Comments by MichaelNelson

Antoine,

I agree that that such endgames are just fine -- many alternatives are
equally playable but the key thing is choosing which set of playable
alternatives suits your conception of what you want the game to be. I
might have chosen differently, but I believe your are designing an
excellent game.

Cincinnati-style Kriegspiel should be playable by different armies--the
rules specify that only pawn/piece is announced for a capture, not which
piece.  The CWDA promotion rule needs to be modified to allow pawn
promotion only to pieces in one's own army--otherwise you would have to
know what army the other player is using to know your promotion choices.
(This weakens the Colorbound Clobberers a bit in the endgame--the CC's
often promote a pawn to the other side's Queen piece.)

Check announcements need consideration--what does the referee say if the
player is checked by a Camel? This is a Knightish type check, but not on
the same squares as would be indicated by 'check by Knight'.  A check
from a Half-Duck three sqaures away may still be 'on the file', but the
player's legal moves are different than if the same check were by a Rook
or Queen (interposing is useless, but retreating on the file may work.)

Perhaps the best check announcement rule for KWDA is simply to announce
'check' with no directional indication.

A game idea for comment:  

Instead of pieces giving the ability to move, as in Relay Chess, have
pieces take away movement ability.  For this example we will assume a game
with FIDE pieces plus Chancellor(RN) and Cardinal(BN):

Kings and pawns are unaffected, neither losing nor taking away movement
powers.

A piece may not make a Rook move if it is attacked/defended by another
piece using that piece's Rook move.

A piece may not make a Bishop move if it attacked/defended by another
piece using that piece's Bishop move.

A piece may not make a Knight move if it attacked/defended by another
piece using that piece's Knight move.

Attack and defense are calculated non-recursively. Thus if there are Rooks
on b3 and b4, they are immobile--the immobility of R(b4) does not make it
not attack/defend R(b3) and allow R(b3) to move.

Attack and defense are calculated without regard to check. In the example
above, R(b3) still can't move even if R(b4) is pinned.

The obvious variants are applying anti-relay rules only to attack or only
to defense.

Daniel,

Thank you for finding the bug in the ZRF (it actaully affected the
SuperChancellorRider).  I have subbitted a corrected zrf to the CV pages.

This is worth an excellent because the concept's elegant simplicity is
applicable to virtually any variant (though I wouldn't want to apply it
to a game slower than FIDE Chess--Ready Shogi would be interesting but
would take forever to play).  The ready concept is particlary meritorious
in games that are faster and more tactical than FIDE Chess -- slowing them
down might give them a strategic/tactical balance like FIDE whiler hasving
a very different feel.  Examples: Ready Tripunch Chess, Ready Tutti-Fruiti
Chess, Ready Progressive Chess.

This game also works with thematic Kings, which personally I really prefer
(when playable) from an esthetic standpoint.

I really like this game. If a King promotion is desired, perhaps a mW2F2cK
allowing more mobitity with the stipulation that the 2-square move
couldn't cross check (like castling).  This would be worth having as the
promoted King could get out of a dangerous position quicker, but most
mating positions would still be the same.

Let's take a look at promotions:

Knight is a two atom piece that promotes to a five atom piece--this is the
strongest promotion and a good thing -- the 9x9 board weakens the Kinght
vs the Bishop and the stronger promotion rebalances the eqaution.

Bishop is a two atom piece that promotes to a four atom piece, as is the
Camel; the Rook is a three atom piece that promotes to a five atom piece. 
These promotions are of appoximately equal value.

The Silver (FfW) is worth maybe 1 1/3 or so atoms and promotes to a three
atom piece, clearly a a bigger gain than Bishop, Rook, or Camel,  but a
lessar gain than Knight.

The Pawn is harder to evaluate -- it can promote in two steps vs five in
FIDE but does not promote to a decisive piece, so FIDE's 2/3 atom is
probably a good guess.  The Gold (WfF) is worth 1 2/3 atoms, so this is
the weakest promotion--but Pawn promotions collectively can add a lot of
power.

I have already given this game a well-earned 'Excellent'.  I think Tony
is leading the way to some new, exiting Hex Chess games.  The key is
dropping the attempt to translate square geometry into hex
geometry--Heroes is designed to play well in hex from the beginning.  The
email game I have going with Tony is in the endgame--the game is holding
up very well in terms of play value.  

I believe this game is a serious contender to win the 84 Spaces Contest. 
I would be astonished if it didn't at least finish high in the rankings.

I can't help but wonder if dropping the attempt to translate 2D geometry
into 3D would lead to some fine 3D games.

Another idea suggests itself:  make the pieces entirely immobile on the
next move after a capture, but the piecces are self-readying: for
example, White captures a Knight with his Queen on move 28. The Queen 
may not move or capture on move 29, but the Queen may move or capture 
normally on move 30 or later.

If this game were played with thematic Kings, this could allow a King to
administer mate--if Black's King just made a capture, White's King
could move next to it and this is check and mate since Black's King 
can't move and White's king can't be captured (if it could, the 
checking move was illegal). Capturing with a bare King would mean 
stalemate, as would capturing with your only mobile piece, if the 
opponet's move did not release any other or oyur pieces.

I would like to make clear that my comments about games in the 84 Spaces
Contest are absolutely in no way intended as crticism of the judges.
Having judged Group A with Glenn Overby and Michael Howe, I am well aware
of how difficult the judging task is and how diligently the judges do
their work.  No doubt some will disagree with our decisions as well. Given
the overall high quality of the entries, not all of the worthy games can
make the finals. I am also quite sure that many of the decisions were very
close ones.  

It's been a pleasure to be part of this contest, both as an entrant and a
judge.

The author's 'The setup in my diagram is not a mistake' asserts that the
diagram correctly reflects his design--that he really intended the
asymetircal setup, rather than the diagram-maker messing up.

Whether this is a good design decision is an interesting question. I
suspect Ralph had a good reason for his choice and I would be interested
in hearing it.

Maybe this is really 'The Rook problem' 

Consider the following mobitity values and their ratios for the following
atomic movement pieces ard their corresponding riders (Calucated using a
magic number of .7, rounded):

Piece     Simple Piece     Rider       Ratio      Move Length
-----     ------------     -----       -----      -----------
W         3.50             8.10        2.31       1.00
F         3.06             5.93        1.94       1.41
D         3.00             4.89        1.63       2.00
N         5.25             7.96        1.52       2.24
A         2.25             3.07        1.37       2.83
H         2.50             3.20        1.28       3.00
L         4.38             5.43        1.24       3.16
J         3.75             4.45        1.19       3.61
G         1.56             1.74        1.11       4.24


Notice that there is a clear inverse relationship between the geometric
move length and the ratio of the mobility of a rider to the mobility of
its corresponding simple piece, but the relationship is not linear.

Now let's look at the mobility ratios: For the F, the ratio is close to 2
and the Bishop is twice as valuable as the Ferz.  For N, the ratio is
close to 1.5 and the Nightrider is one and a half times as valuable as the
Knight.  The ratios for D and A are about 1 2/3 and 1 1/3 rather than the
1 3/4 and 1 1/4 Ralph suggested, but the discrepency is still within
reasonble bounds. The values for H, L, J and G and completely untested,
but seem reasonable.

So it looks like the ratio of the value of a rider to the value of its
corresponding simple piece is very similar to the ratio of the mobility of
the rider to the mobility of its corrsponding simple piece. Value
ratio=mobiility ratio (between two pieces with the same move type).

But all of this breaks down for the Rook/Wazir: playtesting amply
demonstrates that the value ratio three, but the mobility ratio is only
2.3!  Clearly this suggests that the Rook has an advantage over short
Rooks that the Bishop does not have over short Bishops, that the NN does
not have over the N2, etc.

My guess is that the special advantage is King interdiction--the ability
of a Rook on the seventh rank (for example), to prevent the enemy King
from leaving the eighth rank.  A W6 is almost as good as a Rook, but while
a W3 can perform interdiction, it needs to get closer to the King, while
the R and W6 can stay further away. Can mate is also no doubt a factor.

Consider the mobility ratio of the Rook to the Knight--1.54, a fine
approximation of the value ratio of 1.5 (per Spielman/Betza).  If we make
a reasonably-sized deduction from the Bishop to account for colorboundness
(say 10%), its adjusted mobility is slightly larger than the Knight's and
its value ratios with the Knight and Rook come out right.  But the Rook's
mobitilty must be adjusted downward to account for its poor forwardness
(ruining the numbers) unless the addition for interdiction/can mate is
about equal to this deduction.  Clearly such an adjustment for poor
forwardness must be in order, since by mobility the colorbound Ferz is a
bit weaker than the non-colorbound Wazir, but in practice the opposite is
true.

This suggests that the Wazir loses more value from its poor forwardness
than the Ferz loses from colorboundness, and the Rook would lose more than
the Bishop but for compensating advantages.

Is this a first step toward quantifying adjustment factors so that we can
take crowded board mobility as the basis of value and adjust it to get a
good idea of the value of a new piece?  Any of you mathematicians care to
take up the challenge?