Chess pieces' values

What are the benefits and consequences of knights and bishops?

I tested the mathematical ratios of the pieces using chess programs , and I noticed that when these correct ratios are set in Raubfisch from 2022. year competes with programs from 2024. year that have a newer NNUE . I wrote a scientific paper in mathematics that no reviewer has given any grade to so far , but in chess the receptionist's rating is not required because chess is not science

Chess is my hobby when other things don't tune me then I play chess . I can see checkmate in five moves and sometimes win a rating of 2000 , but very often I don't see myself losing a piece in one move , so even those with a rating of 1000 beat me, especially if I fail to checkmate then I lose on time for 3 min + 2 s . But to test the chess programs , it is enough to study chess theory

You can read post #55 at this topic

I'm not writing about having checkmate in 15 moves by giving 2 pieces , but I'm writing about when the depth is so great that even the computer can't see depth 80 in 3 minutes , so when the depth is great , the computer is given the values ​​of the pieces .

ngl the Bishop should be 3.5

In Raubfisch X48e I set

KnightValueMg = 843 KnightValueEg = 816
BishopValueMg = 843 BishopValueEg = 851

PawnValueMg = 183 PawnValueEg = 272

843 / 183 = 4.6...

816 / 272 = 3

Middlegame = Mg
Endgame = Eg

engine tournament

And when do you think a rook could ever be stronger than a bishop and knight?

checkmate with a rook and king vs lone king is easy to teach and easy to execute.

checkmate with bishop and knight and king vs lone king is difficult enough that many prominent chess teachers ignore it completely.

True.

While pawns are usually in the game then rook is stronger than bishop or knight , but rook are weaker than knight and bishop . However , if you manage to take all the pawns , then the endgame of king and rook against king and bishop is a draw , as is the endgame of king and rook against king and knight is a draw , so chess engines often draw when have a bishop or knight against rook .

A draw is the endgame of a king and a rook and a bishop against a king and a rook , just as a draw is the endgame of a king and a rook and a knight against a king and a rook

I can win with a king and a rook against a king when I play 3 min + 2 s , as I can win with a king and two bishops against a king , while I need to play 5 min + 5 s to be able to win with a king and a knight and a bishop against a king .

However, it is even harder to win with a king and two knights against a king and a pawn, because while one knight blocks the pawn, the other knight and king push the opponent's king into a corner, and then the first knight goes to checkmate while the pawn goes to get the queen, even computers take time to find checkmate .

The king and queen against the king and two knights are a draw , as the king and queen against the king and two bishops is a draw , but the king and queen against the king and knight and bishop is defeated by the side that has the queen , except in exceptional cases . Often two rooks and a king against the queen and a king and two separate pawns is a draw . While a draw is mostly even when the king and a rook and a pawn are on the starting row against the king and queen .

How about a queen vs two rooks?

...

draw ( except in exceptions ) as queen vs rook and bishop or queen vs rook and knight

medium endgame calculus ;

bishop = 2.5 * pawn 
knight = 2.5 * pawn 
rook = 4.5 * pawn 
queen = 8 * pawn 
2.5 + 4.5 = 7 
< 8 < 
4.5 + 4.5 = 9

against a weak player the game can be won the game that is draw ( I learned to open diagonals and lines by watching how chess engine play with each other )

Good.

variant of Pirc-Ufimtsev Defence 1. e4 d6 2. d4 g6 3. Nf3 Bg7 4. Bc4 Nf6 5. Nc3 Nc6 6. d5 Na5

that was played in the game ShashChess33.2-x86-64-avx2 [mcts] _ Kayra 1.6 avx2

Quite complex research you've got. Mind blowing work you've done.