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Comments by MichaelNelson
L. The list of official nominations for the variant-by-committee.[All Comments] [Add Comment or Rating]The pawn rule voted on is that Eaglets do not promote--so no more than 8 stones can be on the board.
Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]I wonder what thoughts Robert and others have about multi-move mobility and its influence on value. For simplicity of figures, let's calculate empty-board mobility starting on a center square. In one or two moves, a Rook can reach all 64 squares, while a bishop reach 32. On the other hand, a Wazir can reach 13 and a Ferz can also reach 13. Are crowded-board, averaged over all starting square numbers for two-move mobility of use for piece values? Would it be necessary to also calculate three-move, etc mobility? Another question from the numbers above--does this indicate that the Bishop is affected more detrimentally by colorboundness than the Ferz is?
Robert With regard to the multi-move mobiltiy calculation, I think we can ignore levelling effects at the M2 etc level as well--levelling effect can't be calculated on a per piece basis at all. For example, in FIDE Chess, the levelling effect brings the queen's value down--but add a Queen to Betza's Tripunch Chess and the levelling effect brings its value up! I think the correct way to allow for the levelling effect is to calculate all piece values ignoring it, then correct each piece value by an equation which compares the uncorrected value to the per piece average (or perhaps weighed average) value of the opponent's army. So the practical value of a piece depends on what game it is in.
Evolution Chess. Game where pieces add the abilities of pieces they capture. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]A very pretty game, more playable than absorbtion. It gives me an idea a variant: When one piece captures another, any DNA the captured piece has that the capturer does not have is added to the capturerpiece, but any DNA that the pieces have in common is removed form the capturer: Rook captures Bishop = Queen Rook captures Queen = Bishop Rook captures Amazon = Cardinal Cardinal captures Queen = Marshall Knight captures Knight = nothing! (suicide capture) I wonder how this would play?
Ideal Values and Practical Values (part 3). More on the value of Chess pieces.[All Comments] [Add Comment or Rating]It's wonderful to hear from the Master on this topic. I really mentioned the geometric move length becuse you mentioned it in the article--the key point was the comparison of mobility ratios to value ratios and the Rook discrepancy. We need about 10 orders of magitude above excellent for Ralph's work on the value of Chess pieces--I would nominate it as the greatest contribution to Chess Variants by a single person. I am convinced that the capture power and the move power are not equal, but that the difference will only be discenable when extreme. An example--compare the Black Ghost (can move to any empty square, can't capture) to a piece that cannot move except to capture, but can capture anywhere on the board (except the King, for playability)--clearly the Ghost is weaker, though its average mobility is higher. I feel that WcR will be perceptibly stronger than WmR but I could be wrong. I suspect the effect is non-linear with a cutoff point where we don't need to worry about this factor. I also think that the disrepancy will be less than the discrepancy between the actual value of the WcR and the average of the Wazir and Rook values. This discrepancy may be non-linear as well.
I would not call the magic number arbitrary--it is empirical, it cannot be deduced from the theory, but I think the concept has an excellent logical basis. For piece values we want to have sometihing that allows for the fact that the board is never empty, that takes endgame values into account, but is weighted towards opening and middlegame values. So let's take a weighted average of the board emptiness at the opening (32/64) and the board emptiness at its most extreme in the endgame (62/64). Let's weight them in a 3:2 ratio to bias the average toward the opening. This gives a value of .6875 -- right in the middle of the range of magic number values that Ralph uses! The 'correct' value can only be determined by extensive testing and it might well be .67 or .70 -- but I am quite certain it is not .59 or .75! A way to verify this would be to do some value calculations for a board with a different piece density that FIDE chess, then see if the calculated magic number for that game yields relative mobility that make sense (as verified by playtesting). Sticking to a 64 square board, imagine a game with 12 pieces per side. This game has a magic number of .7625 -- I predict that the Bishop will be worth substantially more than the Knight in this game. Now a game on 64 squares with 20 pieces per side. This game's magic number is .6125 -- I predict the Knight is stronger than the Bishop in this game.
The is an ideal test bed for the WcR vs WmR question and also the question of asymmetric move and capture vs symmetric move and capture. Run three sets of CWDA games: 1. Remarkable Rookies vs. Remarkable Rookies with WcR in the corner 2. Remarkable Rookies vs. Remarkable Rookies with WmR in the corner 3. Remarkable Rookies with WcR vs Remarkable Rookies with WmR If I can find the time, I will run some Zillions games over the weekend. In thoery, the short Rook used in the standard Rookies is equal to the WcR and the WmR. I predict that testing will show WmR the weakest and the other two quite close, but the only result that would really surprise me is for the WmR to beat the WcR consistently.
Peter brings up an interseting observation about Rook values approximating empty board mobility. Yet the short rooks seem a little weak by this standard, just as the usual crowded board mobility makes long Rooks too weak. The Rook's special advantages over the Bishop and Knight (interdiction, can-mate) are endgame advantages--so empty board mobility or at least a higher than normal magic number might be the way to quantify the value of different length Rooks among themselves. An R7 is much superior to an R3 in both can-mate and interdiction. And Rook disadvantages (lack of forwardness, hard to develop) apply regardless of length so they would cancel out in this comparison.
With regard to the WcR vs the WmR, I wonder if the tendency at least in the endgame is for the capture power to be more important offensively and the non-capturing movement to be more important defensively. I also wonder if unbalnced pieces in general tend to belong to the category of 'it's worth x, but you really should trade it before the endgame.' In the late endgame, an R4 might be superior to both WcR and WmR by a perceptible margin.
Perhaps Ralph's conjecture that mobility has a non-linear (yet fairly close to linear) relationship to value is the real starting place for these calculations, rather than forking per se. What kind of non linear equation would we be looking at if we assume without proof that that the Spielmann values (N=B=3.0 pawns, R=4.5 pawns, Q=8.5 pawns) are correct?
Robert, That is puzzling. Are there value gaps between the other augmented Knights or do they test out fairly equal? Value of NF vs. R I could argue either way as their moves are so unrelated. I would think that the NF would be the strongest augmented Knight (even though less mobile than NW) as it masks two Knight weaknesses: colorswithching and inability to move a single square. NW masks one step inablility but isn't as forward as NF. NA and ND mask colorswitching and give a a lot of coverage to the 2-square distance. These are very likely quite well mathced: NA more forward, ND more mobile. I really never had though of colorswitching as a major disadvantage, I have even doubted it is worth considering. On the other hand one of the nice things about Rooks is that they are neither colorbound nor colorswitching.
More thoughts on augmented Knights: Part of the advantage of the augmented Knights over the Rook may be a Zillions artifact--Knights are strongest in the opening, Rooks in the endgame. Zillions sometimes has trouble getting to an endgame, where human masters would. If my conjecture is correct, setting Zillions to deeper plies would show the gap reducing or increasing much more slowly than normal for repeating a Zillions calc at higher plies. I suspect your results are not anomalous among the augmented Knights. The NF has yet a third advantage--it cannot be driven from an outpost square by an undefended pawn! All other augmented Knights can (as can the Rook, but outposts are more important for short range pieces). This factor is also almost certainly a part of why the Ferz is stonger than the Wazir. I would be curious to see what the numbers are for the various augmented Knights vs Rook and each other if Berolina Pawn are used. I predict NW the strongest but with a smaller gap, and Rook significantly better vs augmented Knights (easier development as well as can't be attacked by an undefended pawn).
Glenn's Decimal Chess. A 10x10 blend of FIDE, Shogi, and Xiangqi influences. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]A most pleasing blend of Western Chess, Xiangqi and Shogi. The piece set is most entertianing and seems to work well together. The Ogyo is more valuable in this game than it would be in a FIDE-like variant: it has the same horizontal King interdiction power as the Rook, and vertical interdiction isn't needed--the King facing rule provides it.
Maxima. Maxima is an interesting and exiting variant of Ultima, with new elements that make Maxima more clear and dynamic. (Cells: 76) [All Comments] [Add Comment or Rating]Roberto, Maxima is a very fine game. With respect to the value of pieces, I wouldn't even attempt to calculate the values in an Ultima Variant--the multiplicity of capture types means that this will be far harder than the value of Chess pieces. But I believe it is doable in principle. The reason I'm interested in the value of Chess pieces is for game design. I want theoretical values so I can have an idea what an unfamiliar piece should be worth. I particularly have an interest in Chess With Different Armies and most especially the 'build your own army' variants. The ideal value won't and cannot be perfect, but it should be a decent starting place--practical values will always be empirical, and will vary by game context. For example, play a lot of Chess using Berolina Pawns--do the Bishop and Rook have the same values relative to each other as in FIDE Chess? Zillions values are about useless for pieces that are even slighty unorthodox--even the Bishop is overvalued compared to the Knight. That's why Zillions programmers have techniques to inflate piece values.
Ryu Shogi. Large modern shogi variant. (7x12, Cells: 84) [All Comments] [Add Comment or Rating]I judged this game in my group during the preliminaries and have I higher opinion of the game than the author does. A refreshing change of pace for the Shogi player. I think the design as submitted is a good one--in fact I voted Ryu Shogi above the eventual winner. The only design decision I would change if it were up to me is to eliminate the rule that a promoted piece reverts to non-promoted if it returns to the first zone--it makes for a stronger defense if you have the option of anchoring your weak pieces with a strong piece. All in all, a fine design.
Outback Chess. New pieces on plus-shaped board. (10x10, Cells: 84) [All Comments] [Add Comment or Rating]Timothy, Congratulations on a well deserved win. There were so many fine games that any number of them might have been chosen, but the judges certainly made a very reasonable choice. Outback gets gets better and better as you have more exposure to it. You know it will be a fun game by reading the rules--play a few times and you will know it is also a very fine game. You have created a real gem.
Invent-and-Play. A design contest and a small PBEM tournament, combined![All Comments] [Add Comment or Rating]A really fine contest--Tony Quintanilla and I have been doing this informally among ourselves. I'm looking forward to more games with more designers!
Ivan Derzhanski is almost certainly right. Ancient peoples would think of a move of three squares as including the starting square but more modern people with a better understanding of zero would think of a move of two squares not including the starting square. There may be areas of confusion in ancient sources espaecially compilations from multiple sources--this might be the real origin of the rule in Tamerlane that the Bishop cannot move one square, for example. Comparable examples in other fields: Julius Ceasar often sent coded messages using the alphahbetic substituion A=D, B=E, C=F, etc. He and his contempories described this as advancing four letters, we would say three. According to the New Testament, Jesus died on Friday, was in the tomb Saturday, and rose from the dead Sunday--expressed in the creeds as 'On the third day he rose from the dead.' No doubt we would say 'On the second day . . .' if we hadn't heard it so many times the other way.
Ryu Shogi. Large modern shogi variant. (7x12, Cells: 84) [All Comments] [Add Comment or Rating]Jared, I would suggest eliminating rules 2, 6 and 7 and rephrasing rule 4 to conform to the elimination of rule 6. The bare King rule is unnecessary--if the player has only his King and nothing in hand he can be checkmated quite easily. I suggest rewriting rule 1 to allow drops in the fourth zone with these provisions: 1. You may not promote as you drop (same as Shogi). 2. To promote, you must move the piece you dropped in the fourth zone within the fourth zone (contrary to Shogi, where you can promote a piece whose move starts in the promotion zone and ends outside it). I would also consider eliminating the pawn drop restrictions--definately the file restriction and possibly the checkmate restriction as well.
Wizard's War. Game with piece-creating Wizards and a board divided into arena and enchanted sections. (10x10, Cells: 84) [All Comments] [Add Comment or Rating]I had never been happy with the 150-move limit, but I just wasn't able to write an an adequate 50-move rule in time for the contest deadline. In fact, I have several me vs Z and Z vs Z games in my library that were in doubt on move 150 but won by move 170, where a draw would have been declared even though progress was being made. By the way, games of this length are extraordinary--the most recent involved me making a very long comeback from being within a hairbreath of lost at move 75. On the other hand, I have seen games that were pretty dea by move 100 or so that the new rule will stop before move 150. The new 50-move rule is complex, but is an accurate adaptation of the FIDE 50-move rule to the radically different conditions of Wizard's War. In actaul play, the irreplacablity of a piece will be more obvious than it seems from reading the rule.
Ryu Shogi. Large modern shogi variant. (7x12, Cells: 84) [All Comments] [Add Comment or Rating]Actually, the change to rule 1 is the one I feel least strongly about--you make a good case and your way is simpler. My contribution is not great enough to have a variant named for me--I'd be comfortable with a thank you on the game page, if you insist. On the no checkmate by Pawn drops, you may well be right also -- but this may be less necessary with no drops in zone 4. Personally, the one Shogi rule I have never liked or understood is why it is legal to check the King with a Pawn drop, but not to mate. To me, prohibiting both or neither would seem more logical.
L 
. Chess variant designed by committee.[All Comments] [Add Comment or Rating]Plays poorly--but what an excellent example of Zillions programming that it can play this complex and difficult game legally.
L. Fun contest: Help us create a new chess variant by committee.[All Comments] [Add Comment or Rating]I've been playtesting this and I find two flaws: The Diagonal Bypasser is too weak on a board of this size--since it must move at least three squares to capture, it has few opportunities. The Tower of Hanoi is much too powerful. Potentially you can make eight single stones which equals 8 commoners (non-royal Kings). This is on the high side of 16 Betza atoms (Queen=5, Amazonrider=8) just considering that the commoner is the strongest 2-atom piece. Then there must be an unknown addition for the value of the right to recombine. The endgame is entirely dominated by the tower. I've been experimenting with two revisions to address these issues: The Diagonal Bypasser can capture on any square orthogonally adjectent to its path, even though the square is also adjacent to the starting or ending square. DBb2-d4 can now capture b3, c2, c4, or d3 (but not a2, b1, d5, or e4). Thius makes it a more useful in the middlegame and fairly stong in the endgame. Te Tower's maximum move is reduced to one less than its height: a full tower can move 7 squares, a three-stone tower can move 2, a one-stone tower is immobile. You cannot split off a single stone, but can leave a single stone behind when splitting. The potential value of the tower is more like 8 atoms and considerable plus values, still dominating, but its dominance is much less absolute. Preliminary playtesting indicates that these two rules make for a more balanced game. Both Eaglet promotion and The Cube seem quite workable. Early promotion, (especially to Mules) is quite easy unless the enemy works to prevent it, but the opponent can adopt a symmetric strategy and stand pretty well. With players who use the cube sparingly (only for a large material/positional gain or to prevent a large material/positional loss), The Cube shifts the advantage to Black--making it about the same size as White's advantage in FIDE, I'd guess. If players use the cube liberally (to get small gains or prevent small losses), the game is nearer even. I suspect that a player using the cube sparingly will beat an equally skilled opponent using the cube more liberally unless the conservative player's standard's are too high (for example only to give or prevent immediate mate).
I'm further experimenting with giving the Diagonal Bypasser the ability to make a one square non-capturing orthogonal move. This addition makes the piece more powerful by removing colorbinding. It also elimnates an oddity in Eaglet promotion--under the offical rules, you can't promote to DB without the use of an enemy piece, since two DB's can't be oriented correctly.
I've submitted a ZRF for Mike's Camel Chess--a variant with the enhanced Diagonal Bypasser and more limited Tower of Hanoi as defined in my previous comments. It seems to be considerably more playable, but preserves the essential flavor of Lùotuoqí. The biggest difference between Lùotuoqí and FIDE Chess (IMO) is not the Tower, the Bypasser, or the Cube but the Eaglet promotion rule--promotion is possible early and will normally occur on the player's own side of the board.
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