Thoughts on Chess with Different Pawns

By Ralph Betza

Introduction

Jeff "Cavebear" Stroud recently wrote to Ralph Betza, mentioning he has interested in the topic of Chess with Different Pawns. The following note is Ralph's reply, and is of general interest.

On Chess with Different Pawns

Alternate Pawns in a game with different armies requires great precision because there are so many of them. If you misvalue your Knight substitutes, well, there are only 2 of them and perhaps a compensating error in some other piece will save you. With Pawns, your errors are multiplied by 8 (assuming 8x8 board).

Value of promotion, unknown, unknown how to calculate it, but important. A standard Pawn has 3 movements (2 capture-only, 1 move-only) compared to 16 for a Knight, that's nearly a third of a Knight, give a bonus because the powers are very forward, it looks like promotion is worth nothing. But al-Adli thought a Pawn was worth one fifth of a Knight! You must respect the ancient masters! A Shatranj Pawn can promote only to a Ferz, and a modern Pawn is thought to be worth 0.33 Knight instead of 0.2 Knight, so one thinks(as I already thought in 1981) that a huge part of a Pawns's value comes from promotion.

Page 227 of Murray. The paragraph that starts on 227:

"Both al-Adli and as-Suli made an attempt in their chess-books to estimate the relative values of the chessmane in the early part of the game."

Hmmm. Promotion doesn't happen in the early part of the game. Perhaps, all these years, I've been misled by faulty memory or loose reading.

Page 228, "Rook vs. four concordant Ferzes loses" -- loses by bare King, not by mate, obviously -- what a strange endgame, how many moves it must take.

P. 228, "I adopt as the unit of my scale the value of the Rook's Pawn" -- another place where faulty memory or loose reading may have betrayed me. King's Pawn in estimated values in Shatranj is worth twice the value of a Rook's Pawn, and in Modern Chess, the same as in Shatranj, but sometime in the endgame an "outside passed Pawn", due to the value of promotion, a Rook's Pawn is better. Nobody makes this estimate in modern Chess, but central Pawns are generally preferred.

Taking value of average Pawn, ratio of value between Knight and Pawn is the same in Shatranj as in Modern Chess. I have made an error, and publicly published it in both 1996 and 1981. However, the error is irrelevant with respect to importance of promotion because in Shatranj with the rule of winning by bare King, promotion of a Pawn to a Ferz could often be as decisive as promotion of Pawn to a Queen is in FIDE Chess.

Catch that last sentence. I'd like to have this email posted to the CV pages so some of the excellent minds there could absorb it and either agree or disagree.

Promotion is very important to the value of Pawns, but as long as you promote to something decisive the value of what you promote to is unimportant. Page 229 points out that being stalemated loses, just like being checkmated; Rook versus four Ferzes of the same color is a draw in FIDE Chess, but in Shatranj the ancient masters say that the four Ferzes win.......

The Berolina Pawn is thought to be worth much more than the FIDE Pawn because its additional movement allows it to promote so much more easily. I don't know if anybody has really tested this. If it's true, would a Berolina Pawn able to promote to Bishop be worth as much as a FIDE Pawn able to promote to Queen? (A Berolina Pawn is worth less than FIDE Pawn in opening and midgame, I think. Pawn fork? What's that?)

Page 232:

"The eleventh (grade of odds-giving) the F and a P; or what is equavalent, a N; for though the F and P be slightly inferior to the N in the beginning, yet you must take into account the possibility of the P becoming a second F".

You must respect the ancient masters! Reading a passage such as this fills me with self-awe: for I have made real progress on a problem that has been worried at by intelligent folk for a millenium and more! (I've made progress; my answers are not complete, and no doubt in many cases they are not correct.)

Alternate Pawns! I wish you luck! When I started trying to make chess for different armies in 1977 or so, I had no idea how tough a problem it was, nor did I know how long it would take me. In my chess with different armies, both sides have the usual King and both sides the usual Pawn, and this is a simplification that I came to only after mature understanding of the difficulties involved in having different Kings or Pawns.

If you can find alternate Pawns, I will be in awe, taking my hat off to you.

And, to keep you from feeling complacent, I'll ask you to try chess with different Kings. I now fade away, leaving nothing behind but an evil grin.

Written by Ralph Betza.

HTML Conversion and some Editing by Peter Aronson

WWW page created: November 19th, 2001.

Comments

Thoughts on Chess with Different Pawns. The difficulties of composing Chess with Different Pawns.

H. G. Muller wrote on Thu, Feb 12, 2015 06:14 AM EST:

> and noting that it is forbidden to give permanent check in Shatranj

This is the first time I hear of this. The rules in the Sjatranj article on this website make no mention of a ban on perpetual checks. Where does this come from?

Steven Streetman wrote on Tue, Feb 10, 2015 06:44 PM EST:

Concerning chess with different pawns on one side...

In Spartan Chess the White side, the Persians, are a conventional FIDA army. For the black side, the Spartans, everything is different.

The pawns (a variation of Berolina pawns) and the pieces, are all different. In addition, the Spartans have two kings, not one (historical). Despite all of the differences (pawns, pieces, Kings) the game has proven in thousands of computer vs. computer games to be more balanced than FIDA chess. In FIDA chess white has a winning percentage advantage of 54% and a draw rate of 33%. Spartan Chess has proven to have a winning percentage of 50.5% for the Spartans (Black) and a draw rate of 25%.

Hence, Spartan Chess is more balanced and less drawish than FIDA chess. I have pondered why this is true and I really do not know why.

Spartan Chess Web Site
Spartan Chess on Chess Variants

Jörg Knappen wrote on Thu, Nov 18, 2010 10:27 AM EST:

A very interesting note worth reading again from time to time.

What makes me wonder here are the remarks about old shatranj and that
K+4F (same colour) should win against K+R. I tried this by hand and found no way of confirming this claim. 5 Ferzes of the same colour are a different thing: A chain of Ferzes along the long diagonal can confine the rook in one diagonal half of the board (with the help of the King and noting that it is forbidden to give permanent check in Shatranj). Then, the net of Ferzes can be tightened until the rook is caught in a net and can be taken by the King.

There is still considerable counterplay by an active defending King, and exact play is needed.

I think, the mentioned scenarioes are worth a computer analysis.

--Jörg Knappen

George Duke wrote on Tue, Jun 2, 2009 09:03 PM EDT:

Even if they are the same type, different Pawns have inherently different values from the get-go. That makes sense just by imagining arrays of wild-eyed variantists. A Pawn in third rank has to be worth that noticeable fraction more than 2nd-ranker. Keying off some pages in Murray around 228, Betza says, ''King's Pawn in estimated values in Shatranj is worth twice the value [!] of a Rook's Pawn, and in Modern Chess, the same as in Shatranj....'' Does this come up in 20th Century Chess literature? Less so than you would expect since they do not even give odds like in 18th Century Philidor's time, where a good player might omit one Knight, and so on. I meant to mention at Fourriere's Pocket Polypiece Chess that Russians have periodically banned or shunned blindfold chess, because of supposed damage it does to mental faculties, and the same can be said of ''Polypiece-ing,'' moving any piece changing the piece-types of 33% of the pieces on board until the next move of piece flips some 1/3 of them again; and again.