Thoughts on Chess with Different Pawns
By Ralph Betza
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?)
"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
Written by Ralph Betza.
HTML Conversion and some Editing by Peter Aronson
WWW page created: November 19th, 2001.