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Polypiece Chess

By Ralph Betza

Polypiece Chess is a game in which moving, a piece changes the rules of movement for all pieces of that type on the board, both yours and your opponent's.

Precedents

Many Rules in One Game specified different rules for whole armies -- the whole army would change at once -- and the change was periodic.

Quite a few games specify that a single piece may move according to different rules according to its situation. Greener Chess is one recent example.

Innovation

The two key ideas in Polypiece Chess are that the rules change whenever a piece moves, and that the change affects all pieces of the same type, both yours and the opponent's.

There may have been games, other than Turning Chess, where the rules for a particular piece changed at every move.

Having the change affect all pieces seems to be a new idea. Because this idea creates interesting and distinctive tactical possibilities, I think I would have remembered any game where this happened.

Rules

Rule Zero, of course.

Before the start of the game, an ordered list of powers is chosen for each type of piece.

When a piece moves or captures, it and all other pieces of the same type change their movement/capture powers to the next entry on the list; and after the last entry comes the first entry again.

Castling is a King move. Pawn promotion is a Pawn move.

The List of Powers

There need not be the same number of entries on the list for one piece type as for another. For example, in the example that follows, Kings and Pawns have only one entry, and therefore never change their powers.

A long list for every piece type will make the game confusing to play. A long list for Queens combined with a short list for the other pieces would probably be playable; each player has only one exemplar of the Queen piece type, which should make the long list easier to cope with.

The powers on a given list need not be equal, nor nearly even so. For example, a Bishop that changes to Wazir and then back to Bishop would be interesting. Remember, both players have the same army, and both players are affected by the changes, so the game remains equal even if individual pieces fluctuate wildly in strength.

Different Armies

It would be possible to play with different armies. For example, White starts with Knight which changes to Waffle and then changes back to Knight, while Black starts with Fibnif which changes to fwNW and then changes back.

However, Polypiece Chess seems to me to be a rare example of a game which ought to be played without different armies. Having different armies adds complexity in a second dimension; if you want to add complexity, it seems cleaner to do so by using longer lists.

Example

In the following examples, the Kings and Pawns do not change value, each other piece has two values, the values of each piece remain the same when it polymorphs, and the movements are chosen so that there is minimal overlap -- except for the Queen, each piece changes its field of fire completely when it changes, completely abandoning its old set of moves and adopting instead a completely different set that touches none of the same squares.

This is a very simple list of powers, but I think both that it produces interesting play and that its simplicity makes it a good introduction to Polypiece Chess.

List for the Examples

And here is the example list of powers:

Knight (N)	Woody Rook (WD)
Bishop (B)	Short Rook (R4)
Rook (R)	Nightrider (NN)
Queen (Q)	Squirrel + Wazir (WAND)
King (K)
Pawn

Here is how to read the list: the Knight changes to WD when one moves, but then when a WD moves it changes back to a Knight; the Bishop changes to R4 (a short Rook which can move no further than from a1 to e1) and back; the Rook changes to Knightrider and back; and the Queen changes to Wazir plus Alfil plus Knight plus Dabaaba and back. King and Pawn do not change.

Opening Example

1. e4 e5 2. Ng1-f3=WD

The Knight on f3 is now a WD on f3, and does not attack the Pawn on e5. On the other hand, 2...WDg8-g6=N? allows 3. Nf3xe5=WD and the Knight on g6 also becomes a WD, which cannot recapture on e5. What's worse, the usual 3...Qd7-e7 cannot be played.

2...Bf8-c5=R4

Defends e5 and impedes White's development because R4 is an awkward piece to have on f1 and c1.

3. WDb1-b3=N

White attacks both e5 and c5, and the R4 cannot move without undefending e5. In retrospect, 3. b2-b4 should be much stronger.

3... Nb8-c6=WD! Black's move changes White's pieces, and so defends against the threats in a way that can be seen nowhere else but in Polypiece Chess.

4. WDf3-f5=N

White renews the threat against c5, and also threatens g7.

4...Qd8-f6=WAND 5. Nb3xc5=WD WDc6xc5=N 6. d2-d3

With 6. b2-b4?, White could hope to win a piece because if the Nc5 moves away, the Nf5 becomes a WD and takes the Queen. However, 6. b4? WANDe4+=Q 7. Ne3=WD Qe4xg2=WAND+ and so on.

The alternative 6. Nf5xg7+=WD Kf8 7. WDg7-g5 Nc5xe4=WD is better, but still not very good for White.

Therefore, the quiet 6. d2-d3, renewing both threats.

6... WANDf6-g6=Q! 7. Nf5-g3=WD O-O

The terrible threat of Qg6xg2=WAND, with check, forced the humble retreat (g2-g3 makes such a weakness!), and now I think Black has at least an equal game.

Two Endgame Examples

With WKb7, WPa7, WNc3, BKd7, and BNa8, we get a deceptively simple position which was composed by Andre Cheron in 1926, and which is given by him as position number 998 in his Lehr- und Handbuch der Endspiele.

In FIDE Chess, White wins whoever moves, for example 1. Nd5 Kd8 (other K moves allow Kxa8) 2. Nb6 Nc7 3. Kc6; but in Polypiece Chess, 1. Nd5=WD+ Kd8 and Black threatens WDa8xa7+, so things are different.

In Polypiece Chess, Black to play draws by 1... Na8-c7=WD+ or White to play wins by 1. Kb7xa8 Kc7 2. Na4=WD 3. WDa5=N 4. Nc6=WD.

With Wkb7, WPa6, WNe4, BKa5, and BNb5, we have number 999, composed by Richard Reti in 1929. The win is easy if it's Black's move, but White to play takes ten moves, with two exclamation marks in the main variation and nine subvariations!! One of the greatest joys of FIDE Chess is that a position as simple as this can contain such complexity!

In Polypiece Chess, and using my example list of powers, White's Knight may not move because doing so puts himself in check when the Nb5 becomes a WDb5. There is nothing better than 1. a6-a7 Nxa7=WD+ 2. Kxa7, and is this a draw?

If White can confine the Black K to a corner, there is a mating position: WKg6, WNe6, BKg8, 1...Kg8-h8 2. Ne6-f8=WD checkmate.

What it it's White's move? 1. Ne6-d8=WD keeps the K confined, but how can you win? The Black K moving will always have made an even number of moves when it gets to g8, and so the only way to win is to make three King moves: 1. Ne6-d8=WD Kh8 2. WDd8-d6=N Kg8 3. Nd6-f7=WD Kh8 4. Kg6-g5 Kg8 5. Kg5-f6 Kh8 6. Kf6-g6 Kg8 7. WDf7-d7=N Kh8 8. Nd7-f8=WD checkmate.

Can W confine the enemy King to a corner? Unfortunately, the answer appears to be "Yes" (although it isn't easy; but it is no harder than K+N+B versus K in FIDE Chess). I say "unfortunately" because this means that the endgame N+P versus N is much simpler in Polypiece Chess with my example list than it is in FIDE Chess.

Perhaps the N should alternate with AD (Alfil plus Dabbabah) instead of with WD, and the Bishop should alternate with -- what? fbNW puts too many Knightly atoms in the game. Perhaps Ferz plus Langskipet? The Langskip is a bit Knightly, but not too much so perhaps. (The Langskip is a long Barc: it makes the (1,3) jumping move, wide forwards and narrow rearwards. For example, a White Langskip on e4 could go to b5, h5, d1, or f1. The funny notation is fsLbbL.)

It doesn't matter. My example list need not be perfect. It demonstrates the basic idea of Polypiece Chess quite well as it is.

Midgame Example

In the final position of Morphy-Brunswick, Black could play Rh8-g8=NN, and White's Rook at d8 would become a Knightrider, thus cancelling the checkmate.

This sort of defense seems to render most classical mating attacks unprofitable. This is a defect, not in the game of Polypiece Chess, but in my example list of powers. Apparently the idea of making the moves as different as possible has problems; however, the strangely different tactics may compensate for this defect.

Variants of Polypiece Chess

One might consider every possible list of powers to be a different variant; however, all of these hundreds of thousands of variants have been defined as simply part of the basic game of Polypiece Chess.

In Atomic Polypiece Chess, when a fbNW makes a W move, the W atom changes value in all pieces that use that atom. Defect: there is no way to become a Rook. Even so, it would be an interesting game.

In Phased Polypiece Chess, using my example power list, W would start with N and Black would start with WD, and 1. Ng1-f3=WD would change the WD at g8 to a Knight.

Summary

Polypiece Chess is a good game in itself, but it is also a building block for scads of new possible variants.

Written by Ralph Betza.

WWW page created: February 19th, 2003.

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Created on: February 19, 2003. Last modified on: February 19, 2003.