go" as an interim goal for those (human or computer) who cannot foresee the final checkmate.  But it can be a trap,
leading in the longer run to checkmate or loss of even more material.  The
problem, in Chess, is that the computer can see far enough ahead to know
the difference.  Again, the branching factor, and the number of moves
involved, is a factor.

Still, your point about material is well taken.  In Chess, material gains
are almost always good, and if there is a trap, it is generally sprung
quickly or not at all.  When it is sprung quickly, a computer can foresee it.  But consider that this need not be equally true in
all types of Chess.  For example if you play on a larger board, with more
geographically localized pieces, then a trap might take longer to spring,
and the warning that how much material you have might be less important than where your
pieces are on the board, is something that might remain true for a longer period.

"Humans typically suffer more than computers from large branching
factors."
___________________________________________________________________________

Although the quoted remark is not generally untrue, I find generalizations

about the playing strength of humans at any particular game of little,
practical use because it varies radically between individuals.

A game with a high branching factor will (almost) certainly throw a dense,
cognitive fog around the tactical & strategic play of a novice, human
player [in the majority] yet an experienced, incisive human player [in the
minority] can usually see through this dense, cognitive fog to
consistently, correctly identify the most important offensive and/or
defensive move on the board and execute it.  Humans are better than
computers at quick-and-accurate pattern recognition which is conducive to
being able to play many chess variants well.  Computers use different,
non-geometric techniques to evaluate potential moves, anyway.

By contrast, I do not take exception to generalizations about the playing 
strength of computers at any particular game because they are predictably,
reliably useful.  The best available hardware running the best known 
programming, customized to play a given game as well as possible, is the 
given assumption.

A game with a high branching factor will certainly trap a computer player
within a search ply where it becomes intractible (i.e., unable to complete
it in less than a tremendous amount of time).  All except the most trivial

chess variants with the lowest branching factors become intractible at some
point.  Critically, it is a matter of how many plies can be completed
before this occurs (if very long time controls are allowed) and whether or
not this average number of completed plies represents a formidable AI
opponent to an intelligent, competent human player.  If not, there is a
serious problem which can only be overcome by heavy pruning within an
evaluation function.

Light to moderate pruning will not address the problem to a non-trivial 
extent.  Heavy pruning is risky.  Any errors in the evaluation function are
potentially catastrophic and there are many places for such game-specific
errors to exist unknown.  If an evaluation function occasionally throws
away from consideration a move(s) that needs to be made, then the human
player will likely soon discover tactics to routinely, successfully beat
his/her computer opponent every time.

Sorry, I still don't know what you mean.  The rules of Chess and Go, and
the criteria for victory, are equally unambiguous.  Computers use similar
methods to analyze both.  It's just that with Go, the computer runs out of
steam sooner, because of the large branching factor and the higher number
of moves.  Of course, it is also important that these factors do not
prevent human skill from operating in ways that computers cannot yet
replicate.

But no, I am not denying that there may be ways to fine tune a computer program to more closely approximate human skill.

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.