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Comments for H. G. Muller
Gala. Medieval game of German farmers. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]
Anonymous wrote on Tue, Aug 20, 2002 01:52 PM UTC:Good ★★★★From the german Book by Theodor Müller-Alfeld I can add some more information: The pieces of Gala have special names: Gala (King), Korna (Rook), Horsa (Bishop) and Kampa (Pawn). Historical games have bigger pieces for the Galas, Kornas have green heads and Horsas have red heads, while Kampas are left unmarked. The pieces are represented in Theodor Müller-Alfeld by simple geometric shapes: Gala by octothorpe (#), Korna bei square, Horsa by cross (x) and Kampa by circle (o). Unfortunately, I cannot answer the open questions about the movement of the pieces from my source either. --Jörg Knappen
Shatranj. The widely played Arabian predecessor of modern chess. (8x8, Cells: 64) (Recognized!)[All Comments] [Add Comment or Rating]BLOCKADE STALEMATE IN 20 MOVES:
Using Zillions, I played out this sample game, which ends with the 4 remaining Black Pawns blockaded by 4 White pieces, while a Black King, Chariot, Knight, Counselor, and Elephant are locked in behind the Pawns. Even if this was a variant allowing Kings to move into check and be captured, Black would still have no legal moves in the final position:
alf-chaturanga.zrf VariantName=Shatranj 1. Pawn h2 - h3 1. Pawn a7 - a6 2. Pawn h3 - h4 2. Knight b8 - c6 3. Chariot h1 - h3 3. Elephant c8 - e6 4. Chariot h3 - f3 4. King d8 - c8 5. Chariot f3 x f7 5. King c8 - b8 6. Chariot f7 x g7 6. Elephant e6 - c8 7. Chariot g7 x h7 7. Chariot a8 - a7 8. Chariot h7 x h8 8. King b8 - a8 9. Pawn a2 - a3 9. Pawn b7 - b6 10. Pawn a3 - a4 10. Knight c6 - b8 11. Pawn a4 - a5 11. Pawn b6 x a5 12. Chariot a1 x a5 12. Counselor e8 - f7 13. Elephant c1 - e3 13. Counselor f7 - e6 14. Elephant e3 - c5 14. Counselor e6 - d5 15. Chariot h8 x g8 15. Counselor d5 - c6 16. Chariot g8 - g5 16. Pawn e7 - e6 17. Chariot g5 - e5 17. Counselor c6 - b7 18. Knight b1 - c3 18. Pawn c7 - c6 19. Knight c3 - e4 19. Elephant f8 - d6 20. Knight e4 x d6
[EDIT 10/22/2024] H. G. Muller posted an applet in the Comments (May 3, 2021). You can click "Play it!" and copypaste the following (eighteen move) game. Clicking "Move" at the end makes the applet appropriately respond with *** I resign! ***
1. a3 a6 2. a4 b6 3. a5 b5 4. Ra3 Ra7 5. Rh3 Be6 6. Rxh7 Kc8 7. Rxg7 Kb7 8. Rxf7 Ka8 9. Rxf8 Bc8 10. Rxg8 Rh5 11. Nc3 Qf7 12. Rg5 Qe6 13. Rxh5 Qd5 14. Nxb5 Qc6 15. Nd6 Qb7 16. Be3 c6 17. Bc5 e6 18. Re5
Ultima. Game where each type of piece has a different capturing ability. Also called Baroque. (8x8, Cells: 64) (Recognized!)[All Comments] [Add Comment or Rating]Done! Look at http://home.hccnet.nl/h.g.muller/ultima.html
Modern Shatranj. A bridge between modern chess and the historic game of Shatranj. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]It is interesting to observe the simultaneous use of modern Bishops and your Elephants in Courier-Spiel, a more modern variant of Courier Chess, and Shako, a 1990 variant on the 10x10 board. As H.G.Muller points out, Courier-Spiel also has the modern Queen and your General (called a fool or schleich). I am inclined to agree with his theory that the evolution of pieces happens on larger boards, and later on the more successful pieces take over the standard size board. Compare the long history of Japanese experiments in 12x12 Chu Shogi and 15x15 Dai Shogi.
Fairy-Max
. Free open source chess variant software.[All Comments] [Add Comment or Rating]This is a developers-only snapshot of a program that may become a usable chess variant engine. However, there are a number of issues that need to be worked out:
- There is no documentation on how to actually use fairy max. The only way to figure out how to use the program is to read the C source.
- The C source code does not contain any license text. I would like to know under what license the program is released, and whether the terms are OSI-approved Open Source compatible (GPL, etc.)
- The program itself has no built-in help
- There is also WinBoardF, which has support for a few chess variants. However, there is no documentation about how to interface WinboardF with fairy max.
- Sam
P.S.: I will change my rating once documentation is available to actually interface fairy max with WinboardF. I will change my rating to one even higher if a well integrated fairy max + WinboardF package is made, which doesn't require any messing around with .ini files to play fairy chess against the computer.
Originally published in Science Express on 19 July 2007 Science 14 September 2007: Vol. 317. no. 5844, pp. 1518 - 1522 DOI: 10.1126/science.1144079 Prev | Table of Contents | Next Research Articles Checkers Is Solved Jonathan Schaeffer,* Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, Steve Sutphen The game of checkers has roughly 500 billion billion possible positions (5 x 1020). The task of solving the game, determining the final result in a game with no mistakes made by either player, is daunting. Since 1989, almost continuously, dozens of computers have been working on solving checkers, applying state-of-the-art artificial intelligence techniques to the proving process. This paper announces that checkers is now solved: Perfect play by both sides leads to a draw. This is the most challenging popular game to be solved to date, roughly one million times as complex as Connect Four. Artificial intelligence technology has been used to generate strong heuristic-based game-playing programs, such as Deep Blue for chess. Solving a game takes this to the next level by replacing the heuristics with perfection. Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada. Present address: Department of Computer Science, Reykjavik University, Reykjavik, Kringlan 1, IS-103, Iceland. Present address: Department of Media Architecture, Future University, Hakodate, 116-2 Kamedanakano-cho Hakodate Hokkaido, 041-8655, Japan. * To whom correspondence should be addressed. E-mail: [email protected]
Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]'... the Battle-of-the-Goths tournament was played at 1 hour per game per side (55'+5'/move, the time on the clocks is displayed in the viewer). And you call it speed Chess. Poof, there goes half your argument up in smoke.' Sorry, I could not find the time per move on your crude web page. Nonetheless, less than 1 minute per move is much too short to yield quality moves ... at least by anything better than low standards. _________________________________________________________ 'Not that it was any good to begin with: it is well known and amply tested that the quality of computer play only is a very weak function of time control.' WRONG! The quality of computer play correlates strongly as a function of ply depth completion which, in turn, is a function of time where exponentially greater time is generally required to complete each successive ply. ___________________________________________________________________ 'The fact that you ask how 'my theory was constructed' is shocking. Didn't you notice I did not present any theory at all?' In fact, I have noticed that you have failed to present a theory to date. I apologize for politely yet incorrectly giving you the benefit of the doubt that you had developed any theory at all unpublished but somewhere within your mind. Do you actually prefer for me to state or imply that you are clueless even as you claim to be the world's foremost authority on the subject and claim the rest of us are stupid? Fine then. ____________________________________________________________ 'I just reported my OBSERVATION that quiet positions with C instead of A do not have a larger probability to win the game, and that in my opinion thus any concept of 'piece value' that does not ascribe nearly equal value to A and C is worse than useless.' When you speak of what is needed to 'win the game' you are fixating upon the mating power of pieces which translates to endgame relative piece values- NOT opening game or midgame relative piece values. Incidentally, relative piece values during the opening game are more important than during the midgame which, in turn, are more important than during the endgame. Furthermore, I am particularly wary about the use of relative piece values at all during the endgame since any theoretically deep possibility to achieve checkmate (regardless of material sacrifices), discovered or undiscovered, renders relative piece values an absolutely non-applicable and false concept. I strongly recommend that you shift your attention oppositely to the supremely-important opening game to derive more useful relative piece values. _______ 'So what have I think I proved by the battle-of-the-Goths long TC tourney about the value of A and C? Nothing of course! Did I claim I did? No, that was just a figment of your imagination!' I did not claim that I knew exactly how your ridiculous idea that an archbishop is appr. equally valuable to a chancellor originated. This 'tournament' of yours that I criticized just seems to be a part of your 'delusion maintenance' belief system. __________________________________________ 'It might be of interest to know that prof. Hyatt develops Crafty (one of the best open-source Chess engines) based on 40/1' games, as he has found that this is as accurate as using longer TC for relative performance measurement, and that Rybka (the best engine in the World) is tuned through games of 40 moves per second.' Now, you are completely confusing a method for QUICKLY and easily testing a computer hardware and software system to make sure it is operating properly with a method for achieving AI games consisting of highest quality moves of theoretical value to expert analysts of a given chess variant. I have already explained some of this to you. Gawd! ____________________________________________________ 'The method you used (testing the effect of changing the piece values, rather than the effect of changing the pieces) is highly inferior, and needs about 100 times as many games to get the statistical noise down to the same level as my method. (Because in most games, the mis-evaluated pieces would still be traded against each other.)' First, you are falsely inventing stats out of thin air! If you really were competent with statistics, then you would know the difference between their proper and improper application within your own work attempting to derive accurate relative piece values. Second, you do not recognize (due to having no experience) the surprisingly great frequency with which a typical game between two otherwise-identical versions running a quality program with contrasting relative piece values will play into each other's most significant differences in the values of a piece. Here is a hypothetical example ... If white (incorrectly) values a rook significantly higher than an archbishop AND If black (correctly) values an archbishop significantly higher than a rook, then the trade of white archbishop for a black rook will be readily permitted by both programs and is very likely to actually occur at some point during a single game or a couple-few games at most. Consequently, all things otherwise equal, white will probably lose most games which is indicative of a problem somewhere within its set of relative piece values (compared to black). __________________________________________ 'If you are not prepared to face the facts, this discussion is pointless.' When I reflect your remark back to you, I agree completely. ___________________________________________________________ 'Play a few dozen games with Smirf, at any time control you feel trustworthy, where one side lacks A and the other B+N, and see who is crushed.' relative piece values opening game (bishop pairs intact) Muller pawn 10.00 knight 35.29 bishop 45.88 rook 55.88 archbishop 102.94 chancellor 105.88 queen 111.76 Nalls pawn 10.00 knight 30.77 bishop 37.56 rook 59.43 archbishop 70.61 chancellor 94.18 queen 101.60 So, what is your problem? Both of our models are in basic agreement on this issue. There is no dispute between us. [I hate to disappoint you.] What you failed to take into account (since you refuse to educate yourself via my paper) is the 'supreme piece(s) enhancement' within my model. My published start-of-the-game relative piece values are not the final word for a simplistic model. My model is more sophisticated and adaptable with some adjustments required during the game. For CRC, the 3 most powerful pieces in the game (i.e., archbishop, chancellor, queen) share, by a weighted formula, a 12.5% bonus which contributes to 'practical attack values' (a component of material values under my model). Moreover, the shares for each piece of the 12.5% bonus typically increase, by a weighted formula, during the game as some of the 3 most powerful pieces are captured and their share(s) is inherited by the remaining piece(s). Thus, if the archbishop becomes the only remaining, most powerful piece, then it becomes much more valuable than the combined values of the bishop and knight. Notwithstanding, I'll bet you still think my model is 'worthless nonsense'. Right? In the future, please do the minimal fact finding prerequisite to making sense in what you are arguing about? ____________________________________ '... the rest of the World beware that your theory of piece values sucks in the extreme!' No, it does not. Your self-described 'far less than a theory, only an observation' comes close, though.
Joe Joyce wrote on Tue, Apr 22, 2008 10:07 PM UTC:HG Muller, you are certainly allowed, and encouraged, to post on piece values in the Piece Values thread. Joe
Joe Joyce wrote on Wed, Apr 23, 2008 06:39 AM UTC:These are Aberg's values: A Archbishop 6.8 C Chancellor 8.7 Q Queen 9.0 These are Reinhardt's recent values: High Priestess: 8x8: 6+1/28; 10x8: 6+5/36; 10x10: 6+19/45 Minister: 8x8: 6+5/7; 10x8: 6+3/4; 10x10: 6+44/45 So, for 10x8: The high priestess comes in at 6.1 vs the archbishop's 6.8 - about a 10% difference. The minister comes in at 6.8 vs the chancellor's 8.7, a difference of over 25%. Why is the high priestess so close to the archbishop's value, compared to the minister being noticeably [about 30%] weaker than the chancellor? Why is the value of the high priestess and the minister so much closer together than that of the archbishop and chancellor? This falls in line with HG Muller's argument, though at the lower value, not the higher value. This should imply [at least] something about the 2 types of pieces, the shortrange leapers vs the infinite sliders, no? But what? I said I was better at asking than answering questions; these I find interesting. Now, it's way past my bedtime; good night, all. Pleasant dreams. ;-)
Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]All very true. But in practice, I never have seen piece values that were extremely different in the opening from what the are in the end-game. The rason is probably that in the beginning there are so many pieces that even being one or two behind does not immediately decided the game by checkmate. The opponent can almost always fight it off for a long time by trading material. And by the time the board is half empty, most pieces start approaching their end-game values. So if the disadvantage of two pieces was only transient, the pieces being present, but merely useless on the full board, he would effectively have earned them back. In addition, pieces are seldomly totally useless. The Rook, which is the most notorious example of a piece that is difficult to develop early, still make itself very useful as a defender behind the Pawn line, preventing your position to collapse under the attack of quickly developed pieces of the enemy. It would perhaps be different if a CV had pieces that by rule were not allowed to move at all before 75% of the Pawns had been captured, but than suddenly became very powerful. For such pieces it would be very questionable if you could survive long enough for them to be of use. But with Rooks as defenders, you can realistically expect to survive to the point where the Rooks live up to their full potential at least 90% of the cases. R for N or B gambits are almost non-existent. It is very questionable if the instantaneous advantage of having N in stead of R would allow you to win a single Pawn before the advantage evaporates. I did make an early end-game test on the Archbishop, though, because it was the compound of two 'early' pieces, and some players suggested that it had its main use in the early middle-game. So I set up a tactically dead A+5P vs R+N+6P position ( http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it play a couple of hundred times to see who had the advantage. Turns out the position was well balanced. This could be considered as a direct measurement of the end-game value of the involved pieces.
H.G.Muller: | I think the following array would be more logical: | C H A M K A H C | where M=Amazon and H=Nightrider. Yes. I was thinking about putting a Q+N piece besides the K, too. The nightrider may be too powerful though, and may be hard to learn for humans. | ...but my guess is that it would make the | game too tactical, without quiet positions, almost reversi-like... One function that the minor pieces have in orthodox chess, is being suitable for sacrifice. So having only powerful pieces could loose out on the tactical side too. | Only the poor King has no enhancement. You could replace it by a Centaur, | but this might make checkmating it too difficult. The king, as piece for becoming mated, is just fine. I thought about the K+N piece a bit too. One variation I am thinking about is 'Spartan kings': two kings, just as the Spartans, where When two kings remains, one can be taken; game ends when the last remaining king has become mated. But one must think carefully about the design objectives: orthodox chess has a particularly good blend of strategy and tactics. With the Capa variation I gave, the idea is to preserve as much as possible of that, while lessening the amount of draws by adding some material.
H.G.Muller: | I set up a tactically dead A+5P vs R+N+6P position ( | http://home.hccnet.nl/h.g.muller/BotG08G/KA5PKRN6P.gif ), and let it | play a couple of hundred times to see who had the advantage. Turns out | the position was well balanced. This might be the way to go, because the standard exchange is equal pieces. The next step is a refinement: 'if I exchanged my R for a B, what do I need to keep a balance?' - something like 2 Pawns. The piece value system probably cannot predict well the balance in more complicated unequal exchange positions, but humans would probably try to avoid them, and they do not arise naturally, at least in human play. So if an A is exchanged for a C, what is needed to keep the generic end game balance? And so forth. With a list of balanced combination, perhaps a reliable piece value system can be constructed. It would then only apply to the examined exchange combinations.
Great Shatranj. Great Shatranj. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]💡📝Joe Joyce wrote on Wed, Apr 23, 2008 08:22 PM UTC:HG Muller - you are not on the list of applicants. Please go to this page to register: http://chessvariants.org/index/registeruser.html Thank you for the comment. The goal was to design a game that clearly played like chess, that had an essential 'feel' of chess, but was clearly different from FIDE. The king/'general' pieces, attacking all 8 squares around, complement the minor pieces nicely, with all attacking 8 squares unblockably. The 2 major pieces are obviously 'shatranjized' versions of the A and C. As they each attack 16 squares, double the others, but still have the same range of 2, they've made a nice fit with the basic concept. But this game is part of a shatranj series; thus the names. They are consistent across the series. [Heh, maybe not good names, but consistent. I admit to a naming disability. I've always thought Minister and High Priestess were good names, clearly analogous to Chancellor and Archbishop, and among my personal best efforts. Others may differ.] Why the bare king rule? Hubris and laziness, mostly. When the final design for this game and its sister game, Grand Shatranj, gelled, I felt it was so obvious that both games were clearly easily and readily playable as is that I posted them without first playtesting them. The bare king rule serves 2 purposes: it gives an air of shatranjness to the games, which I wanted whether or not the games deserve it; it gives me a bail-out against draws in case the games turn out to be very drawish. So far, except for Modern Shatranj, I don't think the series has had a draw, in the admittedly few games of each completed. I guess it serves mostly as window-dressing. But at high-level play, it may well diminish the number of draws. How much is another matter.
Aberg variation of Capablanca's Chess. Different setup and castling rules. (10x8, Cells: 80) [All Comments] [Add Comment or Rating]H.G.Muller: | Well, this is basically how I got the empirical values I quoted. Except | that so far I only did it for opening positions, so the values are all | opening values. But, like I said, they don't seem to change a lot during | the game. For the complete list of exchanges that I tried, see | http://z13.invisionfree.com/Gothic_Chess_Forum/index.php?showtopic=389&st=1 There might be some problems here: For the classical piece value system, basically, what one gets is determining balance when the position is positionally equal and when both players play 'correctly'. By contrast, you take a statistical approach, and as you say for opening positions. The classical piece value system depends on a deeper analysis; perhaps the statistical approach can serve as a first approximation. So the approach I suggested is to find a set of end-game positions where the outcome is always a draw or always a win, with extreme positions excepted. This might produce different values. In this setup, it is not possible to set values as exactly, as equal material means 'always result in draw for the positions considered'; perhaps it leads to only integral values, as a fraction pawn value cannot be used to decide the outcome of games. The fractions might be introduced as position compensations, like in orthodox chess reasoning, for example 'the sacrificed pawn is compensated by positional development'.
|| So the approach I suggested is to find a set of end-game positions || where the outcome is always a draw or always a win, with extreme || positions excepted. This might produce different values.' H.G.Muller: | The problem is that such positions do not exist, except for some very | sterile end-games. There is a difference between finding formally proved positions, and those that have such an outcome by human experience. If one in middle game exchanges ones queen for a rook and temporary very strong initiative, suppose this initiative does not lead to an immediate mate combination - it might be very effective to threaten a mate, which the opponent can only avoid by giving back some extra material - how much more material is needed in order to ensure a draw? A bishop perhaps, if the pawns are otherwise favorable, otherwise at least some more material, a pawn or two. This is a different judgement than a statistical one: a purely statistical judgment can probably be quite easily beaten by a human. It goes into a difficult AI problem: computers are not very good at recognizing patterns and contexts. But the classical piece value system probably builds on some such information.
H.G.Muller: | It seems to me that the example you sketch is exactly what the piece-value | system cannot solve and is not intended to solve. You want to have an | estimate of how much material it wil cost the opponent to solve a certain | mobility or King-safety advantage. Those are questions about the | corresponding positional evaluation, not about piece values. The situation I depicted is the other way around: I see a good queen for rook exchange that looks promising. Can I at least ensure a draw? How much additional material would I need to get to ensure. Next, have a look at the likely pawn development. So the traditional system will tell me whether I need 1, 2 or 3 pawns. The statistical system does not say anything - I am not interested in how players on the average would handle this position.
H.G.Muller: | I suspect you misunderstand what quantity is analyzed. In any case not how players handle | the position. But the very question you do ask, 'what are my chances for a draw with 1, 2 | or 3 Pawns in compensation', can only be answered in a statistical sense. The answer will | never be 'with 1 Pawn I will lose, with 2 Pawns I will draw, and with 3 Pawns, I will | win'. It will be something like: 'With one Pawn I will have 5% chance on a win and 10% on | a draw, (and thus 85% for a loss) with 2 Pawns this will be 20-30-50, and with 3 Pawns 50-| 30-20. And I can count a Passer as 1.5, so if my 2 Pawns include a passer it will be 35- | 30-35).' No, this is the flaw of your method (but try to refine it): Chess is not played against probabilities, as in say poker. There is really thought to be a determined outcome in practical playing, just as the theory says. I can have a look at my opponent and ask 'what are the chances my opponent will not see my faked position' - but that would lead to poor playing. Much better is trying to play in positions that your opponent for some reason is not so good at, but it does not mean that one takes a statistical approach to playing. Playing strength is dependent roughly on how deep on can look - the one that looks the furthest. There are two methods of looking deeper - compute more positions. Or to find a method by which positions need not be computed, because they are unlikely to win. 'Unlikely' here does not refer to a probability of position, but past experience, including analysis. With a good theory in hand, one can try to play into positions where it applies -- this is called a plan. If I have an when the position values applies, I can try to play into such situation, and try to avoid the others. When I looked at your statistical values, I realized I could not use them for playing, because they do not tell me what I want to know. A computer that does not care about such position evaluations may be able to use them. But I think the program will not be very strong against an experienced human. But in the end, it is the method that produce the wins that is the best.
H.G.Muller: | Well, let us take one particular position then: the opening position of | FIDE Chess. You maintain that the outcome of any game starting from this | position is fixed? Since there is only a finite number of positions, there is theoretically an optimal strategy. | A quick peek in the FIDE database of Grand Master games | should be sufficient to convince you that you are very, very wrong about | this. Games starting from this position are lost, won and drawn in | enormous numbers. There is no pre-determined outcome at all. They probably haven't searched through all positions to find the optimal strategy. | Computers that use the statistical approach, such as Rybka, are | incomparably strong. Humans, using the way you describe, simply cannot | compete. These are the facts of life. I suspect that humans are not allowed to search through zillions of positions like computers do. Specifically, if strong human players are allowed to experiment to search out of the weaknesses of the computer programs and using other computer programs to check against computational mistakes, I think that these computer programs will not be as strong. But as for the question of piece values, humans and computers may prefer different values - it depends on how they should be used.
H.G.Muller: | Chess is a chaotic system, and a innocuous difference between two | apparently completely similar positions [...] can make the difference | between win and loss. This is only true if positions are viewed out of context. Humans overcome this by assigning a plan to the game. Not all position may be analyzable by such a method. The human analyzing method does not apply to all positions: only some. For effective human playing, one needs to link into the positions to which the theory applies, and avoid the others. If one does not succeed in that, a loss is likely. The subset of positions where such a theory applies may not be chaotic, then.
Joe Joyce wrote on Fri, Apr 25, 2008 12:08 AM UTC:This is an interesting and thought-provoking conversation. I've got a couple questions. If the game has a large-enough branching ratio that computers can't adequately search in 'reasonable' [however it's defined] time, then wouldn't the different values that a human and a computer might assign to the same pieces *possibly* contribute to or result from the person's 'intuition'/superior playing ability? Following is a quote from a recent HG Muller post: 'Making the branching ratio of a game larger merely means the search depth gets lower. If this helps the Human or the computer entirely depends on if the fraction of PLAUSIBLE moves, that even a Human cannot avoid considering, increases less than proportional. Otherwise the search depth if the Human might suffer even more than that of the computer.' If each side gets multiple moves per turn, this would increase the branching ratio. But without changing other things about chess, the human would probably be even more at a disadvantage; in Marseilles Chess, for example, with its 2 moves/side/turn, because the computer would calculate that out easily, correct? Consider a larger game, with several kings and several moves per turn. Let each side have as many moves per turn as they have kings. Restrict movable pieces on each side to only those friendly pieces within close proximity of the kings. This begins to shift the advantage to the human, I suspect, especially when there are maybe 6 - 8 kings or more per side, the pieces are reasonably simple, easy to understand and use, work well in groups, and number few in variety, with fairly high numbers of each type of piece. This should shift the game more toward pattern recognition and away from pure brute-force calculations, which would seemingly take rather long. Opinions? Btw, I really haven't played FIDE seriously in 4 decades and I never got a rating, but my ratings at CV are 1550ish lifetime and bouncing around in the 1600's for the past 18 months, and I'd really love to get a chance to play against a program in games like the kind described above.
H.G.Muller: | Computers have no insight what to prune, and most attempts to make | them do so have weakened their play. But now hardware is so fast that | they can afford to search everything, and this bypasses the problem. So it seems one should design chess variants where the average number of moves per position is so large that one has to prune. | Making the branching ratio of a game larger merely means the search | depth gets lower. If this helps the Human or the computer entirely | depends on if the fraction of PLAUSIBLE moves, that even a Human | cannot avoid considering, increases less than proportional. Otherwise | the search depth of the Human might suffer even more than that of the | computer. So it is not as simple as you make it appear below. I already said that: the variant must be designed so that it is still very strategic to human. - It is exactly as complicated as I already indicated :-). Therefore, I tend to think that perhaps a 12x8 board might be better, with a Q+N piece, and perhaps an extra R+N piece added.
H.G.Muller: | It never happened to you that early in the game you had to step out of | check, and because of the choice you made the opponent now promotes with | check, being able to stop your passer on the 7th? Early in the game, most things happen by opening theory. And if one is getting an advantage like a passer, one should be careful to not let down the defense of the king, including computing checks. With those computer programs, a tactic that may work is to let down the defenses of the king enough that the opponent thinks it is worth going after it, and then exploit that in a counterattack. | I think that if you are not willing to consider arguments like 'here I | have a Knight against two Pawns (in addition to the Queen, Rook, | Bishop and 3 Pawns for each), so it is likely, although not certain, that | I will win from there', the number of positions that remains acceptable | to you is so small that the opponent (not suffering from such scruples) will | quickly drive you into positions where you indeed have 100% certainty.... | That you have lost! As I said, the outcome is decided by the best playing from both sides. So if one starts to play poorly in the face of a material advantage, that is inviting a loss. So a material advantage of one pawn must happen in circumstances of where one can keep the initiative, otherwise, it might be better to returning that material for getting the initiative hopefully. | What is your rating, if I may ask? I have not been active since the 1970s, just playing computers sometimes. About expert, I think.
H.G.Muller: | Why do you think the bigger board and the stronge piece make the game | more strategical? I said: if one increases the average number of moves in each position, then a full search may fail, as there will be too many of them. Then a different strategy is needed for success. If it is doubled, then in a 7-ply search, if the positions are independent, a search for all would require 2^7 = 128 more positions to search for. If there are 10 times more average moves, then 10^7 more positions need to be searched. Strategic positions is another matter: indeed, in orthodox chess, trying to settle for positions were advantage depends on long term development is a good choice against computers, the latter which tend to be good in what humans find 'chaotic' positions. The design of a variant must be so that it admits what humans find strategic, and so it is possible to play towards them from the initial position. I am not sure exactly what factors should be there. Just putting in more material may indeed favor the computer. In orthodox chess, one can stall by building a pawn chain, and then use the minor pieces for sacrifices to create breakthrough. The chess variant must contains some such factors as well.
H.G.Muller has written here 'It is funny that a pair of the F+D, which is the (color-bound) conjugate of the King, is worth nearly a Knight (when paired), while a non-royal King is worth significantly less than a Knight (nearly half a Pawn less). But of course a Ferz is also worth more than a Wazir, zo maybe this is to be expected.'
Ralph Betza has written here 'Surprisingly enough, a Commoner (a piece that moves like a King but doesn't have to worry about check) is very weak in the opening, reasonably good in the middlegame, and wins outright against a Knight or Bishop in the endgame. (There are no Commoners in FIDE chess, but the value of the Commoner is some guide to the value of the King).'
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The description contains several errors: The right corner of White A ('South') must be a dark square. The book written by Theodor Müller-Alfeld contains a rather long explanation why this MUST be so. The position of the Queens and Kings must THEN be exchanged so that the Queens are on the square of their own color. Ralf