Comments/Ratings for a Single Item

(6) Neto's Mutators. Mutators, the right Mutator may give programs difficulty.

"There was one huge difference between a brain and a computer. And that's that a computer, if you poured a bucket of water on it, would short out, whereas the brain is wet...." --Miles Herkenham neurologist, 'Mapping the Next Millenium'

To the four last time add (5) Partnership Chess Games. In cards I did not check yet how they do it in four-player two-team Bridge whether one or two Computers versus two humans to test Computer dominance. There are other Chess Team games, but here is one made up for this comment.

Two Boards of OrthoChess 64 are good enough. Board 1 is A White B Black, and Board 2 C Black D White clockwise. Say D is the only Computer. Partners are B and D and A and C. Up to two points per round if one team wins both games. Play is synchronized so that each Move 1, 2, 3 each side takes place same time. In lieu of a Move, player may switch places with any *same* piece-type the other board of the same color. So for example, Computer D can make her Move 5 switching Bishop on c1 with corresponding White (non-partner) Bishop on f4, ending the turn with D board 2 Bishop on f4 and A board 1 Bishop back on c1. Now focussing on Computer D, strategy is to win own board but also be sure Partner B does not lose and preferably wins on Board 1. Human players may have an advantage judging performance expectations. In subsequent rounds Computer and everyone else will have different partner and position for White and Black in say a 12-game match.

There are already 50 well-thought comments here. To look at in follow-ups: (1) Huge boards even up to Charles Fort's 1000 squares; (2) Chess Different Armies again; (3) Polypieces that change their type upon each move; (4) Changing the rules entirely once or many times in play a single game.

While Game Courier can use cards, using the Knightmare Chess cards would likely be a copyright violation. Although I did make a card-based variant called Magic Chess, I did not program rule enforcement for it.  I don't think I have any GAME Code functions for identifying cards in play, and that would be critical for enforcing the rules of a card-based variant.

Hi Fergus

Might you have an idea of how difficult it could be for an experienced Game Courier programmer to write a preset (rule enforcing or not) for Knightmare Chess? I'm not sure I could find any number of opponents to play against over-the-board in Ottawa, but the game makes me curious. I'm getting ready to move with my family to another place in town in the coming months, but after that I may resume Game Courier play at some point.

Basically, Watson can locate relevant texts on moral issues and summarize their main points, but it can't draw any conclusions. That's not moral reasoning. That's text processing.

Hi Fergus

Someone pointed out to me on a Canadian chess message board that computers are already being programmed to debate moral issues. I suppose this alone puts my variant idea to waste:

http://www.ibtimes.co.uk/ibm-supercomputer-watson-programmed-debate-moral-issues-1447413

Speaking as an expert in morality, a Philosophy Ph.D. with an emphasis on ethics, I daresay that a game like this would trivialize morality. Morality is about real-life situations, and the arbiter of morality is reality, not a so-called expert who gets to decide whether you will move in a game. Before people could play such a game, they would have to agree on who to accept as experts. Although moral truth is not a subjective matter, it is not a subject met with univeral agreement, and it is one on which people sometimes strongly and sometimes violently disagree. Besides being computer-resistant, this game would be human-resistant.

Knightmare Chess involves intuition and ingenuity. It is not mere randomness like throwing dice to determine which pieces to move. It is the closest a Chess variant gets to Calvinball without losing structure.

I've edited my previous message a bit, in case anyone missed it.

I recall Fergus mentioned to me that Knightmare Chess might be computer resistant. I now doubt that it ultimately will prove to be, even though there is a quite random element involved in the game (which doesn't appeal to me to begin with, though strictly speaking as a standard chess player). Computers are now great at other games with random elements present, Bridge for instance, and so I expect programmers can succeed with Knightmare Chess too, given time to absorb how skilled humans play it. Not only that, there is still the spectre of things like neural net techniques, or the development of quantum computers.

It struck me today that one thing that might allow a computer resistant chess variant to be produced is to introduce a quasi-random element instead, one that often gives humans the edge. If the idea is workable, chess engine assisted cheating or the superiority of engines over even top humans may largely go away as concerns in the minds of possibly many. Computers as yet cannot be programmed to do advanced moral thinking, as far as I know, and I suspect they might never be able to even if nominally Technological (AI) Singularity is achieved. Morality takes into account even emotional feelings, and there seems little doubt that computers can never be given a soul of the sort many think we may have.

How might such a chess variant based on humanity's grasp of morality work? Well, the best we have for an expert in morality could be a law school or seminary teacher, for example. For the sort of chess variant I have in mind, it would be a kind of combination of the knowlege of moral issues and chess that a player has, as well as his chess skills (kind of like chess boxing combines chess and boxing - another variant that may be computer resistant to some extent). Before making a move in such a chess variant, the moral expert (teacher) or an assistant arbiter asks the player a skill testing question (could be multiple choice). If his answer is acceptable, he gets to move, otherwise he loses his turn, much as in some dice chess variants. Like chess boxing, this is perhaps not the sort of chess variant you can play on your coffeetable at home with a guest, but you could play it in a tournament hall or on the internet (securely guarded large trivial pursuit-style card decks, or databases, of moral Q & A's might be used). Young children may be at a disadvantage at times, but at least some adults might not mind that at all. [edit: Now that I think of it, a sort of trivial pursuit style card could also be a small database device that also lights up red (wrong) or green (right) for 1 of 2 answer choices offered and selected from; that would make this variant idea more workable at a tournament hall I'd suppose.] [edit: An example moral question might be: "A man drops a $5 bill and walks away. Do you: 1) offer him the bill, or 2) take it, because you found it"? A less simple one might be "You're a healthy boy and there are three similar cookies. Your younger sister is blind and cannot speak. Do you: 1) split 1 in half, take 1 and 1/2 & offer the rest to your sister, or 2) take 1 and offer 2 to your sister"?]

Intelligent Adversary Searches
https://pdfs.semanticscholar.org/b536/49ac430195dccbcff62a34e0c800a4782c97.pdf

Fwiw, below is a wikipedia link re: technological (AI) singularity, i.e.
the notion that someday, perhaps inevitably, and soon, AI will exceed human
intelligence. This notion is one more reason why I am now pessimistic about
any chess variant being computer-resistant for very long (e.g. for
decades), if it gets popular enough to receive serious attention from board
game engine programmers. On the faint hope side, perhaps, I seem to recall
something ancient being written about evil inventions to come, in the
latter days, before the better times that would follow, so who really knows
what the future holds:

https://en.wikipedia.org/wiki/Technological_singularity

P.S.: I got this link while looking at wikipedia's Driverless Cars entry -
such vehicles are perhaps a sign of the rapid rate of progress for AI these
days. I had been trying to put the difficulty of making a strong playing
engine for large board chess variants into perspective somehow.

I've edited my previous post a bit, to include discussion of Arimaa and
some features I think desirable if there is ever to be a Next Chess (in
terms of dominance like chess currently has). I may elaborate further on
the latter in another thread in future, perhaps beginning with why I
personally chose or rejected certain chess variants as ones I might play if
I take up playing on Game Courier again (such as after fully recovering
from recent dental work). Perhaps ones I rejected are more interesting
cases to mention, since some I accepted were at least partly for the sake
of anticipated fun/novelty (e.g. Smess, Circular Chess).

George wrote earlier:

"...If little Los Alamos 6x6 had been the old standard, it would be
replaced by something bigger. And the mere fact OrthoChess is on little
8x8, and the other world CV types are 9x10 and 9x9, China and Japan, should
be embarrassing to their GMs. That's why Stanley Random started 15 years
ago calling f.i.d.e. "Simpleminded Chess" and now I do..."

Historically chess variants strongly resembling today's standard version of
chess have been tried on larger boards, but there may have been legitimate
reasons why the lesser 8x8 size was settled upon for so long. Perhaps the
expected length of an average game on any bigger board size was thought
undesirable (the same could go for a smaller sized board). What chess lacks
in comparison to Shogi or Chinese Chess it may, at the least, make up for
in other ways. 

The unique combination of chess' features, none of which may make it
particularly unique when taken seperately, have made chess enduringly
popular thus far, and no one knows exactly why. The game has held up well,
though nowadays extensive databases, engines, the difficulty for top
players to win with many Black openings, tablebases, and the increased
possibilities for cheating (especially on the internet) are putting chess
under pressure. The question may be whether any chess variant can hope to
replace it anytime soon, in terms of dominance, and so far I haven't
noticed any obvious candidates for such, perhaps even in terms of merit
IMHO.

[edit: For some years Arimaa seemed a golden candidate to be the Next Chess. I used to Google it and see comments like "they've fixed chess". Before a computer finally beat top players in 2015, though, one of Arimaa's supposed strengths over chess, that there was no set opening setup, had already been weakened since there were certain setups thought better than others. There is a similar problem with Fischer Random, I've heard, in that any number of starting setups are apparently not very interesting. In any case, I actually prefer a chess variant that has a fixed start position, for merchandising and study purposes, assuming the opening phase is at least as rich in possibilities as standard chess. Also, I think a variant that looks nice on someone's coffeetable could further help to popularize it, and a fixed start position assists with this. Unfortunately this doesn't bode well for variants with many more cells than a game of Scrabble (15x15), which might be otherwise desirable for possible computer-resistance. Arimaa also had a problem hurting its speed of spread, in that its inventor imposed various licensing requirements, such as on websites, clubs or literature, although many apps for the game may have been sold, at least. Meanwhile, below is a link about Arimaa, which notes the history of its man vs. machine challenges.]

https://en.wikipedia.org/wiki/Arimaa

On a Canadian chess message board (chesstalk) a poster (Mario
Moran-Venegas) wrote today, re: AlphaGo's loss in game 4 of the match: 

"AlphaGo's Policy neural network does not care about the quantity of point
lost or won by. It's highest priority is maximizing winning probability or
(when losing) minimizing losing probability. After move 78, it should have
followed what you say chess engines do: attempt to prolong the game by
complicating it.
The Policy neural network is the boss of hundreds (literature says a max of
1200, I don't know how many were actually used) of brute force engines
similar to chess engines.In the future versions I see the following
changes:
1.A change in the dynamic depth-of-analysis assigned to an engine. My guess
is that which ever engine was given the task of tackling the area around
move 78 was not going deep enough thus affecting the overall assessment of
the entire board as a loss for Black (AlphaGo). Many (including commentator
Michael Redmond) are now saying move 78 "did not work".
2.A change on the Policy NN to make use of complexity on the board."

If Mario's guess above, concerning move 78 of game 4, is correct, an
implication might be that the large 19x19 board used for Go may be close to
the upper limit of what the neural net technique (plus brute force engines)
used is currently capable of allowing a computer to beat top humans at, for
the game of Go, as played on an nxn size board. Make n significantly larger
than 19, that is, and a computer might fail to beat the top human players.
Not sure if the same would apply for a very large board size chess variant
too, as more calculation than intuition would be used than for Go, but
maybe there's something to the idea.

Much earlier in this thread Joe Joyce mentioned a very large board war game
of his invention that was arguably a chess variant, too. Fwiw, I've
invented a couple of 5x5x25 4D chess variants (625 cells) which would have
more cells than standard 19x19 Go, though I recall Joe's war game was even
larger. In any case, a very large board size might appeal to more potential
players of a given chess variant than other ideas that have been mentioned
in this thread, such as changing the rules a game is played by every other
turn (or the same for how a given piece moves).

https://www.technologyreview.com/s/541276/deep-learning-machine-teaches-itself-chess-in-72-hours-plays-at-international-master/

Hi George

The game of (19x19) Go is more intuitive than chess, which concentrates more on calculation, and is played on a much smaller (8x8) board. Go had been thought to be possibly more computer-resistant than chess until the latest defeat for the human side. A forlorn hope may be that neural net
programming techniques don't work as well for games (e.g. most chess variants!?) which are based more on calculation, though for the sake of accepting the challenge, and in a case of overkill, programmers are now aiming to beat top human chess players with self-teaching (neural net) techniques as well.

The 8x8 game of Arimaa (barely a chess variant IMHO) suffered a similar
fate as Go last year, as far as humanity is concerned, for that is when a
program (not using neural net technichiques afaik) finally beat top Arimaa players in the annual computer vs. top humans contest. Arimaa was thought to be promising for humanity for a different reason, in that there is a high branching factor at each ply (17000+ legal moves on average available), which might put a dampening effect on Greg's suggestion earlier in this thread concerning Marseilles (i.e. 2 move) Chess, since, as he noted, it has a branching factor of about 900 legal moves per ply.

Unless there can be a chess variant that is surprising computer-resistant,
and with the potential to be popular enough to be widely played, my flights
of fancy are turning more and more to the outside chance that in our
lifetimes there may be a global divine intervention that in effect pushes a
reset button (hopefully gently), e.g. on some of the worst aspects and/or
misuses of modern technology (including any forms of cheating).

[edit: much earlier in this thread you wrote:

"Kevin Pacey began recent topic here December 2015 with the term "next chess." And weeks later adds interesting questioning whether any CV diverges much from OrthoChess, probably meaning from programming standpoint. "Next Chess" originates with Joe Joyce wording and then by series of threads in abeyance since 2014 we made a list of over twenty contenders: NextChess9."

While hoping this thread won't wander too far off topic, I'll note that:

1) I happened to notice the term "next chess" used on a random message board some years ago (I think), where a poster whose name escapes me was noting that he thought many people were trying to invent a board game of skill that would replace chess in terms of dominant use worldwide, with some such people taking their game to trade shows, getting into quarrels involving threats of lawsuits...;

2) It has seemed to me that many of the more viable/popular chess variants that I've seen (thus far, in my early exploration of chess variants) may not differ from standard chess all that much, in that they might allow a skilled chess player to soon be equally skilled in playing them too. However trying to define what makes any one chess variant more like chess than another chess variant is would seem hardly possible. Yet, sometimes the case can be clear, at least to me. Circular chess, or Capablance Chess, for example, seem a lot more chesslike than Rococo, and a chess master may well need longer to master the latter than either of the former variants. Also, some variants use rules governing at least some of the pieces which are radically different than is the case for chess or other chess variants, e.g. Fusion Chess, or variants that use an Anti-King. Again, a chess master might often get the hang of how to play with an Archbishop or Chancellor (in Capablanca Chess) sooner, I would guess. I haven't yet touched variants which have slightly bizarre objectives, such as Losing Chess, for example.]

Regarding computer-resistant variants, Marseillais Chess is probably a good
candidate.  Since each player's move actually consists of two moves, the
branching factor is extremely high.  If a typical position has 30 possible
moves in Chess, then in Marseillais a player has about 900 options.  This
is much higher than in go so computers won't be able to see very deeply. 
Actually, it's somewhat less than 900 because some of them are effective
duplicates.  (a1-a2, b1-b2 is no different than b1-b2, a1-a2).  Also
evaluating a position is problematic because there are no quiet positions. 
The usual computer chess answer to this, quiescent search, is out the
window.  On the other hand, humans probably can't see very deeply in this
game either...

If that doesn't work, here's an alternative idea.  Computer-Resistant
Chess, copyright (c) 2016 by Greg Strong.  All the standard rules of Chess
apply, with the addition of the "Swizzelstick" rule: A player must make
each move with one hand, while touching the tip of his nose with the other,
and calling out "Swizzelstick!"  Any player who fails to do this
automatically forfeits.  Oh, and when you checkmate your opponent, it's not
official until you pee on his king.

As I alluded to much earlier in this thread, the problem with computers
being good (let alone dominant) at chess (or its variants) is at least
twofold in my eyes, and that would be irrespective of whether comparing
human and computer play is like comparing apples and oranges:

1) Computers being dominant at chess, for example, hurts the estimation of
chess and chess players in the eyes of the public, which can only be
educated so much (if they buy it) that it is a case of 'apples and
oranges';

2) Far more importantly, perhaps, is that cheating in chess (for instance)
by means of computer assistance can become rife, if not yet in over-the
board events, then it certainly already has in the play of internet chess,
for example. I don't think I need list the ways this can be seriously
harmful to the game, such as for its esteem by the public. That's even if
tournament directors can do a relatively good job of catching cheaters. The
danger of even purely partner-assisted cheating in the card game of Bridge
may be one of the reasons why there is little in the way of cash prizes
offered in that game's competitions, except in high level play, such as
world championship play, where even just recently there was another case of
cheating, I seem to recall.


Perhaps playing a variant that uses Betza's "Many rules in one game", as linked to much earlier by George, would be the way that's best suited to get around the problem of neural net programming techniques (apparently about to slay the human dominance of Go) or the coming age of quantum computing power on top of that. However, I'm not at all sure of how often games are played that use "Many Rules", or how popular such games could possibly become. So far I haven't noticed any examples as played on Game Courier, for instance, so I'm wondering a little how easy it is to make a Game Courier preset for such, or even enjoy playing such.

I honestly think all this "human vs computer" thing is nonsense as it's comparing totally different things.

In one side you have a group of computer scientists and mathematicians that model the game in a way it can be understood and played by a machine, it is all about making a mathematical model and reducing the solution space to the most powerful moves; in the other side you have a person that learnt playing normally doing games and studying. A Chess player can study how Deep Blue was implemented, but this won't make him playing much better. At the end of the day it's comparing apple and orange.

Anyway. What makes a game hard for computers? Usually it is:

• Search space (how many meaningful moves you can do?)
• Long term effect (the move I do now for all long it affects the game?)
• Hidden information and it's counterpart: what information I can get deduce from the game state?
• Number of rules (exceptions and special case makes computer programming much more difficult)

For example Go was unbeaten by computer for so long for the first two reasons, Magic The Gathering (a subset of it actually) is still unbeaten for the last two.

So I guess if you really want to develop a game just to make life to computer scientists and mathematicians difficult you have to point to increase all the point points as much as possible. However, it's very difficult to obtain a game that is FUN. Because if you overdo to most humans the game will appear random.

Personally I would point to a mix between Gess (but with a larger board) and Netrunner card game...

Off topic, but perhaps related to the previous post (which is a hopeful
post, to me), on a Canadian chess message board some years ago a Canadian
inventor of games currently residing in the US argued that at least one
over-the-board competitive event (ideally with cash prizes) might be held at some point, which would involve the playing of more than one type of
chess variant, perhaps including chess itself. That is, much like there are
competitions held that involve the playing of more than a single Poker
variant within one particular face-to-face Poker competition.

The game inventor's idea is to some extent already being carried out
online, e.g. in the case of Game Courier on this website, but note that in
that case the contestants agree to the chess variants that they will play,
if an invitation from a fellow player is issued. That's as opposed to what
I thought the game inventor had in mind, i.e. a relatively small set of
chess variants, as selected (in advance of such an event!?) by an over-the-board event organizer, to be chosen from by the players (or else all the chess variants in the selection would have to be played by all the players). 

What I thought he had in mind didn't seem like such a good idea to me since
chess itself normally takes a lot more study to master than, say, the basic
form of Poker (or any of its variants), and I assumed that learning any
chess variant worth playing might also take a lot of study, so that a chess
variant player could not hope to be truly skillful in more than a handful of chess variants at best. However, I have now combed through
chessvariants.com for some time, in looking at variants that are on various lists given (aside from my not looking directly at much of the main alphabetical list), or in looking at popular variants as found on Game Courier. That was in the process of selecting variants with existing presets that I think I might like to play on Game Courier. I am now wondering how fundamentally different from standard chess that a lot of the most viable chess variants really are.

On the other hand, for the 17 variants (so far) that I think I might wish to play, if I start playing on Game Courier again at some point (after some looming dental work), I was happy to see that they each fit into at least 1 of 11 categories in total (some of which were designated by me, such as "10x10 board variants"). That represents considerable variety, for my currently preferred 17, plus 11 are games that I've not played against people more than once or twice online or offline, if ever (one being my own Sac Chess variant).

Much earlier Ben Reiniger posted: Go is now starting to fall to computers:
http://www.bbc.com/news/technology-35420579

I've been told it was a 2 Dan strength player who recently fell to a
computer program, but without the player giving it any stones as a
handicap, and thus it's still a shocker for me. Neural net techniques now
seem to make any board game of skill vulnerable to computer dominance in a
relatively short time. Go seemed to hold every advantage for being
computer-resistant, especially given its huge 19x19 board, but now the end
seems near for human Go players. I had thought Go might not come to that
for about 100 more years. This was even taking into account any
development in the field of quantum computers. 

So, I am personally waving the white flag, as far as hoping that any chess
variant might in future be computer-resistant for any significant length of
time, if serious computer programmers target it for computer dominance.
Serious organizers of any kind of board game of skill competition will from
now on inevitably need to hope for effective anti-computer assisted
cheating measures, it seems. One of the reasons I became more interested in
chess variants was the hope that I had that this scenario could somehow be avoided at
least for a considerable while, with some chess variant periodically
invented that would become reasonably popular at some point. If I am to
remain interested in chess variants (i.e. inventing, appreciating or playing them), I'll
need to concentrate now more on enjoying them for their own sake, though
afaik a number of modern organized cash prize events are starting to happen
more regularly, say in Canada, in the case of bughouse at least.

Go is now starting to fall to computers:
http://www.bbc.com/news/technology-35420579

Of course you also have to take account of the fact that in the bulk of the tree on every other level only a single move has to be searched, to refute the previous move. Engines are pretty clever at picking the right move for that, based on the search of the previous depth. This means that for a game with 36 moves per position, the effective branching factor would only be sqrt(36) = 6 per half-move, without any selectivity whatsoever.

Through simple-minded depth reduction (2 or 3 half-moves) in positions where the opponent proves unable to exploit a turn pass, this can already be brought down to around 4. Conditionally reducing the non-captures (i.e. reducing their search depth 1 or 2 half-moves until this reduced search proves that the move is worthwile score-wise), the EBF falls to around 3. By sorting the moves somewhat cleverly based on the statistics of their success as refutations in the entire tree, and reducing the moves late in that sorting even more, you get branching factors like that of Stockfish, which ly around 2.

Up to that point, no knowledge about the game has been used at all to guide the search. Of course the engine needs knowledge to play strong, but it is all in the static evaluation. It is not needed to get the EBF low.

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.

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.

"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.

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.

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.

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).

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.

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.

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.

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'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.

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

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.

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.

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

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

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

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.

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

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.

People are welcome to post their ideas for what might make for chess
variants that would make it hard for computer engines to beat reasonably
skilled humans (better yet would be a way for this website to indicate
whether a particular chess variant promises to be computer resistant). I
see the game of Go as promising for this purpose, except unfortunately IMHO
it lacks kings that can be checkmated, for the thrill of the chase that
helps make many chesslike games attractive.

If a chess variant becomes popular enough that it attracts serious
attention from skilled engine programmers, and they fail to beat fairly
skilled humans with their machines for at least decades, it could be game
on as far as that chess variant becoming the next chess, aka the new
version of standard chess. Chess may be well overdue for some serious
changes to its basic rules, in any number of conceivable ways.