4 ms·

Neat results! I am very much a rank amateur, but it looks like these results roughly align with the traditional 1-3-5-9 point values for the pieces, with a coup

Neat results! I am very much a rank amateur, but it looks like these results roughly align with the traditional 1-3-5-9 point values for the pieces, with a couple exceptions. Advantages of a single pawn, minor piece, or rook have proportionate values similar to what you'd expect. In particular, bishops and knights are very close with bishops being worth a tiny bit more. Winning the exchange is a sizeable advantage. Trading a rook for two minor pieces is an advantage except at the lowest skill levels. Two rooks turn out to be significantly worse than a queen instead of slightly better. But the most surprising thing to me is that having the two bishops seems to be worth almost nothing -- close to 50% odds across skill level. A single pawn advantage is more valuable! (The article says "4-5% more likely to win" at Elo 1200-1400, but that doesn't match the graph.) These surprising results were also more consistent across skill level, while the well-known advantages are worth significantly more to skilled players.

rmetzler 3y ago
> In particular, bishops and knights are very close with bishops being worth a tiny bit more. I don’t think so, and I would like to see the author look in the data for 2 knights vs 2 bishops. My gut feeling is that knights are hard to block and can attack every square, while bishops can only attack their color, so half the board. They can’t protect each other and rely on pawns for this. I’m happy to trade my knights for the pawns, but I would like to see if I’m wrong.
- compiler-guy 3y ago
  Bishops have a great deal more mobility than knights. A knight in the wrong corner takes several moves to catch up to a distant passed pawn. A bishop needs far fewer. Generally the trade off is a bishop pair, where you do have all the squares covered, vs the slower knights, who are also the only pieces that can threaten a piece without being threatened back. The advantages are highly position dependent, with closed games largely going to the knights and open games going to the bishops pair. But most games turn into open games at some point, so statistically the bishops end up better.

rmetzler 3y ago

> In particular, bishops and knights are very close with bishops being worth a tiny bit more. I don’t think so, and I would like to see the author look in the data for 2 knights vs 2 bishops. My gut feeling is that knights are hard to block and can attack every square, while bishops can only attack their color, so half the board. They can’t protect each other and rely on pawns for this. I’m happy to trade my knights for the pawns, but I would like to see if I’m wrong.

compiler-guy 3y ago
Bishops have a great deal more mobility than knights. A knight in the wrong corner takes several moves to catch up to a distant passed pawn. A bishop needs far fewer. Generally the trade off is a bishop pair, where you do have all the squares covered, vs the slower knights, who are also the only pieces that can threaten a piece without being threatened back. The advantages are highly position dependent, with closed games largely going to the knights and open games going to the bishops pair. But most games turn into open games at some point, so statistically the bishops end up better.