Comments by jlennert
Currently, a stalemate in Chess is widely recognized as a draw.
Why?
My understanding is that, originally, Chess had no prohibition against moving into check, so "stalemate" didn't exist. The rule against moving into check was added to prevent interesting games from ending early due to a dumb mistake. (I personally think this is a dubious justification--there are many blunders that could lead to the swift and unexpected end of an interesting game, and my gut feeling is that an opponent should be allowed to retract any of them in a casual game and none of them in a tournament or other serious game. I don't see why this specific blunder should be enshrined in rule.)
That changed the win condition from "capturing the king" to "checkmate", and as a side effect created the possibility of "stalemate". But the situations that we now call "stalemate" would have been wins for the side delivering the stalemate before the above rule modification, and the above rule modification was not (so far as I know) specifically targeted at such situations, so it's not clear why it ought to change how the game is resolved in those situations.
Wikipedia has a brief history of the stalemate rule, and points out various people who have argued for or against changing the current rule. But I'm looking for a game design reason, rather than a historical or political reason--is the game BETTER because stalemate is a draw rather than a win? Why or why not?
Kamikaze III. If the lone queen checks, she wins.[All Comments] [Add Comment or Rating]Building an unbreachable defense is probably a part of any winning strategy for white, but surviving long enough to build it looks like the hard part. After what opening is it possibly safe to castle?
If your main goal is just to incorporate "hit-and-run" attacks, you could put them on a less powerful piece. For the Crown also has a piece called the Charger that moves as a R3 but can "overrun" an enemy piece and continue moving up to its maximum range (and even capture multiple pieces in a row). I've seen a couple of other variants with similar pieces. I estimated its value in a FIDE context as ~6 pawns, but that hasn't been tested and might be far off. If you happened to produce any new information on its value, I'd be interested. (Trivia: The last expansion for For the Crown originally had another unit called the Behemoth with the same "overrun" mechanic, but on a Q3 instead of a R3. It got scrapped because it made it too easy to obtain a perpetual check.)
Joe Joyce's piece is almost the same as the Warlord in my game For the Crown (the Warlord is allowed to return to its own square, though I don't think I've ever seen someone exercise that option). I priced it slightly lower than the Queen, but that's only because I believe long-range moves are more important in For the Crown than in FIDE; I will still often promote to Warlord over Queen (since the promoted piece is already on the enemy back rank). I've found it's important to plan your defense against a charging Warlord at least a turn or two before it arrives. (Though in For the Crown, that usually means "drop some pawns in front of your King", which doesn't translate to FIDE.)
Seems pretty complex for a single piece. The combination of double-move AND leap, and the nuanced anti-trading restrictions, jumps out at me as being an evolutionary design and not very elegant. Kind of like FIDE pawns (with initial double-move, en passant, promotion...). Pawns have been heavily tweaked over the years. That probably makes FIDE a better game, but I would be reluctant to import all of those quirks into a new game--especially one where pawns weren't a major focus and/or where the target audience wasn't already familiar with them. (And in fact, many casual chess players don't even know about en passant.)
Buypoint Chess. Buy your fighting force - each piece costs a number of points.[All Comments] [Add Comment or Rating]Is there a page somewhere that summarizes all of your experimental results for piece values?
There seems to be a bug on the recent comments page: Mark Bates' comment, which is on another game, immediately folllows H.G. Muller's comment (below) with no intermediate heading row, as if they were on the same game, and yet the two comments after that, which are both on Buypoint Chess, each have their own separate heading. Not sure where to report that.
On the topic of Rook development, it seems possible to me that an R4 or R5 might have its development hindered less than an R7 would, since by advancing past the pawn wall the piece will also become somewhat more centralized, which seems of some benefit to a short rook but probably not to a full one. But I certainly could be wrong.
On the topic of software, For the Crown includes some sufficiently exotic pieces that it seems unlikely I will find any software that can represent all of them without modification (I'm a programmer and could potentially perform some modifications myself)--but testing only a subset of them would still have some value. You can download the rulebook from here (near the bottom of the page) if you're interested in the details, but some highlights include:
- Asymmetrical pieces
- Long-range leapers (bison)
- Bent riders
- Nightriders
- Pieces that can promote as if they were pawns
- A long-range rider with a minimum move distance
- A piece that can exchange places with another friendly piece as a move
- A piece that stays in its original square when making a capture
- A piece that can capture mid-move and continue moving
- A piece that, when captured, goes into it's owner's hand and can be dropped back into play
The ideal software would also handle multiple royal pieces on a side (win by capturing all of them, no restriction on moving into check; corollary: no stalemate) and the option to start with pieces in hand that can be dropped into an empty square on the first rank in place of a move (some pieces can be dropped on the first or second rank).
There's an expansion coming out in a month with yet more weird pieces (example: a piece that moves once "for free" each turn, before you move a different piece).
IIRC, when Betza was considering cannons, he concluded that a standard cannon (move along rook lines, capture by hopping along rook lines) was likely stronger than a bishop, but thought that replacing bishops with cannons in the FIDE opening might not reveal this advantage because it would make development too difficult. He commented that "even replacing bishops with rooks is not that easy", or something like that. I'm curious, have you tried a test where one side replaces its bishops with additional rooks? Also, is your testing software available for others to use? I try to assign values for importing the For the Crown pieces into something like buypoint chess, and it would be nice to check my guesses against a computer. I think I asked this once before and you suggested I wait for Sparticus, but it's been some time...
Well, you somehow decided that the values would follow the formulas:
R2 = R1 * (1 + p)
R3 = R1 * (1 + p + p^2)
R4 = R1 * (1 + p + p^2 + p^3)
and so forth.
That looks like a mobility calculation to me, but whether you choose to call it that or not, the fact remains that your "interpolation" is following a curve that you derived based on ONE of Ralph Betza's ideas regarding piece value while ignoring many other important ideas that he also had about piece value.
I'm saying that I don't think the intermediate piece values are actually going to fall along that particular curve.
Jörg, I'm not sure you've given due consideration to board geometry. Betza's mobility calculations attempt to account for both the probability that a move will be blocked by another piece AND the probability that a move will be blocked by the edge of the board. If you assume that pieces are distributed randomly, then the odds of being blocked by a piece are p^(distance-1), as your formula suggests, but the odds of being blocked by the edge of the board follow a completely different pattern (e.g. for a rook, it's 1 - (distance/8)). That means it can't be accurately represented simply by plugging a different value for p into the polynomial shown in your post.
You also seem to be assuming that piece value is directly proportional to mobility. Most people believe that value has a super-linear relationship to mobility; the evidence being that compound pieces tend to be worth more than their component parts. There are also many things other than mobility that might affect a piece's value; Betza attempted to compile a list here.
Finally, you might want to consider that Betza believed a full Rook had a value closer to 3/2 of a Knight than to 5/3 of a Knight. If that's the case, then it's unclear whether a piece priced at 4 points should aim to be worth 4/5 of a Rook or 4/3 of a Knight--a difference of perhaps 10%, or roughly the difference in your calculated mobility between an R4 and a R5.
You also CAN consider a white pawn on e3 and a white pawn on d3 to be different kinds of pieces, because one of them is only allowed to move to e4 and the other is only allowed to move to d4.
But it is also POSSIBLE to construct the rules in such a way that all pawns share the same rules, and location and owning player are treated as accidental, rather than essential, properties.
You have failed to define the term "piece", which seems to be pretty important. Under your proposed definitions, I think one could make a reasonable argument that StarCraft or baseball are "board games" (in that they are entertainments with rules and goals that contain things that could reasonably be described as "pieces" that move among a predefined set of possible "locations"), which is probably not what you intended. Your definition of "battle game" also seems very overbroad; it includes many games that most people would say have nothing to do with "battle", such as Klondike (card solitaire), Pandemic, etc. You've defined "piece type" as "a group of pieces that are identical to each other". That definition seems to imply that it is a set of specific pieces, whereas I think most people think of a "piece type" as a taxonomical grouping. Furthermore, your definition seems to imply that pieces owned by different players are never the same type, which I think also conflicts with common usage. Your count of "over 2,000 documented board games", while technically accurate, is far short of the true number. BoardGameGeek's game database currently contains 61,611 board games, and if your definition of "unique game" is generous enough to include all the variants on chessvariants.org, then I'd wager the true number is at least 100 times that. You say that "at some point everyone will need to pick a game to play." If you mean that everyone will need to agree on one game to be the only game ever played by any person ever again, I think the idea that this is necessary, desirable, or even feasible is extremely naive. Conversely, if you only mean that a single person typically will not want to play 2,000 games SIMULTANEOUSLY, and therefore any specific individual will need to settle on one game to play on any given lunch break, then the segue to talking about the "best game" seems unjustified. Furthermore, your suggested criteria of "originality" seems to directly undermine the concept that such a thing as a "best game" is possible, since it implies a yearning for novelty. No single game will remain novel forever.
Rococo. A clear, aggressive Ultima variant on a 10x10 ring board. (10x10, Cells: 100) (Recognized!)[All Comments] [Add Comment or Rating]Cannon pawns are hoppers, not locusts. They capture by displacement. They would not be hindered in ANY way by the absence of border squares.
You calculated the probability that a randomly-placed piece will threaten at least one enemy piece. I suggested you could instead calculate the average number of enemy pieces it threatens, which is a different number, because sometimes it will threaten multiple enemy pieces at once. If a King has probability p of threatening a piece in any one of its 8 directions of movement, then the average number of pieces it threatens is simply 8*p, whereas the probability that it threatens at least one piece is 1 - (1-p)^8.
Zillions' estimates are suspect at the best of times, but IIRC it is also known to grossly undervalue capturing power compared to mobility (for example, I believe it considers a ghost to be worth several times as much as a queen). Since capturing is the only difference between most Ultima pieces, I would place exactly zero faith in Zillions' estimates in this case.
I don't have a lot of experience with Ultima or similar variants, but some thoughts occur to me: I think you've overlooked an important advantage the Long Leaper has compared to the Displacer: the Long Leaper may have a choice of several squares it can stop on after making a capture, while the Displacer only ever has one choice. Not only does this give the piece increased mobility, but it makes it harder to defend a piece that is threatened by a Long Leaper. The Advancer/Displacer is an interesting comparison. The Advancer has strictly fewer possible moves than the Displacer, BUT you can "defend" a piece against a Displacer simply by threatening the square it rests on, while defending against an Advancer requires threatening different squares depending on the angle of attack, which seems like it is probably an advantage for the Advancer. I suspect that the traditional FIDE army would still beat an army of equivalent capture-by-approach pieces, but perhaps a mixed army would be more powerful than either simply because it would make defending pieces much more complex for the opponent? I would consider using the average number of possible captures a piece can make rather than the probability of having at least one capture available. For one thing, having a choice of several things to capture sounds useful, especially if some are defended. For another, I think you'll find it's noticeably easier to calculate. Of course, having a choice of 2 possible captures is very different from having the ability to capture 2 pieces at once, which seems to indicate that at least one of those things is going to require special consideration... The value of an Immobilizer might be estimated by computing the moves that your opponent would normally be allowed but that the Immobilizer prevents...though that suggests you're probably going to need to consider mobility and not just capture potential. Also, this might be a case where assuming random distribution could be very misleading. Perhaps immobilizing a piece is really more like a suicide-capture, where you effectively remove the target piece(s) from the game, but also neutralize your own Immobilizer, which now cannot move without releasing its captive? I believe Muller did some experiments suggesting that chess pieces typically got about 1/3 of their value from non-capturing moves and 2/3 from capturing, if their capturing and non-capturing movement patterns were similar in overall power. Is this heuristic likely to hold for Ultima pieces?
I wondered about that possibility, but I was concerned about endgames where there are a couple of pawns stuck somewhere such that they couldn't interfere with a normal mating strategy but where a weak piece that has been artificially designated "can-mate" cannot capture them safely, and therefore the game is technically not a KXK endgame.
> h . . h . . . . . k . . . . . . . K . . . R R . I'm not sure I follow this diagram, but I think I can now envision an arrangement with the properties you describe. Does the same thing still happen if you have nightriders BUT NOT rooks? I suppose you could substitute queens for the rooks, though that would require a promotion...
Dynasty Chess. Missing description (8x8, Cells: 64) [All Comments] [Add Comment or Rating]I don't think that's true about the bishops' value, David. In addition to being color-bound, bishops also suffer a significant loss in mobility near the edges and corners of the board, while rooks suffer much less--due to the fact that the board edges line up with the rooks' moves. (There are also several other strategic differences of uncertain importance, such as the fact that the rook can interdict the movement of the enemy king, and the differing ways each of them interact with pawns.) In fact, I would guess that this loss of mobility is far more important than colorboundness, because players of cylindrical chess (where bishops do not lose mobility at the sides of the board) have reported bishops to be roughly the equal of rooks--despite still being colorbound. It wouldn't surprise me if BK and RK are closer in value than B and R, though at a quick guess I'd expect RK would still be noticeably stronger.
How does the inclusion of Nightriders lead to a mutual perpetual check? Betza also believed the crooked bishop to be worth about a rook, but that's also colorbound, so I suppose it would have the same problem as BD. The "aanca" (W>B bent rider) might also be close enough to be an intersting test, if you want a long-range non-colorbound piece. It's almost certainly noticeably stronger than a rook, but should still be closer to rook than queen. Of course, those both assume your engine can handle nonlinear riders, which may not be the case...
You might also consider repeating your experiment of adding mating potential to a bishop. Another consideration: does the value of mating potential depend significantly on how many other pieces already have it? If you replaced rooks on both sides with a similarly-valued but non-mating piece, does the value of commoners relative to knights go up? If you replaced the bishops on both sides with a similarly-valued piece with mating potential, does it go down? I think Betza suggested once that it was important for a side to have a piece with mating potential, but not so important how many pieces had it.
Arimaa has a special set-up step at the start of the game where white (gold) arranges all his pieces on the board, and then black (silver) gets to arrange his own pieces after seeing white's arrangement, and then white gets the first move. Seeing your opponent's piece arrangement before arranging your own pieces can only be an advantage, so in this case each side receives an asymmetrical advantage in the opening, and it's not obvious how to compare them. It may be less a case of the first-move advantage being small, and more a case of these two advantages canceling out. Or not; I'm just speculating wildly.
The increased knowledge of mating potential has raised the apparent value of Commoner, then?
Alibaba. Jumps two orthogonally or diagonally.[All Comments] [Add Comment or Rating]> > Under what circumstances would you possibly be able to exclude it? > When I have run the test games with an engine that does take full account of the mating potential or lack thereof. And how will you know that there isn't some other potential flaw that you haven't thought of? Presumably a less thoughtful person in your position could have failed to consider the issue you are now addressing, and would therefore already be just as convinced as you expect to be after your next test. Should we dismiss a bunch of experts that have made no mistake you can point out simply because we also can't point out a mistake that your engine has made when it gives a different result? Alternately: there are significant differences between the ways humans and computers play chess, so theoretically some pieces could have a different effective value in human vs. human games than in computer vs. computer. I don't see any particular reason that Commoner should be such a piece. But if it were, a bunch of human experts agreeing on one value and computer tests reporting a different value is pretty much what we would expect to see, right?
> Not 'probably'. I just cannot exclude it. Under what circumstances would you possibly be able to exclude it?
I thought the Rook measurement was off by at least half a pawn, but perhaps my memory is in error. In any case, we have: - (Commoner) One situation where your empirical measurement differs from common wisdom, and you think it is probably due to a failure of your engine; - (Rook) One situation where your empirical measurement differs from common wisdom, but you think it's a failure of definition and you weren't really measuring the same thing; - (Bishop-Knight) One situation where there's a strong possibility that your empirical tests have shone light on an important lesson for theorists, but we still don't know WHY this particular piece would have such a high value, so we can't extrapolate from it (for example, we can't make reliable guesses about the value of a Bishop-Camel or a Bishop-Nightrider) I have great respect for your work and I think it's very valuable, but these still strike me as emblematic of how far we have yet to go.
> In my empirical piece-value determinations I never noticed any significant discrepancy with the orthodox values. Odd, I seem to remember reading about your Joker engine testing material values for FIDE and getting a Rook value that was unexpectedly low. I also seem to recall the same engine testing the Bishop-Knight compound and finding its value unexpectedly high compared to the Queen and Rook-Knight (closer than the values of their component pieces). And I do not recall anyone offering a predictive theory capable of explaining that. Betza also performed computer tests and human playtests on the value of the Commoner (nonroyal King), and was convinced that the computer value was wrong. I recall that you disagree with him on this point, but that Wikipedia article I linked a couple of posts back cites two sources that seem to at least vaguely support his conclusions (end-game fighting power of the king placed higher than knight or bishop). Have your formulas for short-range leaper values been verified by anything other than your own chess engine? It's certainly impressive, and it's plausible, but if it's based entirely on one source, then it's hard to tell how far we should trust it. Perhaps more importantly, symmetrical short-range leapers are a rather special subclass of pieces; I would be hard-pressed to name a single CV whose pieces all fit into that class. Incidentally, did you ever finish that new chess engine you were working on that you said you wanted to complete before running more complicated tests? Spartacus, I think.
I don't have any specific experience with computer players for multi-move chess variants, but I think it is worth noting that while a computer will not be able to see as many TURNS ahead, it should be able to see just as many MOVES ahead as normal. Depending on how you measure quality of play, one could argue that they should play single- and multi-move variants with equal proficiency. Perhaps we should ask: how well do HUMANS play multi-move variants?
Alibaba. Jumps two orthogonally or diagonally.[All Comments] [Add Comment or Rating]There have been many attempts to write mathematical formulas or create tables of piece values, but I don't think any have gained widespread acceptance. Authorities can't really even agree on the values of the orthodox pieces in FIDE Chess, so there's no accepted way to determine whether any given valuation is "correct" (or even precisely what it would mean if it were). Some people have tried computer tests to determine values empirically, which I think is a promising direction, but results don't always agree with other computer tests or with the accepted values (such as they are) of the orthodox pieces, so it's not always clear what they mean, and they're not much help in predicting the value of any piece that wasn't specifically tested.
Most people agree that value is primarily related to a piece's "mobility", or how many different ways it can typically move or capture (after somehow accounting for the fact that certain moves are more likely to be possible than others; e.g. a Bishop can move 7 squares, but only in rare situations).
But then there's a bunch of other factors that we're pretty sure are real but that no one really knows the true value of, like mating potential, development speed, colorbound pairs, stealth, how they cooperate with allied pieces, and so forth. Notice that many of these aren't even intrinsic to the piece, but relate to the other pieces on the board, which means that they change from variant to variant (and even over the course of a single game, as pieces get captured and removed from play).
I found Ralph Betza's About the Values of Chess Pieces to be helpful when I started researching piece values for For the Crown, so that might be a good place to start reading if you want to know more.
The alibaba has similar qualities to a knight (leaping piece, similar range, same number of moves), but its movement pattern confines it to 1/4 of the board (similar to how bishops can reach only 1/2 the board, but moreso).
Betza suggested somewhere in this article on the Crooked Bishop that a non-colorbound piece would be 1.1 to 1.2 times more valuable than its colorbound equivalent, which means a colorbound knight ought to be worth ~87% of a knight. But the alibaba is colorbound "twice", which I would imagine warrants at least applying the penalty a second time, giving ~76% of a knight--a very good match for your estimate. (Though I wouldn't be surprised if "double-colorbound" turned out to warrant a greater penalty than that.)
However, Betza appears to have been talking about pairs of colorbound pieces on opposite colors (like the bishops in FIDE Chess), which are generally believed to be more than the sum of their parts. So that estimate is probably only good if you start with 4 alibabas, one on each "color"--they will be less valuable individually, especially in the endgame (when it becomes harder to find targets on your own "color").
Finally, if you are playing with bishops, rooks, and queens, I would guess that the knight is also benefitting from a "stealth" bonus, due to its ability to threaten these pieces without being threatened in return. The alibaba can only do this if there is another piece in the way (that it can jump over but the other pieces can't), and so I would guess that its true value would be a little bit lower again than the estimate above.
So, in summary, I would guess than 3/4 of a knight is close, but probably a little too high, and would expect the value to fall significantly in the endgame or if you don't get a complete set.
Well, as long as white sometimes wins and black sometimes wins, the "noise" is large enough to overcome all other factors SOME of the time. But if you collect a giant database of master-level games and find that white is winning 53%, then I think it still makes sense to say that white had an advantage, regardless of the theoretical perfect-game result. SOMETHING has to be responsible for the fact that white wins more often than black. So if white wins only 1% more than black, or only 0.1% more, or only 0.01% more, at what point do you declare that the noise has "overwhelmed" the signal and that there is now "no" advantage? I don't see any non-arbitrary way to draw a line anywhere other than zero exactly (i.e. the point where the advantage passes from white to black). So I'm assuming that the "advantage" is the hypothetical difference in win rate between white and black that we would converge upon if we sampled an ever-larger number of games played by "skilled" players. The definition of "skilled" is a bit hand-wavey and probably depends on context, but I think the rest of that is rigorous.
I feel I need to ask again whether you are arguing about the SIZE of the first-turn advantage, or the EXISTENCE of the first-turn advantage? Because you said earlier you were arguing over its existence, but all of your arguments seem to be about its size. You could be a thousand moves away from mounting a credible attack, but that doesn't mean the value of a move is zero. After you move, you will only be 999 moves away from a credible attack, which surely must be at least a tiny bit better than 1000? Your typical player probably won't notice that advantage. But then, a lot of players probably don't notice the first-turn advantage in FIDE, either. Small is not the same as zero, and what counts as "small" depends on how good you are and how many times you're playing. And zero first-turn advantage isn't even necessarily desirable. Suppose we have a game where players are allowed to pass on their turn, the initial array is symmetrical, and the players know that there is no first-turn advantage. Since there is no first-turn advantage, passing is (by definition) at least as good as anything else you can do on your first turn, so you might as well pass. Then the second player is in exactly the same position as the first player on his first turn, so he might as well pass. So not only is the perfect strategy obvious, it's also incredibly boring. But even if passing isn't allowed, the first player either has a move that is EXACTLY AS GOOD as passing--which I'm not sure is possible, and I don't think it changes the outcome compared to allowing passing--or else the best possible move is WORSE than no move at all, which means we've simply traded a first-turn advantage for a SECOND-turn advantage. All else being equal, I think we want the first-turn advantage to be "small". We might even want people to be uncertain whether the advantage lies with the first player or the second player, perhaps by using an asymmetric starting array or placing special restrictions on the first move (such as moving half as many pieces as normal). But if you could somehow prove that the first-turn advantage was exactly zero, I think that would probably end up being bad (not so much because the advantage was zero, but because you were able to prove it).
Joe, notice that all the theories you have advanced to explain the lack of a first-turn advantage are general properties of the game, NOT unique to the opening array. The reversible pieces don't suddenly become irreversible in the late game; the short-range pieces don't turn into long-range ones; etc. If those properties were sufficient to prevent a move from having value, they would prevent ANY move from having value, not just the first or second one. But as Muller points out, it seems pretty obvious that you will quickly lose if you pass ALL of your moves, which means moves must have some value at some point. IF there truly is no first-turn advantage whatsoever, the reason needs to be something special about the opening array, NOT the general properties of the game. The things you cited MIGHT make each move less valuable, but they cannot possibly reduce the value all the way to zero. And while it is conceivable that there is something special about the opening array that puts the first player in a position of zugzwang, it is intrinsically unlikely. Most possible positions in most Chess-like games are NOT instances of zugzwang. And the facts that the opening array appears to be a "calm" position, and that the pieces are reversible, both make it substantially LESS likely to be a position of zugzwang--after all, if my second move can be to reverse my first, and my opponent cannot do anything to hurt me in the meantime, it is difficult to see how the first move could have harmed me. Asking us to verify the non-existence of a first-move advantage by pushing a few pieces around is silly. Based on this conversation so far, the first-move advantage in FIDE is barely large enough to be noticed by masters (it's estimated at approximately one "quantum of advantage"). Perhaps you understand Chieftain Chess as well as a master understands FIDE, but the rest of us certainly do not. Hypothetically, Chieftain could have a first-turn advantage that is substantially larger than FIDE and it would still be all but impossible for us to demonstrate it to you. We "proved" the existence of a first-turn advantage in FIDE only by recourse to a statistically-significant sample of high-level games. Unless you have a similar statistical collection for Chieftain, then none of us have any real evidence one way or the other, so we are reduced to arguing generalities--and IN GENERAL it is safe to assume that a randomly-selected Chess variant has a first-turn advantage.
I wouldn't expect that the addition of noise would EVER completely eliminate the first-turn advantage, just make it less significant. Assuming that players strictly alternate full turns, and that nothing other than the positions of pieces affects the game (e.g. there's no time limit), and general chesslike properties such as perfect information, the only way I can see to have NO first-turn advantage is if the first player has literally nothing useful to do with his turn. No possible piece development, no moving forward to claim extra territory, no starting to launch an attack or race for a promotion, NOTHING. And I question whether that would even be desirable.
If white gets to take an entire turn before black starts, then I think it's appropriate to measure game length in turns, not in moves (if different). Though I've seen several double-move Chess variants that restrict white to a single move on the first turn in an attempt to counteract the first-turn advantage; have you considered a Chieftain variant that only allows white to make half the usual number of allowed moves on the first turn?
If the race metaphor is accurate, I would expect the head-start to be compared not to the length of the runner's stride, but to the length of the entire race. I would guess that a 10m head-start would be much more likely to be decisive in a 100m sprint than in a marathon. Perhaps we should not be looking at the mobility of individual pieces, but the length of the overall game? Piece mobility would likely be a factor in game length, but board size, number of pieces, and several other factors could also be highly significant.
What do you mean by "demonstrated"? You have some proof of the absence of first-turn advantage in Chieftain Chess? Could you perhaps share this proof? I am so far unconvinced. You tell me that you pretty much always win your Chieftain games, which suggests you have not played against any opponents that seriously tax you, which in turn suggests that you have no sample games with high-level play on both sides to use for reference. But you also say that you win with an aggressive strategy, which suggests that you think you can get some advantage by doing something rather than idly maintaining your position, which suggests that tempos have value (at least, you are playing as if they do). Unless you have solved the game or you have a large, high-quality statistical sample showing that black wins at least as often as white, I'm not sure how you could demonstrate the absence of a first-turn advantage, nor does such an absence seem inherently likely to me based either on your testimony or from reading the rules. Keep in mind that the first-move advantage in FIDE Chess is thought (at least by Betza) to be approximately the minimum advantage that MASTER level players will notice in practice; I would hazard that no one currently alive is as good at Chieftain Chess as a master-level player is at FIDE, and so it seems plausible to me that you might not easily notice the first-move advantage even if it were LARGER than the one in FIDE.
So, is your personal standard strategy in a game of Chieftain Chess to maintain a holding pattern and let the enemy come to you? If both players do that, it seems like the game would be awfully boring.
Joe, just to be clear: are you saying you believe that white has NO first-turn advantage in Chieftain Chess, or are you saying that you believe white has a first-turn advantage, but that it is SMALLER than the first-turn advantage in FIDE Chess? I think it is entirely plausible that weaker pieces will lead to a smaller first-turn advantage, since the weaker your pieces, the less you can accomplish each turn, and therefore the smaller the value of a turn. But saying that there is NO first-turn advantage is equivalent to saying that the null move, if it were allowed, would be the best possible opening move. Do you recommend moving as few pieces as possible in the early part of a Chieftain Chess game? Do you think that the best possible second move is to reverse the move(s) made during your first turn? If not, it seems unlikely that the null move is really optimal. Zugzwang certainly exists in Chess, but it's pretty rare. Also, your proposed "Moving 1 Square Chess" rules for knights appear to boil down to "knights move as wazirs". You mandate changing parity every move, but a wazir move changes color, so it will always change parity, while a ferz move preserves color, so it will never change parity.
The first event in a causal chain can be important. I completely fail to follow the "always" part. Perhaps you can find a hurricane that wouldn't have formed if a particular butterfly hadn't flapped its wings, but not every flap of a butterfly's wing causes a hurricane.
But you seem to have missed the thrust of my last post, which was that, even if you were right, that would contradict your earlier suggestion that we can learn something about Chess based on the importance of its first move. If the first move is always the most important, then we cannot learn anything at all from the fact that the first move is most important in this particular case. (See also: Bayes' Theorem.)
But you are also wrong about the first move being the most important, for reasons I have already explained. If we ask how important X is to the outcome of some system, we are comparing two hypothetical situations, one where X obtains and one where it does not, and exploring the difference in the evolution of these two hypothetical systems. So if we ask how valuable a move is in a Chess game, hypothetical examples where we break the normal turn sequence are not only relevant, they're mandatory.
Or, here's a completely unrelated point: ever heard of zugzwang? It's important in, among other situations, the KRvK endgame. The fact that zugzwang exists proves that a move can have negative value, and from that it seems fairly safe to assume that some move after that point has a value higher than it. So that alone shoots down your theory that move-value is strictly decreasing.
In other words, it is possible (fairly easy, in fact) to devise a chesslike board game where black (that is, player two) has a forced win. Therefore, the first move cannot always be the most valuable.
You suggest that we should take the prime importance of the first move as a "clue", and then you justify your belief in the importance of the first move by saying that the first move is always and by definition the most important in all games?
Um.
If I told you we were discussing "value" rather than "importance", would that short-circuit this loop and get us back on topic?
> So the difference between playing white or black ('1 tempo')
Shouldn't the difference between white and black be half a tempo? Giving
black a free tempo at the beginning of the game doesn't cancel out white's advantage, it transfers it to black, so the tempo must be
twice that advantage.The first move in a game of Chess isn't even CLOSE to the most important one in a typical game. If you look through the log of a decisive game, I bet you will easily find at least one point where allowing the player who eventually lost to take 2 moves in a row would EASILY have turned that loss into a win (for example, maybe around the time the queens were exchanged?). I recall reading about a variant on this site where each player begins the game with the right to make a double-move at one point of their choice during the game. The author suggested that forcing your opponent to use up this ability was critical, having an equivalent material value of AT LEAST queen + rook--almost two orders of magnitude above the 1/3 of a pawn we've been assigning to the first-move advantage in this thread. I also see no particular reason to think that a Bishop moving 7 squares has equivalent value to taking 7 consecutive moves in a game of checkers--but if it were true, that would seem to severely undermine your theory that the first move in Chess is the most important one, since no piece can move farther than 2 squares on the first turn.
I'm no expert on Chess, but I think about it this way:
It seems to me that in the opening position of FIDE Chess, most pieces are in quite poor positions, with their mobility greatly restricted by overcrowding and no immediate opportunities to threaten enemy pieces. An extra move can be used to develop your pieces into more advantageous positions, which translates into a higher probability of winning. As a corollary, the value of an extra move changes throughout the game based on how rapidly your position can currently be improved.
In On Numbers and Games, John Conway develops a theory of combinatorial games (Chess doesn't quite fit in this set, but it's close) as being a superset of numbers. Certain games (or sub-positions within larger games) have an exact numerical value because their existence gives a direct advantage to one player (positive) or the other (negative). But other positions have a "fuzzy" value; it's not clear how much advantage they give because it depends on how many moves each player takes (and in what order) trying to improve that particular sub-position rather than some other sub-position elsewhere in the game. He has a concept of "heat" that corresponds to the volatility of a position; the "hotter" a game is, the more advantage can be gained by whoever makes the next move.
(Note: I don't quite follow all of the math in this book and it's possible my description of his theory isn't entirely accurate.)
As for Betza's "quantum of advantage", I think his position was a little more complicated than that. He said that a third of a pawn was roughly the smallest advantage that a master player would notice in practice, and therefore that it makes a good approximation for lots of different minor advantages that are NOT actually equal but all roughly on that scale, and lists a tempo as one of several examples. I believe he talks about this in part 3 of About the Values of Chess Pieces.
Relativistic Chess. Squares attacked by the opponent are considered not to exist. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]The game has certain rules stating what moves are legal and what moves are not. All the stuff about squares not existing is just a metaphor to help explain what moves are legal. Unless you're arguing that we've misunderstood the rules and the pawn in that example isn't actually allowed to make a capturing move to the king's square (supposing for the sake of argument that there was a non-royal piece on that square), then any images or terminology you come up with to describe the situation differently is just window-dressing. The goal of Chess is to capture the enemy king (all the stuff about check and mate is just legal boilerplate). If you let me capture your king, you lose. If you choose to envision the board in a way that implies that I can't capture your king--while simultaneously agreeing that, by the actual rules, I *can*--then you're just practicing an elaborate self-deception. What matters (as far as victory conditions) is the set of legal moves, not the metaphor that describes them.
Carlos, that sounds pretty weird to me. I think the spirit of the rules of Chess is that you really are trying to capture the enemy king, we just forbid moving into check to prevent games ending prematurely due to a dumb mistake; in variants, unless the intent is clearly otherwise, I think we ought to follow that spirit, which means "check" must be construed to mean "your opponent could capture your king next move". Playing on because white doesn't "perceive" the danger, and then forbidding black from actually making the capture because "the goal is to checkmate", seems to me to fly directly in the face of that spirit.
There's no reason you can't make a game that works like that, but inferring that as another designer's intent seems extremely implausible.
...
I think I see a potential for paradox in these rules. Suppose white pawn d3, black pawn d5. At first glance, both pawns seem to threaten e4. But that means that e4 doesn't exist for either player, which means neither pawn can move there. But that means that it isn't threatened, so it does exist...
Or you look at one side at a time, and say, for example, that white is threatening d4, so black can't go there, so black doesn't threaten it. Then there's no contradiction...except that you could equally well rule that black is threatening it and so white isn't! How do you decide between them?
Rules of Chess FAQ. Frequently asked chess questions.[All Comments] [Add Comment or Rating]If it is black's turn, his king is in check, and he has no legal moves, then it is checkmate and he loses the game. You can never have a stalemate while you are in check. I can only assume that either the computer you played with had a bug, or you aren't remembering the details of that situation correctly.
Archabbott Chess. Introduces the Archabbott piece which moves like Bishop + Wazir + Dabbaba.[All Comments] [Add Comment or Rating]Wikipedia and All the King's Men both name the (0,3)-leaper the "Threeleaper" and the (3,3)-leaper the "Tripper", but neither lists an inventor or a variant that uses them.
Betza's notation uses H for a (0,3) leap and G for a (3,3) leap, but I don't recall ever reading how he chose those letters.
Such an app would basically just be an interface to a giant table listing pieces for every possible combination of moves. Assuming you could create that table, the app would be straightforward. I question its usefulness, though.
Firstly, most of the table would either be empty or taken up with obscure pieces that few would be interested in. For every combination of squares you could light up that corresponds to a common compound, there's a ton of combinations like "forward and left as a knight, forward and right as an alfil, or backwards as a ferz or rook" that are just weird. I'm sure you can dig up names and variants for several pieces like that, but it could take a lot of work if you're really being thorough, and the odds of a user stumbling upon any particular one of them are pretty low.
Secondly, for popular pieces, there would be an unwieldy amount of information to display. Take a look at the Piececlopedia page for the Bishop-Knight Compound, for example; it's got a bunch of different names and has been used in a ton of variants (the list on that page can't possibly be complete, but it's already more than one screen of info).
Thirdly, your database would have to leave out (or misrepresent) a lot of important and interesting pieces, because pieces aren't defined only by which squares they move to. The Knight, the Mao, and the Moa all move to the same squares, but they take different paths to get there. Some pieces, like the Cannon, require a hurdle to move. Some pieces capture differently than they move; Ultima is a variant based around giving every piece a different method of capture. Some pieces can make special moves under specific circumstances, like the pawn's initial double-step or en passant capture in FIDE. Some pieces just have weird special rules, like the ability to capture multiple times during their movement, or copy another piece's movements, or move other pieces with them.
The variant you describe is listed on the site under the name Compromise Chess.
For the Crown. A commercial crossover with deck-building games. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]Now seeking playtesters for the second expansion. There's currently an announcement at the top of the Victory Point Games main page; instructions to apply are here.
Courier Eurasian Chess
. Eurasian Chess meets Courier-Spiel.[All Comments] [Add Comment or Rating]Oh. I guess I overlooked it because it has no moves shown.
Looking at the wiki page source, it looks like most of the page is actually embedded HTML rather than normal wiki script. Based on your description, it sounds like you're not seeing that part.
I doubt that someone who is not already familiar with Cannons could deduce all the movement rules of the Cannon and Arrow from those diagrams. The Pawn diagram does not indicate whether it can cross the river (as every other diagram does). Is the rook really estimated to be worth only 8/7 of a bishop? The bishop no doubt benefits from the wide board, but that's a larger effect than I would have guessed. Is there another factor I'm missing?
I never thought it was supposed to be a handicapping system, I thought it was supposed to be a system for creating an initial board position from which a typical player would have equal chances of winning regardless of which side he played. So I am pointing out that: 1) At best, this sytem merely provides MOTIVATION for creating such a position. That's kind of like adverising a "method for lifting heavy objects" and then revealing that the method is to offer a higher wage to employees who can lift more. You aren't solving the problem, you're hiring someone else to solve it for you; the actual problem still needs to be solved by someone at some point. 2) Although this method aligns the player's incentives with the goal in an idealized case, there are many realistic cases in which the player can actually gain a larger advantage by strategically UNbalancing the game, rather than making it as balanced as possible. So you need to carefully consider your circumstances before employing it, even just as a motivator.
Nothing is wrong with adding any gameplay element, skill-based or otherwise, if the players feel it enhances the game. But the subject of this thread does not advertise a skill-based gameplay element, it advertises a method for achieving game balance. Those are completely different things! If I'm acting as a game designer, I don't want a technique I use for balancing my game to change the nature of that game or alter the skills required to win.
Is it unfair if it amplifies the inherent advantage one player already has? More to the point, is it desirable for it to amplify advantages in this way?
Also, I think there are real differences between the skills required to play well, to evaluate positions accurately, and to design an interesting and balanced opening position. There's certainly some overlap, but it's also quite possible to be noticeably better or worse at one of those things than the others. I could perhaps make a better guess at the material value of many fairy pieces than some chess grandmasters could; that wouldn't imply I could beat them with those pieces.
On a related note, if there is a particular piece that I'm very good at using and that my opponent is not so good at using, I can give myself an advantage by giving that pieces to BOTH sides. If I were playing against a chess grandmaster, I certainly wouldn't give both sides FIDE pieces. In fact, I would be tempted to give one side FIDE pieces, and then deliberately make the other side stronger, in the hope that my opponent will just choose the familiar pieces that he knows how to use.
The whole pie-cutting problem just becomes a whole lot messier once the question of skill comes up.
Actually, that's very often not what it does. The pie rule only works when both parties are highly adept at their assigned tasks. If the slicer is poor at balancing but the chooser is good at gauging each side's strength, then the slicer cannot help but include some imbalance that the chooser will exploit, and thus places himself at a disadvantage no matter what he does. Conversely, if the slicer is good at design but the chooser is poor at evaluation, then the slicer may deliberately provide misleading cues and trick the chooser into selecting the weaker side.
Thus, in many cases, applying the pie rule to game-balancing encourages confusing and misleading design decisions, to minimize the odds that the other party can correctly identify or utilize the advantages of each side. I think that would generally be regarded as undesirable.
But even in the best possible case, it only motivates you to balance the game, it doesn't provide any tools for doing so.
The pie rule merely prevents the pie-slicer from cheating; it won't magically make him any better at game design. If you have two players who both understand the game very well and your problem is that neither of them trusts the other to create a fair initial position, this will solve your problem. But if a designer already intends to make a balanced game and is having trouble with the execution of that intent (which is the assumption I see in most discussions about how to balance games), this doesn't help you at all.
Every Man a Pawn. Each piece has the powers of a Pawn (except promotion) in addition to its normal powers. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]A game rule is not a collection of words, it's an abstract specification of how the game transitions between different states. People who are playing Chess according to rules written in English and people who are playing Chess according to equivalent rules written in another language are playing "the same game", regardless of the fact that different words are used to describe it.
By the same token, "pawns may move 2 spaces forward on their initial move" and "pawns may move 2 spaces forward when beginning a move from their second rank" are the exact same rule in the context of FIDE Chess, because "the rule" is actually just a specification of which game states can transition to which other game states, and the set of possible transitions is the same in both cases.
They are different rules in the context of some Chess variants because they no longer describe the same set of state transitions. When someone is inventing such a variant, it is reasonable and appropriate for them to choose whichever generalization of the rule is best for their variant, regardless of which exact words someone somewhere decided to use to describe the original rule.
Though game designers who hope eventually to release expansions for their games should definitely think about how their rules will ultimately generalize in order to avoid headaches down the road...
Chess with Different Armies. Betza's classic variant where white and black play with different sets of pieces. (Recognized!)[All Comments] [Add Comment or Rating]Thanks, Muller. This is a neat little tool. Could you go into a little more detail about how the columns work when some of the pieces are colorbound? With two colorbound pieces, I get two columns in rep2.txt, which appear to be same-color and different-color, respectively. But with 3 colorbound pieces, I get 4 columns, one of which is all zeroes (including its total board positions), and none of them are labeled. (Also, none of them are identical, even when all 3 colorbound pieces are the same piece-type and owned by the same player...) I did some experimenting with mismatched royal pieces. Interesting result: while it is commonly known that KNN v K is drawn, it appears that NK v K (that is, a single royal knight + commoner vs. king) is generally won! (89% won with black to move, longest win 29 moves, if I'm reading these results correctly.) I suppose that shows the value of sacrifice. How difficult do you think it would be to modify this code to accommodate 'lame' leapers, bent riders, crooked riders, and/or pieces with only 2-fold symmetry?
Doublemove chess. Move twice per turn, with by King capture, not checkmate. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]The fact that you can't capture the king in FIDE chess is a *consequence* of the check rules, not a separate rule. Any move that would give your opponent the opportunity to capture your king is illegal; the issue of whether you're allowed to make the capture if you had the opportunity therefore never comes up, but the easiest way to explain the concept of check in the first place is by reference to the hypothetical capture of the king. So, to recap, the laws of chess do not allow you to make a move that leaves your king 'in check'. If 'in check' means 'able to be captured by your opponent before YOUR next move', then when your opponent is about to get 2 consecutive moves, it would be illegal for you to make a move that results in a board position where your king could be captured within 2 opponent moves. Thus, players would need to foresee the capture 2 moves in advance just to check whether a particular move was legal. It would still not be possible to actually capture the king, because every possible series of legal moves would result in the king being checkmated (and thus trigger the end of the game) before such a capture actually occurred. (Exactly as in FIDE Chess.)
Fearful fairies. An experimental army for CadA, featuring the Dullahan (Ferz-Knight compound) and the Banshee. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]On a related note, has anyone tried playing with the Avian Airforce from Ideal and Practical Values part 3? That army features WDD, FAA, and WFDDAA, and so should also be able to make long-range attacks on the back rank.
I would be wary of declaring an opening array safe on the basis of the way it interacts with a specific opposing array. The FIDE army happens to have a piece on b/g that starts defended, is worth about the same as a Frog, and can flee without moving a pawn first. Suppose we shuffled the pieces on both sides with some algorithm similar to FRC. Would that be likely to produce a problematic case like your b/g test, or a calm one like your a/h test? Put another way, are the problems you had with the Frogs on b/g a special case that is unlikely to recur with different armies, or is every future CwDA army going to need to carefully check to make sure the Fairies can't easily win a piece against them in the opening?
Hmm. A Banshee (or even just a Nightrider) starting on d1 can reach c4 within 2 moves, forking king and rook. Black can play d5 or b5 to discourage it, though for some armies 1...d5 would invite 2. BNNxd5 (still threatening 3. BNN-c4+). I suppose d6 or b6 could also be used to preemptively block one tine of the fork. (And I'm not sure if white would be wise to develop his superpiece on turn 1...) Of course, even a compound with (0,3) such as the Frog or Half-Duck can likely threaten an undefended back-row piece within 2 moves. For example, a Frog starting on b1 can go to b4 and then a5, threatening an undefended rook if playing against the FIDE army. Perhaps not terribly difficult to defend against, but I don't know about 'tactically quiet'. Do you feel this is acceptable but, say, a Camel (1,3) is not? If I were forced to play against a Bison in a FIDE-like game, I imagine I would try to deny it early access to my fourth rank by guarding any space it appeared be aiming for with pawns. But I've never actually tried it.
Doublemove chess. Move twice per turn, with by King capture, not checkmate. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]So you're suggesting that checking the enemy king with the first of your two moves would result in a stalemate? Interesting, though it seems like that could be unsatisfying, and might cause a lot of draws. The obvious generalization of the rules of check is that the king is in check if it could be captured before the owner's next move (which in a doublemove variant would often mean within 2 opposing moves), but this has a couple of issues: 1) It is not always easy to tell when a piece could be captured within 2 moves, making it hard to determine when someone is in 'check' 2) The force required to checkmate a king that can move twice consecutively is quite substantial (see Betza's commentary on Monster Chess here: http://www.chessvariants.org/d.betza/chessvar/muenster.html ) And thus, various alternate rules proliferate to attempt to solve these problems. I invented a doublemove variant in high school (which I imagine has been duplicated by many other inventors both before and since) that required the two moves on a turn to be made with different pieces, and also stipulated that the second piece to move could not pass through the square that the first piece started on (thus, no instant revealed attacks). This has the advantage that a king is in check in any given board position if and only if he would be in check under the FIDE rules, and the doublemove helps only a little bit in escaping check (since the king cannot move twice). I don't know if that would be considered a 'true' doublemove variant, though, since no indivual piece can move twice during a turn. My variant also has obvious generalizations to three or more moves per turn that probably play equally well. I only ever played it once, though.
Chess with Different Armies. Betza's classic variant where white and black play with different sets of pieces. (Recognized!)[All Comments] [Add Comment or Rating]
Ideal Values and Practical Values (part 6). A study of the value of the Furlrurlbakking piece.[All Comments] [Add Comment or Rating]
On Designing Good Chess Variants. Design goals and design principles for creating Chess variants.[All Comments] [Add Comment or Rating]I suspect there's several concepts concealed in J�rg's [23]. One could be that squares differ only by their relative positions; for example, there's no square where you become immune to capture, or that can only be crossed by certain piece types, or whose occupation immediately wins the game. Though this would be violated not only by the river and palace in Xiangqi, but also by piece promotion in FIDE and Shogi, which perhaps calls into question the validity of that criterion. On the other hand, you can still make many kinds of 'terrain' just by altering the connections between squares; for example, you could have a 'wall' between squares (causing them to not be considered adjacent), or a 'portal' (that causes two otherwise distant squares to be considered adjacent), or a 'rotated' square (that turns forward movement into backwards movement, or orthogonal into diagonal, for example), all of which can be completely described purely as changes to the connections between squares. So perhaps you want a rule something like 'the squares comprise a regular tesselation of the playing field'. And possibly another requirement specifying the overall shape of the playing field (e.g. rectangular). Side-Topics: - Chess variants on boards with semi-regular tesselations - Chess variants played on an arbitrary graph
Good game design is ultimately a matter of generating appropriate reactions in players. Analyzing how people feel about games they've played (and why) can suggest new ways for a designer to elicit (or avoid) particular reactions. Making lists of things that contribute to an overall 'chess-like' impression seems like a pretty reasonable thing for chess variant designers to spend time doing. Assigning actual point values is probably reaching beyond the available data, though. Verify your models carefully before you trust them.
I don't buy it. By that definition, it seems that Descent: Journeys in the Dark is a Chess variant, because the heroes win (in most scenarios) by killing a specific boss monster, but Losing Chess is not, because the victory condition is extinction, and Nemoroth also is not, because the victory condition is stalemate.
I would say rather that being a 'chess variant' is a matter of family resemblance. Games that resemble Chess more closely than they resemble other well-known games are deemed chess variants. Checkers escapes being termed a 'chess variant' mostly because it is, itself, well-known; someone with long familiarity with Chess who was introduced to Checkers for the first time could plausibly decide it was a chess variant.
This resemblance is generally a result of having several key mechanics in common with chess (including a uniform tesselated playing area, armies of pieces with different movement capabilities, alternating turns in which a single piece belonging to that player can be moved, capture by displacement, and a single royal piece whose checkmate or capture ends the game)--and also NOT having too many key mechanics that Chess lacks. But no single feature is either indispensible or verboten; it's just a question of whether the game, taken in whole, reminds us of Chess more than it reminds us of something else.
The FIDE laws of Chess do not forbid threefold repetition; rather, law 10.10 allows either player to claim a draw in the event a threefold repetition occurs.
In the absence of such a rule, the game would presumably go on forever, with neither player willing to break the cycle. The threefold repetition rule is simply an observation of the fact that if both players find an endless loop preferable to other options, then they have both implicitly consented to a draw. It doesn't change whether any position is theoretically won, lost, or drawn, it just cuts short the infinite loop.
For the Crown has many unorthodox pieces, and is adding more with each expansion. However, material values are quite different than they would be in a FIDE-like context, due to differences in piece density, deployment (dropping) rules, and various other factors. And mate #s are completely irrelevant, since both players have the ability to bring new pieces into play as the game goes on, and therefore bare king endgames do not arise.
I have composed rules and recommended piece values for using the For the Crown pieces in a point-buy chess variant, which are available on the publisher's product page. I believe I have subjected these values to rather more rigorous analysis than George has used in this thread, but I still consider them to be educated guesses, at best; I haven't tried to get more precise than nearest-pawn, and it wouldn't surprise me if several were wrong, even by that loose standard.
If you're calculating mate #s based on your own variant chess laws instead of the orthodox ones, you should have stated that up front. And if your variant laws include removing the 50-move draw and making repetition illegal instead of a draw, then the numbers you are calculating are likely much closer to helpmate numbers than forced mate numbers. Eventually, ALL non-mate positions will be exhausted, and black will be forced to collude in his own checkmate by process of elimination.
If you suppose your king will always maintain opposition to the enemy king, then it can block the rank with no help at all. But if you don't maintain opposition, then the enemy king necessarily has a head start towards one side or the other, and can break your line there before your king can get close enough to defend, since you are vulnerable on both sides. And since maintaining opposition at all times will require all of your moves, it cannot be part of any plan to force mate. But a pair of DD (with leaping power) plus a king CAN force the enemy king back using zugzwang, unless I am much mistaken. For example, suppose white DD on a2 and b2, king on c3, black king f3. 1. Kd3 Kg3 (black tries to stay on rank 3) 2. Ke3 Kh3 3. Kf3 Kh4 (black is forced back a rank; only legal move) 4. Kg2 Kg4 5. DDb4 Kg5 (King threatens f3, g3, and h3, DD threatens h4 and f4) 6. DDa4 For thoroughness, we should also advance our own king to rank 5 without breaking the line, so we can repeat the process... 6. ... Kf5 7. Kg3 Kg5 (black tries to maintain opposition) 8. DDc4 Kf5 (white loses a tempo to break opposition) 9. Kh4 Kg5 10. Kh5 The final mate is only slightly more complex. Suppose white DD a6 & b6, white king c7, black king f7. 1. Kd7 Kg7 2. Ke7 Kh7 3. Kf7 Kh8 4. Kg6 Kg8 5. DDf6 Kh8 (f8 is threatened; black confined to corner) 6. DDa4 Kh7 (white loses a tempo) 7. DDa8+ Kh8 8. DDf8# (or DDh6#) I trust it's easy to see why this doesn't work if the DDs block each other.
Black's goal is to draw. He doesn't have to avoid threefold repetition; white does.
'Lame' is Betza's technical term for a piece that can be blocked on a square that it cannot land on. Say you've got a DD on a6 and another on h6. What do you do when the enemy king moves to b7? If they're full Dababba-riders, the one on a6 just moves to g6, and you still cover the whole rank. But if they block each other, you're stuck. If he moves anywhere on the same rank, he blocks the attack from h6 to b6, and the king slips through. If he moves anywhere on the same file, he is no longer covering c6, and the king slips through. If he doesn't move, the king captures him.
As far as I can tell, George gets all of his piece stats from about 95% sheer intuition and 5% wildly unrepresentative examples. If you actually went through his numbers rigorously and systematically, I suspect you'd discover that many of them are total fabrications.
He even gives a mate # of 2 for Water Rook, a piece that George himself defined as specifically only moving on light-colored squares (the piece that moves in exactly the same pattern on dark squares has a different name), which therefore obviously cannot force a mate with any number! That's like giving a mate # for Bishops that are all on the same color.
...and even if he hadn't defined them in this bizarre way, two is definitely not enough of them to force a mate in general. I believe two Dababba-riders can sometimes force mate, if they are on different colors and can cut the enemy king off from the 'safe' edge of the board, but the Water/Land Rooks are lame Dababba-riders, and therefore cannot control an entire rank/file even when working together.
Incidentally, if we're playing fox-and-geese with rotating spearmen, I think you'll find that 3 spearmen + king is sufficient to win most reasonable starting positions (use two spearmen pointing forward to confine the enemy king to a corridor and then just chase him down).
Yeah, I don't necessarily agree with Hubert's criticism, but in my opinion Jepps' behavior in this thread has been indefensible. If you're not prepared to tolerate criticism of your work, you shouldn't make it public. The suggestion that only positive commentary should occur is childish and transparently self-serving, especially for someone who drummed up attention by rating his own game 'excellent' four separate times.
The 'Poor' rating is there for a reason, and anyone who thinks you can distinguish good amateur content purely by the quantity of attention garnered is sorely lacking in experience of such matters.
Chess 2. Different armies, a new winning condition, and duels. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]The rulebook is poorly written; information is not presented in a logical order, it is difficult to tell in some cases what is a new rule and what is intended merely to explain the implications of another rule (which might not appear until later in the rulebook), and it glosses over several crucial details. Some of the diagrams depicting unit movement are exceedingly confusing (I defy anyone to look at the diagram for Jungle Queen and guess how it moves without reading the text), and one depicts a board position that is (as far as I can tell) completely impossible. Very low marks for editing. The armies are rather interesting; I was expecting pieces similar to FIDE but with different movement patterns, along the lines of Chess with Different Armies, but most of the new pieces in this game have unique special rules. There's only about 10 new things between all 5 armies, though, so if you were expecting CwDA amounts of new pieces per army, you will be disappointed. I don't know whether any of it is balanced; it seems unlikely unless quite a large amount of testing was done (but maybe it was, I don't know). And I wouldn't be at all surprised if a computer could discover a short forced win from some opening positions (even with the simultaneous-action dueling mechanic). In particular, Reaper vs. Reaper looks like just a race for the midline with no significant risk of checkmate at any stage of the game. It is also my suspicion that a computer could play this game very easily. 'Dueling' increases the branching factor (as do some of the armies), but I expect games would be much shorter, and I think computers would be better at handling most of the new elements (especially deciding when it's time for the king to make a break for the midline).
Suffix Index to Man and Beast. Alphabetic list of suffixes used in the Man and Beast series.[All Comments] [Add Comment or Rating]As has been repeatedly pointed out, CGs directly behind a pawn wall is a uniquely favorable starting position; those CGs have very high POSITIONAL value, but even if they win (which I'm not confident they would) that proves nothing about their MATERIAL value. Start those pawns on rank 3 instead of rank 2 and which side do you think will win? And I can't actually perform your test, since you've removed both kings from the board and haven't stated a new win condition. Which makes me pretty confident that you haven't actually tried this test either, since that issue would be pretty hard to miss if you actually sat down and played. So even if this were a fair test (which it's not), it's not a test that has actually been performed, so to say that the CG is 'measurably' above Camel is just a bald-faced lie. You have yet to measure anything. How about this? Give each side 8 pawns, a king, and either 6 camels or 6 contragrasshoppers. Put the kings on their usual starting squares, and distribute the rest of each side's pieces RANDOMLY throughout their half of the board (I guess we'll forbid pawns on the first rank just so we don't have to pick a special initial-move rule). I won't even require that the camels are split between different colors. Pawns promote to queen. If a king starts in check, his side gets the first move, otherwise pick randomly. I'm sure each side will win some possible random positions. I'm reasonably confident the camels would win the clear majority--but I haven't tried it, so I could be wrong! (I suppose I really should look into getting some software to run computer tests like Muller has been doing...)
Looking only at the best-case mobility of a piece can be hugely misleading, especially when that best case is highly dependent on the exact positions of other pieces. My piece threatens every square on the board, instantly and automatically winning the game...provided that I have 8 pawns all positioned on my seventh rank. Clearly it is stronger than your entire army! You suggest that CG is very good behind a pawn--but as soon as that pawn moves one space forward, the CG is stranded with no moves at all! It cannot even follow the pawn up to regain its lost mobility. A G behind a pawn can only move to the space directly in front of the pawn, but at least it retains that ability as the pawn advances, and can threaten any piece that tries to stand in the pawn's way. You talk about imagining substituting a G or CG for a FIDE piece as if it were some great revelation, but despite your protestations, merely imagining this scenario for a few moments does not magically allow you to accurately determine a piece's value. At least, it does not allow ME to do so, and clearly it does not allow you to produce predictions that are consistent with any accepted method of estimation, nor am I aware of any instances so far in which your unorthodox predictions have been proven true by empirical study. The only actual evidence you have presented so far is an analysis of best-case mobility--which, at 19 squares, should (if it were meaningful) put its value at 1.35 Rooks, higher than either of the two different values you have already guessed! As far as I can tell, your numbers are based on nothing but intuition, and your intuition isn't even consistent. As for me, I'd happily take the Camel in preference to either of these pieces in most positions. By the way, George, your posts would be much more readable if you used an occasional paragraph break.
Grasshopper and Contragrasshopper are certainly similar, and have the same Betza mobility (3.2 with magic number = .7, which would suggest a value around 1.5 pawns). Since both will lose value rapidly as the board empties, I suspect their practical worth will usually just be a question of what you can trade them for. The Grasshopper (but probably not the Contragrasshopper) is very good at threatening undeveloped enemy pieces behind a pawn wall; replacing ANY of white's backrow pieces with a Grasshopper in an otherwise FIDE game allows a fork on turn 1. But without such a favorable opening (for example, if you start the pawns on ranks 3 and 6), I'm skeptical whether they are even as good as a Wazir or Ferz.
Drunken Nights. A toned down version of the Nutty Knights for Chess with different Armies. (8x8, Cells: 64) [All Comments] [Add Comment or Rating] Dragonchess (R). Commercial large chess variant. (16x10, Cells: 124) [All Comments] [Add Comment or Rating]I'm no expert on these things, but while the patent's SUMMARY suggests it protects the game as a whole and also separately protects the board and the Q3 piece, the CLAIMS section in the patent never lists the board or the piece as a separate claim--only several versions of the full game. (And the game description appears to cover, roughly, any chess variant played on a cross-shaped board and including the orthodox pieces plus the Q3--or maybe some different specific piece, since 'three spaces in any direction' certainly seems like it could be construed as covering more than 8 directions). So if I understand this correctly, neither the name nor the movement pattern of the piece is protected. (Which makes sense, on account of all the prior art we've already cited.) Though of course any original artwork you made to depict the piece is protected (no surprise there).
Rules of Chess: Castling FAQ. Frequent asked questions about castling.[All Comments] [Add Comment or Rating]I've always imagined it is because castling is intended as a development move for breaking board symmetry, not as an escape move to get out of a serious attack. If your opponent has already launched an attack on the King's current position, or if (say) he is using a Rook to cut you off from that side of the board, it's considered unfair to get away or to cross the line of control using a special move. Kind of like how en passant capture was added because the pawn's double-step was intended as a development move to speed up the game, and people didn't like that it was being used to leap past enemy pawns without giving them a chance to intercept, thus altering the game's strategy. But I could be wrong.
Concise Guide to Chess Variants. Missing description[All Comments] [Add Comment or Rating] Dragonchess (R). Commercial large chess variant. (16x10, Cells: 124) [All Comments] [Add Comment or Rating]I'm actually quite curious: exactly what rights do you claim that you have to that piece? I am not a lawyer, but my understanding is that game mechanics are not protected by copyright (at least in the US). Furthermore, 'like a Queen but 3 spaces at most' is a trivial and obvious variation on a well-known piece; it has probably been independently invented thousands of times, all over the world, long before Dragonchess showed up. You're also not the first people to give the name 'dragon' to a chess piece, though you might be the first ones with that exact name/movement combination. So what precisely is it that you claim is protected, and what rights do you assert over it?
Man and Beast 02: Shield Bearers. Systematic naming of divergent coprime radial pieces.[All Comments] [Add Comment or Rating] Rules of Chess FAQ. Frequently asked chess questions.[All Comments] [Add Comment or Rating]The FIDE rules cover situations that can occur in FIDE Chess. If a variant allows new situations to arise (such as having multiple Kings, or two pieces in the same square, or Pawns on the first rank), it has to specify how to resolve them; they are not covered simply by saying 'FIDE rules apply'. (Ralph Betza once attempted to codify a few rules that were used often in variants as 'Rule Zero', but while he undoubtedly used those rules a lot, I'm not sure whether they're any more common in general than other options, and in any case are not extensive enough to save very much repeating.)
If you're trying to discern the 'spirit' of the rule, I believe it came about something like this:
- Initially, the goal of the game was to capture the enemy King, and 'check' didn't matter.
People got annoyed when an interesting game ended prematurely because one player made a dumb mistake that allowed his King to immediately be captured, so they decided to prevent that by making it illegal. Thus, if you make a move that would cause you to lose on the VERY next turn, you must take it back and do something else (if you have any other choice).
To get the current FIDE rules, you need to add the additional rule that a player who is not in check but who cannot move without placing himself in check (that is, a player in 'stalemate') receives a draw instead of a loss. It's not obvious (at least to me) why this should be so, and historically various players have resolved stalemates in just about every different way you could imagine, but the modern accepted resolution is a draw.
So the 'spirit' of the rule (in my opinion) is 'the REAL goal of the game is to capture the enemy king, but as a safety net, you're not allowed to make any move that would allow your opponent to win on the very next move.' In a variant that nullifies this safety net and allows you to place yourself in check, the most natural rule would be that the game is won by capturing the King, and placing yourself in 'check' is generally a poor strategy but otherwise has no special significance.
Um. They're called 'variants' because they all have different rules. There's no one rule that all variants follow, on that or any other point.
Man and Beast 02: Shield Bearers. Systematic naming of divergent coprime radial pieces.[All Comments] [Add Comment or Rating]Thanks once again for your very interesting computer tests, Mr. Muller! Notice that if this were simply a matter of the K capturing moves being unusually strong and the K non-capturing moves being unusually weak, we should expect mKcN to be weaker than K, but (if I am reading you correctly) the tests say it is stronger. So if you are correct that K's moves have a higher 'ideal value' but are suppressed by K's overall low speed (which would have been my first guess also), then we must conclude that a piece's 'speed' depends significantly upon its capturing moves, not only its non-capturing moves. This seems surprising to me, because I would imagine that capturing capabilities are only exercised in a small percentage of the piece's movements. Alternately, this could be a matter of special synergy rather than a global bonus or penalty--that is, perhaps the combination of speed and concentrated attacks is particularly valuable, but neither component has significant value by itself. Thus, the mKcN, lacking both, is not significantly worse off than either N or K, which only have one each, but the mNcK stands tall with both. Curious.
I remain skeptical even of your revised claim. Even when the components are non-overlapping and 'similar' (though I can only guess what that means), I see no obvious reason that having divergent capturing and non-capturing moves is better than having the same in the general case; only the capture or non-capture will be legal in any given position, so there is no loss due to 'overlap'. In fact, I've seen the opposite argued, on the grounds that a divergent piece is easier to trap, since it is unable to attack enemies in its way. When the combination lifts a special disadvantage (such as colorboundness), that is a special case; though it would need to eliminate a disadvantage from EACH of the components in order for that to make it stronger than BOTH, in general. (And I am unconvinced that lack of triangulation is a disadvantage of any measurable significance.) If the components were instead Crab and Barc, or Rook and Nightrider, what then? Comparing a Pawn to a Point is like comparing a Queen/Knight divergent piece to a Knight; that is obviously the weaker parent (Ferz is already stronger than Wazir, and loses much less from the forward-only restriction). I strongly suspect that the Pawn is weaker than a forward-only Ferz, despite the Ferz being colorbound, because the fF has more possible moves and does not need to capture to change files (the latter advantage being especially important if promotion is allowed). What is your evidence or reasoning for valuing divergent pieces more highly?
You write, '[Divergent] pieces are stronger than either non-divergent piece, but weaker than the unrestricted compound piece.' This seems exceedingly unlikely. You seem to be claiming that a piece that moves as a Queen but captures as a Knight is stronger than either; in fact, read strictly, I believe you are claiming that a piece that moves as a Queen but captures as a Bishop is stronger than a Queen, even though it has strictly fewer moves. I believe conventional wisdom is that such pieces (which George Jeliss calls 'snipers') usually have a value that is somewhere between the strengths of the non-divergent pieces, closer to the capturing component than the non-capturing one. (Though I'm certain it is possible to craft examples that violate this rule.)
Rules of Chess: Check, Mate, and Stalemate. Answers to frequently asked questions.[All Comments] [Add Comment or Rating]The sort of situation you describe generally results in a draw by one of two rules: The first is the threefold repetition rule, which applies when the exact same game position is repeated three times. For example, if you and your opponent are each moving back and forth between the same two spaces, once you have come back to your starting position after two full loops, the game can be declared a draw. The second is the 50-move rule, which applies when there have been no captures or pawn advances (irreversible moves) for at least 50 consecutive moves of white and black. This is invoked mostly in endgames where the board is very open and so it can take a very long time for (and be difficult to notice when) an exact position is repeated three times. Of course, the game can end in a draw immediately if both players agree, which may cut these conditions short if it is obvious (for example) that the game is going to end in a perpetual check.
For the Crown. A commercial crossover with deck-building games. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]There's an entire sample game available from the publisher's site, including commentary and illustrations, if you're interested.
I could see some value in adding brief examples to this page, but doing so seems awkward, because the editing form doesn't allow me to create new sections, just edit the contents of the existing ones.
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