Comments/Ratings for a Single Item

There will be a ZRF posted.  Until it's on the CV pages, I will send a
copy by email to anyone who requests it.

I think my playing tip about not using the pocket just to mutate a piece
might well be extended to promotion as well -- don't aim for promotion as
your sole objective -- try to gain a material or positional advantage in
addition.

The kind of pawn promotion I like is dropping a pawn on the seventh rank
to fork two pieces and threaten to make a Bishop or Knight.

In general, moves with multiple objectives will be even more frequent than
in FIDE Chess.

Astute readers will notice that the value classes are based on Ralph
Betza's Atomic Thoery of Piece Values.  The equivalances are not exact --
a SuperBishop is measurably stronger than a Rook, but the difference is
small enough (half a pawn, maybe) that positional factors can easily
override it.

If anyone does want an alternate piece set, I would suggest a coherent
set based on a small number of elements.  My piece set is based on three
pieces (Knight, Bishop, Rook) and their combinations plus three
enhancements (change Knight to Nightrider, add Wazir to Bishop, add Ferz
to Rook).

Some thoughts on the pieces:

The pawn is about the same value as in FIDE Chess: while it can only
promote to Bishop, it promotes to a Bishop that is itself promotable.

I don't expect to see an AmazonRider in an actual well-played game, but I
just had to have it for logical completeness. I wonder if an AmazonRider
is really all that more powerful than an Amazon on an 8x8 board: the
difference certainly feels less than the gap between Knight and
Nightrider.

The SuperChancellor can mate unassisted--the only value class 6 piece
which can do so.

The leveling effect among pieces of the same value class is stronger than
in other chess variants, since by spending a tempo, you can mutate one
into another. On the other hand, among pieces in the same value class
their are slight differnces in value based on the type of position.  In
open/wide open positions, the most valuable move components seem to be
Rook, Bishop, Knight in order and Wazir or Ferz is a more valuable
enhancement than Nightrider.  In closed/severly closed positions, the
reverse is true.  In-between positons seem to favor Bishops.

This is an excellent game! The pocket allows for many surprises.
I played its zrf many times and I found a very small error in it. The
piece CancellorRider is missing its one step diagonal move.

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.

I'm presently losing my game of Pocket Mutation Chess against Peter
Aronson in Invent-and-Play Section 2, and it is obviously a very enjoyable game.
I blew up my position at move 5:

1. Rook h1 - WP = Nightrider
1. Pawn d7 - d5
2. Nightrider WP - f4
2. Queen d8 - BP = CardinalRider
3. Rook a1 - WP = SuperBishop
3. Pawn g7 - g6
4. SuperBishop WP - e5
4. Knight g8 - f6
5. SuperBishop e5 x c7 ??
5. CardinalRider BP - g5
6. Knight g1 - f3
6. CardinalRider g5 x c7...

Despite this outcome, I am afraid that the sole advantage of being White
was bound to give me a quick win. (Peter is not so sure.) The Nightrider
can be dropped on c4, threatening King and Rook, or f4, threatening Queen
and Rook. It is forking a fork, so to say.
So, I think that White should be barred from using the Pocket at his
first move. (Peter agrees with me on this.)

Antoine raises a good point.  Consider it done. Rule 2 is amended to read:
'If a player's pocket is empty, the player may remove any of his pieces
(except his King) from the board and put it in his pocket as a move. White
may not use the pocket for the first move.'

I will also submit a corrected ZRF when I am able.

I hav submitted the corrections to the editors. It is a good change in that
reducing White's opening advantage is always a good thing.

However, the original rules do not give White a win.  Black can maintain
equality by symmetrical play. The early loss of one Rook on each side is a
bit of a flaw, though.

In the revised rules, White is safe from the Nightrider attack if he opens
Pawn d2-d4 or Pawn e2-e4. This covers one fork point and he has the tempo
to cover the other if Black mutates a Rook to Nightrider.  Since these are
reasonable opening moves anyway, diffusing the Nightrider threat costs
White little or nothing--this makes for a very balanced game.

Is mutuation when pocketing a piece from the eighth rank optional or
mandatory?  For example, White pockets a KnightRider from a8 -- does he
have the option of retaining a KnightRider or is he forced to 'upgrade'
to a Cardinal or SuperRook.  White may find the NR ability too useful to
give up.

What if you added a new Piece, the 'SuperKnightRider', or 'KingRider',
which moves as King or KnightRider?  Would this be approximately the right
strength for a Class 4 Piece?  If you think it is too strong, perhaps a
FerzRider or WazirRider would be better.

Promotion via mutation is mandatory when pocketing a piece on the eight
rank, excepting the case of the AmazonRider which can be pocketed form
the
eighth rank without promoting since there is no higher rank for it to
promote to. A variant you where promotion is optional also has a great
deal of merit.

Your proposed SuperNightRider would be value class 5.  A Nightrider-Ferz
or Nightrider-Wazir would be class 4, as would a SuperKnight.

Carlos, 

Yes and No.

FIDE Chess rules apply to Pocket Mutation Chessexcept where otherwise
stated.

Under current FIDE rules, perpetual check is not a draw in and of itself
(it once was), but if you are able to give perpetual check, you can always
force triple repetition or the 50-move rule, both of which are draws. 

Note that Pocket Mutation's 50-move rule is different from FIDE:
promotions and captures reset the move count, but Pawn moves do not.

1. P b2-b3 
1... p d7-d5 
2. R a1-p1; I-p1 // pocket nightrider 
2... b c8-d7 
3. I p1-b2 //  is a PMChess Fool's Mate.  Neat!

This variant has the potential to go beyond excellent. Bringing Class 4 up to four pieces yields 21 different pieces for the game, including the King. And 21, being the product of the magic numbers 3 and 7, makes a traditional choice for a complete set. I suggest adding the SuperAlibaba to Class 4, as its WFAD moves make a nice change from long range pieces.

I have an idea for Pocket Mutation Demotion Chessgi. It will use the same
pieces and value classes as PM. 

The rules for using the pocket are expanded:

When you capture an enemy pawn, it is removed from the game. If you
capture any other enemy piece, it is demoted to the next lower value
class, mutated to a friendly piece of your choice in that class, and put
in your pocket. This is mandatory even if your pocket is not empty and
will cause the removal of any piece in your pocket from the game. 

Notice how you can't put a strong piece in the pocket and wait around for
a good drop--in effect you can only capture pawns as long a s that strong
piece is there.

Imagine having a Queen in your Pocket and the opponent checks with a
Knight and the only counter is to capture the Knight. At the cost of a
Knight, the enemy has changed your Queen into a pawn!

This is a very interesting game. I look forward to playing it in GCT #2.

Below is a list of mobility values for all the pieces in Pocket Mutation, as well as a few Chess-With-Different-Armies pieces at the bottom for comparison. The 'average mobility' column is a Betza Mobility Calculation with a magic number of 0.7. This is probably the best estimation of the value of the piece. The second column is the average number of checks this piece delivers on an empty board without being counter-attacked. The third column is the average number of different 'directions' in which this piece attacks. The fourth column is the average number of squares attacked on an empty board.

Greg,

Excellent work in doing all the calculations. 

Your figures confirm my designer's intuition that the value classes
(desinged based on Betza's atomic theory of piece values, with no
detailed math) are well-defined and playable. The worst case scenario is a
discrepancy of 1.47 mobility between Nightrider and SuperBishop in class 3.
This is vitually identical to the smallest difference between two pieces of
differnt classes: 1.48 betweenS SuperCardinal (class 5) and ChancellorRider
(class 6). 

However, some hard to quantify but very real values tend to narrow the
former gap and widen the latter: 

The Nightrider is particularly strong in the opening and as a drop
piece--this brings it closer to the SuperBishop which is not particularly
outstanding in either respect (though hardly poor). 

The ChancellorRider has a Rook move, so it has King Interdiction power
(the ability to prevent a King from crossing a rank or file covered by a
Rook move, thus confining it to a restricted area of the board). As the
SuperCardinal does not have King Interdiction power, this gap widens.

Super-alibaba:
average mobility: 11.81
average safe checks: 5.25
average directions attacked: 11.81
average squares attacked: 11.81

Directions attacked:
Yes, I should better define a 'direction'.  By my definition, the four
directions attacked by a rook are different than the four directions
attacked by a dabbabah-rider.  This is intentional because the directions
attacked is a measure of forking power...  The super-alibaba can
theoretically fork 16 different pieces, so it attacks in 16 different
directions.  This definition is also essential because these numbers are
all calculated by ChessV, and ChessV must consider them to be different
directions -- directions are used in generation of moves/captures, and a
piece which blocks a wazir-rider doesn't necessarily block a
dabbabah-rider.

This is a very interesting game, far from easy to play in a good manner.
Material advantage should be good, but it is much less important than in
FIDE-Chess. Defensive schemes can be good for a team in a slight
disdvantage, because the superior team, if wants a victory, must attack,
and always some weaknesses can appear, because pieces used in attacks
can´t defend weak positions in many cases. The superior team can´t
construct easely the victory positionally step by step as in FIDE-Chess.
In Chess, the main mennace is the convertibility of the advantage in Pawns
which can promote to Queens, here it is not the case, promotions add a bit
more power, but not enough for a victory in many cases. Openings must be
played carefully, conversions to Nightriders can cause serious damages to
the enemy if he plays with some ingenuity about these pieces. isolated
pieces are not good, and unprotected Kings are worse. Positions must
change dinamically and mantaining reasonable solid structures, don´t stay
with the same structure and pieces types all the time, some structures are
more sensitive to some piece types, and other structures to other pieces.
Every player must try to cover his weak points before attacks, or
counter-attacks can be devasting... I have launched the idea of redefining
the Super Cardinal as a class 6 piece, but it seems there is not consense.
This is not only the most powerful piece in its class, but its power is
almost the same as the class 6 Super-Chancellor. Super-Cardinals can cause
demolishing effects in many ends, due the usual sparsity of the pieces, and
a Queen is not equally comparable with it, because it is not only the
mobility in consideration, but the potential attacks against the enemy
King, considering that this piece can be dropped. Classes 7 and 8 seems to
be unnecessary, in my opinion. I know that many players are not gained with
the idea of re-defining the classes, but I want hear more opinions about
it.

Thanks to Joe and Roberto for your comments. Roberto's comment about
drawishness is true with regard to a certain type of middlegame--the
complex middlegame where both sides find launching an attack too
dangerous.

The endgame however is not drawish at all--virtually all endgames are
decisive. King vs anything is a win for the stronger side--you just drop,
promote, drop promote until you have enopugh force for a mate. The lone
King can't defend the whole back rank. This being true, many times a
numerical advantage in pieces can be translated into a win (whether or
not
it is a meterial advantage).

An example: often the simplest way to win King, Queen, and Knight vs King
and Rook is to exchange the Queen for the Rook, which is a draw in FIDE.

I am most honored that Pocket Mutation Chess was selected as the newest
Recognized Chess Variant and the voted Recognized Variant of the Month the
first time out.

Clearly PM is my finest creation but I never imagined it would join such
august company in under three years.

One of the best variants, certainly and Michael Nelson, I think, is also one of the best variant designers.

I would like to see an expanded (more complete) list of pieces added to the classes.

Also, maybe an extension for some of the more powerful pieces, as with tripunch pieces and cylindrical / toroidal pieces? Would be fun to have classes 9 and even 10.

Abdul, can you please tell me what you mean by superknight and supernightrider?

Just want to know.

Yes, definitely a great game - (I won't rate it here, because I've
already provided an excellent rating previously.)

I am not sure that it is a good idea to add more pieces, though.  Going
too far in that direction sacrafices strategy for tactics, with a player
looking through all the pieces for the one that attacks just the right
combination of squares.  Then one would have to pay very defencively,
always keeping all pieces protected, lest he open himself up to a viscious
fork by some strange piece, like a knight+alfilrider...

Yes, maybe expanding the piece types (and classes) would allow tactics to overwhelm strategy.

Your discussion suggests an idea to me, which may characterize either this variant or one similar to it. It is the idea of the wizard's duel, like the one Merlin had against Madam Mim in the movie Sword in the Stone, where they change into different animals, each appropriate to do combat against the other.

Note: Michael Nelson also invented an excellent variant called Wizard's War as it so happens. It doesn't increase greatly the kind of pieces and the wizards aren't themselves chameleons, but they are interesting generator pieces.

At various times Joe Joyce, Greg Strong and myself have stated that it may be unwise to start the game by pocketing a Rook and changing it to Nightrider. As Greg once pointed out, the Nightrider is most powerful when you are holding it in the pocket, but this means that you cannot use the pocket for any other purpose while you are waiting.

Also, I am a big fan of the SuperBishop (Dragon Horse), which is the most powerful [Class 3] piece in 'normal' chessvariants, that do not allow dropping pieces. See this game - 287 days ago for a Nightrider and a SuperBishop working together to win the game. On the other hand, in [Class 5] I prefer the CardinalRider (Unicorn) to the SuperCardinal (which Roberto Lavieri praises in his 2005-04-19 comment). We are a long way from reaching a concensus on piece values in this excellent game.

Even in FIDE Chess, I like to play 1.d4 and 2.e3 with the White pieces. 
In PMChess I may also pocket the Bishop on (c1), changing it to a Knight. 
My style of play does not leave many holes for Nightriders to exploit.

I'm working on a couple of additional piece sets for PM. One is part of the Short Range Project and the other eliminates Nightriders and provides additional enhancements. In both cases I expect a more strategic, less explosive game.

I am in no way dissatisfied with the classic piece set, I just think providing some alternatives will be interesting for players who like the game concept but would prefer a different feel.

When I have them worked up I will amend the game page and submit a new ZRF.

I'm very excited to know that you plan to do more work on Pocket Mutation Chess.

I love Pocket Mutation Chess very much and the 'Excellent' rating I gave it earlier still holds for me. I'm in no way disillusioned. I would really like to see an expanded piece set, rather than alternate piece sets. Joe Joyce believes (and he's obviously quite right) that many short range pieces can compete well against the longer range ones. As evidence, he proffers 'Shatranjian Shooters' CDA and even has a hard time paring down the short range pieces enough to be soft enough to compete against the FIDEs. In other words, short range pieces can compete very effectively against rider pieces. Those who favor short range pieces can enjoy playing against those who favor longer range ones.

I see that you're already committed to a project but I also have talked about wanting to work on a version of Pocket Mutation Chess variant, recently on the chessvariants yahoogroup. This was in response to an email written by Joe Joyce in which he says that Pocket Mutation Chess is his 'favorite chess variant.' Joe there describes it beautifully as a 'fantasy variant' of 'Chess with Changing Armies.'

I propose having more classes, including one or two below (!) pawn (e.g., spacious wazir and lame dabbabas -- of course to be able to put such pieces on the board, you would have to start with one or two very weak ones) and two or three above Amazonrider.

Also, I favor having more pieces in each class, at least five per class. For example: In class 1, there are at least a few more types of pawns you could have, the most obvious ones that come to mind are chinese pawns and berolina pawns.

Thinking it over, I would really like to see nightriders put into Class 4. Then, a nightrider could only come on the board after a Class 3 piece gets to the eighth rank. Being able to pocket your rooks and change them into nightriders immediately really forces your opposing player to protect their bishop five squares (c5, f5 for white, c4, f4 for black).

Likewise, I would shift Cardinalrider into Class 6 (othwerwise queen could immediately turn into cardinalrider), therefore Chancellorrider and Supercardinalrider into Class 7, etc.

There might even be some classes of pieces subtly different enough to fit in between some of the classes you have already.

Obviously this is a variant where the relative values of the pieces matters tremendously. And therein lies much of its appeal because the relative values of pieces is already of paramount importance to any true chess enthusiast.

Michael, email me, please, if you're interested in discussing these things with me more. (I hope you will.)

I agree with Jeremy that nightrider is more valuable than rook in this
game. May be its value is somewhere between rook and cardinal:
* rook - 5 pawns
* nightrider - 6 pawns
* cardinal - 7 pawns.
So, moving all nightrider-combined pieces one class up will probably
improve this game. In any case, this will avoid that most of the game
start with rook->nightrider pocketing as of now. Certainly, some
play-testing is needed to see if really there are situations where you
will prefer nightrider over cardinal.

Other possible alternatives:
1) Add a new piece class between classes 3 and 4 and move nightrider and 
SuperRook there. 
2) Remove nightrider-combined pieces completely to simplify the game and
make it more strategic.

I think this is an excellent game as is, although I am eager to see Mike's new piece sets. [Great to see you back, Mike!] This is also such an excellent game concept that's it's almost impossible to resist speculating about different pieces and piece sets; 'Alternate Pockets' can easily become as varied as Betza's Different Armies, in its own twisted way. And I suspect the 'Mutant Armies' can be at least as difficult to balance as the Different Armies. But I'm sure some of us can have fun trying.

On the nightrider vs rook question, what are the weaknesses of pocketing the opposing rook's pawn after a rook is pocketed and mutated to NN? This threatens RxP, then R-R8 on a following move. The rook is not a bad piece in PM, it pins pieces and projects power along a line very well. The nightrider has a different job, leaping around, forking pieces, and generally making a nuisance of itself. But, a player can do a pretty fair job of covering the back few rows against knight attacks well into midgame, no? If that's so, then the NN 'avantage' is gone from the early game. What's so overwhelming about the NN that it is necessary to change a rook to one?

Just try a game with Jeremy (chose white and DON'T make rook->'nightrider in pocket' move early in the game) and you will see for yourself... Still, I think the game is balanced since white can prevent early forks by black nightrider and have time to pocket nightrider from rook as well. The only problem with this game is a lack of variety in the opening, since the majority of the game starts with pocketing nightrider.

We still have 7 games of Pocket Mutation Chess scheduled in Game Courier Tournament #3. These should answer some questions.