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Comments by LarryLSmith
Games with multiple moves per turn will seriously bog down most search algorithms. The increased potential of field positions does tend to exponentiate. What can 'assist' these plodders is some form of 'intuitive' step in the depth search? Intuition being the ability to reach conclusions with incomplete information. [Somebody has probably already done all the following, but I merely give them as an example.] Humans(most anyway) look beyond their current move toward a position which often there may not be a clear path. Sometimes this is simply a desire which motivates the play and may actually never be achieved. A programmer might accumulate enough data to create a database of 'favored' field positions which the 'AI' could then use to influence its overall play. Another 'intuitive' leap could be the assumption that a series of turns would involve a specific number of pieces. Focusing the search on a specific series of moves and exchanges involving only these pieces. As the ply depth increase, those pieces of this group which were removed from play would not be replace by others which were earlier discarded(new pieces introduced during the search, whether by promotion or changing sides, might be considered part of this evaluated group). Of course, these groups could not simply be made up of the 'best' pieces on the field. There are many possibilities to these 'intuitive' leaps. Games can be evaluated in a variety of ways. A programmer needs to think beyond the linear progression of turns. Maybe a search engine which works backward('seeing' a future position and attempting to un-create it to the current position).
Thanks for the heads-up on the info, Omar. Kinda thought the piece values would be based upon not only their rank(power hierarchy) but also upon their position in relation to the opposing pieces. For example, the Elephant would be a very powerful piece but the opposing Elephant could lower that value simply by being within its area of movement(and this effect could be mutual). Blocking an equal, or even lower, ranked piece could be considered an asset to its value. Particularly when it relates to Rabbits. Keeping the opposing Rabbits as far from their last rank could be considered a positive field position. So, not only the value of the Rabbit could be based upon its particular position on the field but the values of all the player's Rabbits could be used to calculate an effective field position. And Freezing would also be a value. The piece which is 'frozen', and the pieces which is doing the 'freezing', could have their overall value(or simply a sub-value) modified by this condition. This could also be further modified by the positions of other pieces in relation to these. I've already coded a ZRF so that the engine 'randomly' initiates a set-up pattern for both sides. This allows me to test out a large number of potential set-up patterns. Of course, the current code is rather dim, being able to only look-ahead a few full turns. But I can manually create possible positions on the field and see how they will play out(if I have a lot of patience). A simple translation of this code into Axiom will be the first step of the project.
I was thinking of trying out the Axiomatic Development Kit with one of my old Zillions implementation. Now, I've decided to apply it to this game. Not saying that the engine add-on will improve the computer play enough to win the contest. But it will be a challenge to push the code to its limit. Even after simply coding the rules into the application, I plan to run many computerVScomputer games to tweak its dynamics. For example: Are there any optimal set-up patterns which the computer might select from? Does having certain pieces on certain positions improve the play of the program? And, exactly what are the values of the pieces in this game and how would they be expressed? This will be My Summer Project. Looking forward to the vid-strain and the coffee jitters. ;-)
You might check out Chapter 2 of Analysis and Implementation of the Game Arimaa by Christ-Jan Cox (Universiteit Maastricht, Institute for Knowledge and Agent Technology). The paper is available at the site.
I reviewed this game for Abstract Games Magazine, and helped optimize the Zillions implementation. [I recently downloaded the implementation from the game's site and it throws an error message about being unable to render 'board.bmp'(not my creation ;-)). I simply screen-captured the image in Windows Picture and Fax Viewer and replaced the original bitmap. I'm sending this correction now.] I love this game. It's simple and complex. It does resist computer quantification. In fact, its developer has a challenge, which includes a financial reward, to any programmer who can code a program that will play this game well enough to defeat three human opponents(see site for details). There are also several academic papers at the site about Arimaa and computer programming. This should give the interested a serious heads-up about the task. I'm sure that it will eventually be quantified. It will be interesting if it occurs before 2020.
I used 'active' Pawns on both levels. Of course, this did get a little tedious during opening development. But here's an idea(not mine). Dan Beyer created an interesting 3D Pawn which extended through the levels of the field, occupying the cells above and below it. The same might be done on this field. The two Pawns which occupy the same positions on each level would move as a unit to the same destination cell of each level. But would be captured as individuals. This would mean that as a unit they would simply move as Mad Queen Pawns, but when one was captured the other is now free to exercise its 3D pattern in this game. When capturing as a unit, only one of these two moving Pawns need take an opponent. Needless to say that if a friendly piece occupies the similar target cell of the other level such a capture would not be permitted. This would speed up the opening while allowing a sufficient 'barricade' against the advancing opponent. And if the two Pawns were able to maintain their unit upon promotion, the player could gain two seperate power pieces. Thus assuring the players of necessary material in the endgame. Of course, if a single Pawn moves to a similar cell on one level as another friendly Pawn on the other they would then be considered a unit and be moved as such from that point. Just a thought.
Okay, I've run a few games. Just a few knee-jerk reactions. ;-) I like the zig-zag moves. They can just be a little tough to visualize while playing. At this point I do not know how to make this easier. Familiarity should solve it. I'm not happy with the fact that power pieces(in the standard array) are able to threaten several Pawns initially. This can restrict the opening potential, which should be as high as possible to assure a large variety of games. I actually coded a variant with an additional row of (active)Pawns on second field, and moved Black's power pieces to the second field. As stated in the rules, these extra Pawns block the initial assault by their own power pieces, forcing the player to develop to bring most into play. These extra (active)Pawns can get a little crowded at first but they do offer a high potential of promotion which will increase the opportunity for checkmating the opponent. And they can be effective during play by restricting those zig-zag moves.
Vous jouez deux jeux, le vôtre et votre adversaire.
I actually downloaded this implementation this morning. Just haven't gotten around to trying it out. It appears to be an interesting 3D Chess variant. I look forward to playing the game.
Throughout history there have been occasions where persons have purged society's database. Libraries burned, authors executed, inventions destroyed. All for the reason of simplifying their existence and controlling the common man. Did this improve mankind's state? Or did this actually cripple mankind's intellectual evolution? The latter was most likely the case. Chess has evolved from simplicity to it current complexity. The thinking person would realize that it will continue to evolve in complexity rather than slide back into simplicity. If only to continue to challenge the mind. Whereas, before the last of half of the twentieth century, most people had little contact with others outside their direct environment. Their exposure to ideas outside that environment was rare or often slow to arrive. Now, with the Net, all those developing concepts which might have gone un-noticed can be presented to an enormous audience. To evaluate and/or play. No one should be forced to appreciate any particular form of game. This would be self-defeating of the concept of play. Which is a part of the very nature of humans. Likewise, those who desire to either promote a particular form of play or do not appreciate other forms should respect their fellow players. If they desire to apply particular parameters to the development of their particular games, they are well within their rights. But to demand such compliance from others is only a high state of hubris. Consider a mind which has existed within a 'box', surrounding by what it knows within this domain. If it is allowed to peek outside and view the infinity of chaotic potential, it may recoil in fear rather than amazement(or amusement). Unable to accept or comprehend. Such a mind should not be harassed to accept such a challenge. Merely pitied.
Thanks for the kudos.[blush] I will admit that Nemoroth had the strongest influence on this variant. Its interlocking conditions inspired me. But rather than make them 'painful' to consider, I opted for a more 'logical' approach to this interactivity. Not saying that I succeeded, just a goal.
Allow me to list and explain those adjustments which were made with this update. Playtesting determined that the introduction of five pieces during the production phase was rather excessive and could place the second player in a negative position often. Thus the potential introductions were reduce to two. And these introductions were predicated on the presence of a Nurse for each. This now turned each Nurse into a highly desirable target. The loss of each Nurse would reduce or eliminate the player's production phase. The rule that permitted two Nurses to be introduced together was eliminated to strengthen this aspect of the game. The Soldier is now required to be introduced adjacent a friendly piece. This reduced the number of potential introductions, giving the opposing player a break there. This also expanded the power of the Drone. Besides assisting the Nurse in moving some of the pieces around the field and assisting the Soldiers in their attack lines, the Drone now can be used to claim distant positions. This rule also allows for patterns and positions on the field which each player will vie over. The Highborn was only slightly adjusted. The previous form of promotion was merely a change of state but not position. In the interest of keeping the endgame interesting, the Highborn is now allowed to move and immediately promote on its destination cell. Now the Queen is no longer the prime determination of the production phase, it was no longer beneficial to have more than one. So, simply maintaining a Queen on the field became a goal in the game. This eliminated the large potential of attrition-decided games(sometimes very long indeed). One of my personal parameters applied during this 'adjustment phase' was that, as much as possible, the bare bones of this game would remain untouched. For instance, the field, the initial number of pieces and their basic movements. Keeping these changes to those rules which affect the interaction between friendly pieces. And since most of the changes were needed to reduce certain aspects of the interaction of hostile pieces, not adjusting either the simple move or capture ability of the piece proved challenging. At this point I am quite happy with the game. And it appears to play quite nicely. But, fair warning, playtesting continues. Without a large volume of played games, a designer cannot say that a game is completely error-free.
Once again I've updated the rules for this game. Let me first apologize to those who are adverse to unfinished games being published at this site. I primarily presented this form of play as an example of a game which would be difficult to get a computer program to play well. Obviously, these rule changes have reduced that difficulty. Again let me thank Joe Joyce for the discussions which resulted in the modification of this game.
The game can definitely let a player recover from an error. Maintaining the exchange ratio appears to be necessary. I anticipate that the current game I'm playing will exceed 70 turns. Looking at the potential of a hundred-turn game will often scare the impatient. ;-) Has anyone determined the various combinations of pieces needed in the endgame? I like the pattern that a Minister and Dabbaba take when cornering the opposing King.
I am currently playing a round of this game with Joe at the Game Courier. And I really like it. In its simplicity, it has expanded the strategy needed to prosecute a decent game. A player cannot rely on a single line of assault to accomplish the mate, they will need to think in terms of a series of battles to reduce and penetrate the opponent's ranks. Without sliders, the players need to closely engage one another. This can create several areas of serious contention on the field. And each might equally lead to success, so that the opponent risks catastrophe if each are not taken seriously(particularly in the opening). Right now, Joe and I(or at least I am) are testing to determine the effectiveness of Pawn strutures against this large variety of leaping piece. So far, they seem to hold up well. Though the other pieces can quickly bypass them. In itself this is not a bad thing since the opponent can simple maintain a strong defense, and not readily abandon their Pawns. Those players who are familiar with the Mad Queen variant will find much that is familiar. They will not find this game difficult to learn, though application of the Mad Queen's common strategy may prove disastrous.
One way to influence a simple look-ahead is to establish goals within the game. For example(just spit-balling here), the creation of a particular Pawn structure. The engine would modify its evaluation of the play to include achieving this particular condition. Each of these 'goals' might be weighted for both priority and field condition. The engine can be easily 'tricked' by having the positive or negative conditions of these 'goals' affect its evaluation of each plys. The opposing player's achievement of these same goals can also influence the evaluation. There could even be the field position whereby the conditions and/or priority of these goals may change.
Very interesting comments about chess(or simply boardgame) programs. Creating characteristic plays which could translate into any ruleset will definitely be challanging. Take for instance the use of 'pawn' structure. What parameters might be considered within a characteristic play? Also there might be the consideration of territories and patterns of pieces as characteristic play.
I have Kanji fonts for my browser and these characters do not show.
I have updated the rules, limiting the number of Workers on the field for each player to eight. With a little play-testing and a lot of discussion with Joe Joyce, it was determined that unlimited Workers always allowed the first player a significant opening advantage. This restriction actually plays rather nice. With the limitation on Workers follows a limitation of potential introductions, so each player must consider these careful. And this also brings the game closer to being quantified. ;)
Summoning allows the movement of pieces between the 9x9 and 8x8 fields. Notice neither Æther nor Codex are eligible to change fields. The player's Æther would only negate the opposing Elements.
John, Exactly what do you not understand? It would be helpful if you provide some form of analysis(comparitive or otherwise) to justify your position. Please point out these 'complexities'. I will freely admit that this game like Rithmomachia(see Boolean Rithmomachia for an update to this medieval game of numbers) can take more thought processes than the Mad Queen variant. -Larry
I worked up a Zillions implementation of Ecila several years ago. But unfortunately the graphics were rather poor, so I abandoned it. I've still got the code somewhere. I'll probably dig it out and try again.
You can find the rules for Sphinx Chess at this site on the V.R. Parton page. It is in the paper entitled 'Chessical Cubism or Chess in Space'. It is headed as 'Sphinxian: Chess'.
I've updated this page with new graphics. Also, the Zillions implementation.
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