Comments/Ratings for a Single Item
That may often seem like the case, but it is often not the case (at least not in FIDE chess). There are many end-games, for example, when one player has a Bishop of color opposite to that upon which his opponent's pawns rest. And, the other player has a Knight which can attack that player's pawns. I have won many such end-games. In fact, there are end-game books which clearly point out the scenarios in which knights end up being decisively better than Bishops.
It is not obvious to me that this is two. With two Bishops on each color, each Bishop now has two othe Bishops with which it can cooperate. When I have time I will run all combinations BNNN, BBNN, BNBN, BBBN and BBBB against the 4 Knights, to see how the advantage grows. BBNN is known to be more than double the BNNN advantage (the difference being the pair bonus, of about 50cP), while BNBN (like colored Bishops) does give double the BNNN advantage. But I haven't tried BBBN yet. And this measures very small differences, so it should use many games (1000+).
How many Bishop pairs should you count? Two seems right to me. I chose that 4N vs 4B setup to allow standard chess programs to be used, but Zillions seems to be more reliable on Windows Vista than Deep Fritz, which is the only other chess engine I own.
Ralph Betza also writes 'What can you say about the poor Knight? It doesn't get any weaker as the game goes on, it's just that the other pieces get stronger while the Knight stays the same. In fact, it would be reasonable to conclude that the value of the Knight during the opening and middlegame exceeds its conventional value. In fact, that would explain why I have won so many games by allowing my opponent to 'win' a Bishop for a Knight in the early part of the game.'
Why use Zillions for this, if Rybka or any other normal Chess engine can do it? I did actualy try the positions you give with my engines, but I have some difficulty interpreting the results. How many Bishop pairs should I count? Two, or four?
Ralph Betza has written here 'It is clear from the discussions of endgame advantage that the Knight must be actually stronger than the Bishop in the opening and middlegame: if their total value is roughly equal, and the Bishop gets stronger as the number of pieces on the board decreases, and everybody agrees that the Bishop is generally stronger in the endgame, then it must be true that the Knight contributes more to your position in the early part of the game than the Bishop does.' DAVID SAYS: I would not be surprised if a series of test games yielded a surplus of early wins for White in Chigorin Chess. [EVEN SIMPLER EXAMPLE] Both players keep their queens and the games is 4 Knights versus 4 Bishops:
When White has 4 N and Black has 4 B, 'Zillions Chess' values a Pawn at 1847 points and puts Black 2588 points ahead after 1. d2-d4.
When White has 4 B and Black has 4 N, 'Zillions Chess' values a Pawn at 1847 points and puts White 1580 points ahead after 1. d2-d4. The average of 2588 and 1580 is 2084 (1.13 pawns), which would seem to be the value of having 4 Bishops versus 4 Knights, according to Zillions. As to how well the White pieces would score in 'Zillions versus Zillions' games, that is an entirely different matter.
Dave McCooey - Fairy endgames with 3 pieces (8x8 board)
Amazon(R+B+N), Queen(R+B), Chancellor(R+N),
Unicorn(B+NN): a Bishop-Nightrider combination.
||||| Longest Wins for the Strong Side (WHITE) |||||
||||| (strong side has 2 pieces, weak side has 1 piece) |||||
KRRvKQ-----30-------14 f-captr WK(c8) WR(h2) WR(g8) BK(a1) BQ(d1) WHITE
KRRvKU----202--------4 capture WK(b8) WR(d5) WR(h8) BK(d7) BU(e1) BLACK
KRRvKC-----87--------9 capture WK(d6) WR(a6) WR(a7) BK(g6) BC(d3) WHITE
Queens and Chancellors have good chances of drawing by
perpetual check. If they fail, then the game ends fairly quickly.
The Unicorn has little chance of drawing, but it can drag
the loss out to an incredible 101 moves.
Okay, but I don't believe that the Chancellor is worth less than the Q. The midgame forking power of a piece that moves in 12 directions is quite amazing, the Chancellor has exceptional ability to save an inferior game by giving perpetual check, and finally, the drawn cases of K+Q versus K+P are wins in the endgame K+NR vs K+P. Of course there are positions that favor the Q, but all in all, my experience says they are equal.
'Favors Black, you think? Then perhaps you will be willing to offer me substantial odds as we play a game for some enormous stake of money, perhaps a penny on a1 doubled on each successive square?' I had almost put the above statement into the story of getting a regular chessplayer to play Chigorin Chess, somewhere after the part where 'variant rhymes with deviant and that starts with d and rhymes with t and stands for trouble.', and way after the part where the regular chessplayer says with a sneer is that some kind of fairy chess.... (I'm not suggesting that you're the offensive non-PC 'regular chessplayer'; the misinformation about relative values of N and B is part of general unwisdom, that's all.) Read any monograph on the Chigorin Defense. You'll find that many players now believe the N to be superior in the early stages of the game, which agrees with my findings on the theory of chess values so I think it must be right. Given the advantage of the first move to go with the advantage of fast development, the *white* side in Chigorin Chess probably has a large advantage. In order to Castle K-side, Black needs to move two Pawns and two Bishops; and one of those P moves looks suspiciously like a weakening move. White can go 5.O-O at the earliest, but Black can choose to go 3...O-O; think about it! And, of course, this is the whole point of Chigorin Chess! You can get a 'regular chessplayer' to play, because he will want to prove that the Bishops are so much superior...
16 comments displayed
Permalink to the exact comments currently displayed.