You are on the backup site for Any posts, moves, or other changes you make here will not be permanent, because the pages and database from the main site will be backed up here every midnight EST. Additionally, things may not be working right, because this site is also a testbed for newer system software. So, if you are not here to test, develop, or merely read this site, you may want to change .org to .com in the navigation bar and go to the main site.

The Chess Variant Pages

[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Latest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Comments by Jeremy Lennert

Later Reverse Order EarlierEarliest
Stalemate[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2013-10-12 UTC
It sounds like H.G. Muller is saying there's nothing virtuous in the
abstract about declaring stalemate to be a draw, but in the specific case
of FIDE it just coincidentally happens to work out to a net positive
(mostly because of a couple specific endgames).  That implies it might
_not_ be a good rule for chess _variants_, even if it works out in orthodox
chess--would that be your conclusion?

Greg Strong seems to be saying that it's good because it gives the losing
player something to aim for.  I'm perhaps not a strong enough player to
judge, but that seems questionable to me; how often does the stalemate rule
really alter your decision to resign?  And are those endgames really more
interesting than resigning and starting a new game?

Jeremy Lennert wrote on 2013-10-11 UTC

Currently, a stalemate in Chess is widely recognized as a draw.


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]
Jeremy Lennert wrote on 2013-07-08 UTC
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?

Lion Chess[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2013-05-22 UTC
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

Jeremy Lennert wrote on 2013-05-21 UTC
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.)

Jeremy Lennert wrote on 2013-05-16 UTC
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]
Jeremy Lennert wrote on 2013-03-05 UTC
Is there a page somewhere that summarizes all of your experimental results for piece values?

Jeremy Lennert wrote on 2013-02-28 UTC

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).

Jeremy Lennert wrote on 2013-02-27 UTC
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...

Jeremy Lennert wrote on 2013-02-04 UTC

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.

Jeremy Lennert wrote on 2013-02-01 UTC

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.

Variant and a few other chess terms defined[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-11-03 UTC

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.

Jeremy Lennert wrote on 2012-11-02 UTC
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,
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

Rococo. A clear, aggressive Ultima variant on a 10x10 ring board. (10x10, Cells: 100) (Recognized!)[All Comments] [Add Comment or Rating]
Jeremy Lennert wrote on 2012-10-19 UTC
Cannon pawns are hoppers, not locusts.  They capture by displacement.  They would not be hindered in ANY way by the absence of border squares.

Calculating Ultima piece values[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-10-13 UTC
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.

Jeremy Lennert wrote on 2012-10-12 UTC

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.

Jeremy Lennert wrote on 2012-10-12 UTC
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

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

Mating potential and piece values[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-10-02 UTC
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.

Jeremy Lennert wrote on 2012-09-29 UTC
> 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]
Jeremy Lennert wrote on 2012-09-29 UTC
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.

Mating potential and piece values[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-09-27 UTC
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

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...

Jeremy Lennert wrote on 2012-09-27 UTC
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.

First move advantage in Western Chess - why does it exist?[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-09-26 UTC
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

Or not; I'm just speculating wildly.

Mating potential and piece values[Subject Thread] [Add Response]
Jeremy Lennert wrote on 2012-09-26 UTC
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]
Jeremy Lennert wrote on 2012-09-20 UTC
> > 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?

25 comments displayed

Later Reverse Order EarlierEarliest

Permalink to the exact comments currently displayed.