During my continuing research into the values of chess pieces, I have become interested in a number of pieces that seem uninteresting to the ordinary CV-er; pieces that are not very exotic...
The Game of Augmented Knights is almost as humdrum as Almost Chess, but is a game quite easy for the chessplayer to pick up, and all its subvariants are unfailingly interesting and difficult.
"Augmented Knights" is self-descriptive, to the extent that it implies rule 0: "the game is the same as FIDE chess, except for the augmented powers of Knights". Knights, in this game, may move like Knights, but they may also have an extra power.
In fact, Augmented Knights is a set of many different games; at the start of each game, one of the possible sets of rules is chosen at random, and then White makes the first move.
Choosing a set of rules involves choosing one number from 0 to 9, and another number from 0 to 2. For over the board play, a standard deck of cards may be adapted for this use; for postal play, the players may agree to use the Dow-Jones or the S&P 500 to derive the choices.
The first number chooses which augmented power is added to the normal move of the Knight:
G J L H L J G 6 8 7 5 7 8 6 J A N D N A J 8 4 0 3 0 4 8 L N F W F N L 7 0 2 1 2 0 7 H D W . W D H 5 3 1 . 1 3 5 L N F W F N L 7 0 2 1 2 0 7 J A N D N A J 8 4 0 3 0 4 8 G J L H L J G 6 8 7 5 7 8 6 0 Nothing This is FIDE Chess, and the second number is ignored! 1 Wazir W, (0,1): a NW on e4 can move to e3, d4, e5, f4, c3, d2, f2, g3, g5, f6, d6, c5 2 Ferz F, (1,1) 3 Dabbaba D, (0,2) 4 Alfil A, (2,2) 5 (no name) H, (0,3) 6 (no name) G, (3,3) 7 (no name) L, (1,3), "long Knight" 8 (no name) J, (2,3) 9 KnightRider Continues in the same direction; a KnightRider is to a Knight as a Rook is to a Wazir; a KnightRider on e4 can go to d6, c8 (if d6 is empty), f6, g8 (if f6 empty), g5, g3, f2, d2, c5, a6 (if c5 empty), c3, a2 (if c3 empty).
The second number chooses how the augmented power is applied:
0. The new power can be used both for movement and capture.
1. The new power can only be used when capturing.
2. The new power can not be used when capturing.
The only reason for having exactly ten powers in the list is so that postal players can choose by taking a single digit from some agreed-upon source.
Observe that, in variation [8,0], 1.NJg1-d3 threatens two mates, to wit, 2.NJd3-g5 and 2.NJd3-c5; however, after 1...e7-e6, White's first move appears to have been a bad one. It violates Emmanuel Lasker's principle of "Knights before Bishops", which we must re-interpret in this context to mean "develop the weaker pieces first".
It would be possible to play a game where you "throw the dice" to choose a new set of rules every ten moves...
The main reason is that the Knight move, and the Knight's position on the board, are so well suited for the role of the Knight in FIDE Chess: the Knight is the weakest piece, and so should be developed first. All types of Augmented Knights are worth more than Bishops, and so there is an underlying tension between the changed scale of values and the natural role of Knights.
Additional interest is added by my principle of "the weak become strong". As an example of how this works, in FIDE Chess, if a Knight attacks a defended Rook, the Rook must move; but if a Queen attacks a defended Rook, who cares? -- and so, in a sense, the Knight is stronger because it is weaker! With augmented Knights, the Bishops are the pieces that benefit from this effect.
If you want to see this effect in action, simply analyse the opening of a game where White has ordinary Knights, but Black has a pair of NW or NF!
Here is a sample of [2,0]: Ferz
1.e2-e4 e7-e5 2.d2-d4 e5:d4 3.Qd1:d4 NmAb8-c6 4.Qd4-a4 Bf8-c5 5.Bf1-b5 5.Bf1-c4? Qd8-e7! 6.Bc4-b3? a7-a6 traps the Qa4 6.Bc4-d5? NmAc6-d4 7.c2-c3 NmAd4-b6 8.Qa4-b3 9.c7-c6 Black wins a Pawn 6.Bc4-d3 d7-d5!? 7.Bd3-b5 Qe7:e4+ 8.Qa4:e4 d5:e4 9.Bb5:c6+ b7:c6 Black slight plus, material about even. 6.Bc4-b5! NmAc6-d4 7.c2-c3 NmAd4-b6 8.Qa4-c2 unclear 6.NmAb1-d2 blocks the Bc1 and looks bad 5... NmAc6-d4 6.c2-c3 NmAd4-b6 7.Qa4-c2 c7-c6 8.Bb5-d3 d7-d5 9.e4:d5 c6:d5 (Q:d5 10.Be4 Qh5 11.Bf4 advantage White) 10.Bd3:h7 Bc5:f2+! 10.b2-b4! Bc5-e7 (Bd6!?) 11.Bd3:h7 NmAg8-f6 12.Bh7-d3 Black has insufficient compensation for the Pawn. ...Bc8-d7 13.a2-a4 a7-a5 14.b4-b5 ...Qd8-c7 13.Bd3-b5+ Ke8-f8 14.h2-h3 Be7:b4, 15....Qe5+ 13.h2-h3 0-0 (threat B:b4) 14.NmAg1-f3 or to e2 ...NmAf6-h4 13.g2-g3
There are no absolute values for chess pieces; so much depends on the composition of the whole army, and the starting position.
To demonstrate this, play a game where White has two Commoners instead of his Bishops, but Black has the normal army. (A commoner is a piece that moves like the King, but isn't royal.) It should be a fairly even game.
Now try it with Commoners replacing the White Knights (give White back her Bishops!). You should find that it greatly favours Black.
Now try it again, but this time you must realize that the Commoners make wonderful defenders and never have a cramped position (no matter how bad it looks), and that the Commoners always win every endgame if you can trade off your Bishops, and trade all the Rooks and Queens. You will discover that the value of the pieces depends not only on the composition of the rest of the army and on their initial position, but also on whether or not you have found the proper strategy for using the strengths of a particular piece!
In general, though, NA, NH, NF, ND, and NW might be worth a little bit more than Rook in most positions. NG is worth less than a Rook, but KnightRider is just strong enough that KnightRider versus Rook is a winning advantage in many endgames.
NL and NJ, of course, are really strong, maybe halfway between Queen and Rook.
Capturing is more valuable than moving: NcW (Knight augmented by Wazir capture, subvariant [1,1]) is worth more than NmW, but only a little; the material advantage of Rook versus NmW is about half as much as Rook versus Knight, and the advantage of R versus NcW is about half as large as R versus NmW.
There seems to be a general rule here, that adding a movement power is worth about half as much as adding both movement and capture power, and adding a capture power is worth about two-thirds as much as adding both powers.
You may notice that things don't quite seem to add up in these explanations -- capturing plus moving is worth more than the sum of capturing and moving. Equally, a Wazir must be worth less than half as much as a Knight, but adding its powers to those of the Knight produces a piece worth more than 1.5 times as much as a Knight! This seems to be another general rule, one which explains why the Queen is worth more than separate Rook and Bishop.
For me, the exciting possibility is that NA, NH, NF, ND, and NW have almost exactly the same value, so close that you might never notice the difference, so close that positional considerations are always more important than the intrinsic difference in value.
Why is this exciting? Because it means that you can play a game in which the two sides use different Augmented Knights!
Ever since I published my series of articles on "Chess with Different Armies" in 1979, I have been studying (sporadically!) the values of the pieces in order to create a different-armies chess where both sides were so equal that you could play the game in tournaments. (Of course, I wanted to have a game where all the pieces on both sides were different, but sometimes you have to be satisfied with what is possible.)
I therefore append some opening analysis for one of these games:
NA and NW are very equal in value, much closer in value than Bishop and Knight; either NA or NW is worth a bit more than a Rook in a general case, but in an open endgame position with Pawns on both sides of the board, an active Rook might be stronger. (Rooks get stronger as the board empties out.)
Ralph Betza has send me the moves of the following game, which is the first actual game (that he knows of) of Different Augmented Knights, together with comments on it by the players.
Vladimir Roytman (National Master) - Ralph Betza (FM)
email, August to September 1995
White uses NA, Black NW.
1. d4 d5 2. Bg5 (*Z*) Bf5 3. e3 c6 4. Bd3 B:d3 5. NA:d3 NWd7 6. Qg4 Qa5+? 7. b4 Qa6 (*A*) 8. Q:d7+ K:d7 9. NAc5+ Ke8 10 NA:a6 b:a6 11. NAe2 Rb8 12. a3 f6 13. Bf4 Rb7 14. c4 e6 15. c:d5 e:d5 16. 0-0 Kd7 17. NAc3 NWe7 18. NAa4 NWe6 19. Rfc1 Rb6 20. Rc3 Be7 21. Rac1 Rc8 22. Bg3 NWd8 23. f3 f5 24. e4 fe4 25. fe4 de4 26. Bf2 Rb5 27. NAc5+ (*B*) B:c5 28. d:c5 NWe6 (*C*) 29. Rd1+ Ke8 30. Re1 NWe5 31. Rh3 Kf7 32. R:h7 Re8 33. Rh4 a5 34. Bg3 NWd3 35. Re:e4 R:e4 36. R:e4 a:b4 37. a:b4 R:b4 38. R:b4 NW:b4 39. Kf1 NWb3 40. Ke2 NW:c5 41. Be5 NWd5 42. Bb8 a5 43. Kd3 Kf7 44. h4 Ke6 45. g4 NWe5+ 46. Kc3 NW:g4 47. Bc7 NW:h4 48. B:a5 Kd5 49. Kd3 NWh5 50. Ke3 g6 51. Kf3 c5 52. Ke3 Kc4 53. Ke4 Kb3 54. Kd5 c4 55. Kd4 g5 56. Be1 NWf4 57. Ba5 g4 58. Ke3 NWf3+ (*D) 0-1
A clever opening choice. Whatever the right answer is, we can be sure that it's not what I played here! :-(
Suddenly noticing that ...Qa3 is no good, Black accepts the doubled a-Pawns in order to get out of trouble.
Black is about to get counterplay and quite a good game with ...a5, but this sacrifice is hardly necessary. Of course, it's almost good enough.
Black has problems finding a safe place to keep the NW. In fact, d5 and g6 are the only possible safe squares, and if it hides on d5 there's a strong possibility of R:d5 c:d5 and the passed Pawns are strong. Also, he has to watch out for things like 30. Re1 Rb7 31. Re4 Kf7 32. Rce3 Re8 33. Rf3+ Kg8 34. Rfe3 draw by repetition.
However, there's an answer to all this, so the sacrifice on c5 was not good after all.
In the previous position, Ba5 was my only move; any other would let your Knight grab or exchange my Bishop - pretty good illustration of the Knight's power!
I was going to point that out in pretty much the same words, but feared to sound gloating. In fact, I thought Nf4 would be so distressing that you'd raise the white flag at once!
The other thing about it was that 57...Nd3 (if I chose to play it) would be check no matter what your 57th move was. The thing is that this N controls *all* the squares of the opposite color within an area larger than 1/4 of the board, so when it has a good move it can be very impressive.
I just realized that I can't even protect c1 anymore, since your Knight controls all the access squares for the c1-h6 diagonal!
I hadn't thought of that; I just figured that as long as I kept advancing the two widely separated Pawns, something had to break.
Nor can I get to your g4 pawn, also because of the Knight!
That I knew :-)