Value of Pieces for "Infinite Chess"
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hitthepin
Jan 26, 2018
0
#61
Wait, what does everyone know?
Everyone knows that you shouldn't talk about a game that is in progress. But you already knew that, right?
Here is another diagram that shows a representation of the hawk's ability. The blue lines show how far the hawk can move in 1, 2, and 3 moves (but cannot attack every square inside the blue in the number of moves). According to HGMuller, in 167 moves the hawk has 1,004,004 options of different squares to land on. It's being discussed at another forum (link here):
https://chessvariantforum.createaforum.com/variant-theory/math-question-about-the-knight-and-hawk/
Jan 30, 2018
0
#65
Wow. Although the “measly” bishop can go unbounded, the hawk isn’t too bad either!
HGMuller issued a formula to calculate the value of chess pieces which jump. I believe it's based on short-range jumpers, but it might work for other jumpers when the board is large compared to the jumps. The formula simplifies to this:
Value =33(N) + 0.6875(N)^2 (in centipawns)
(N is the number of targets)
So using this formula we get:
knight(8) = 308
king(8) = 308 (same as guard)
hawk(16) = 704
So the hawk is worth more than twice the value of the knight, and maybe the value of a (rook + two pawns). But again, how can anyone know for sure?
I think the extra distance that the hawk can strike from has a value too, it's not a simple case of how many squares it attacks but also from where it can attack.
Feb 4, 2018
0
#68
Both 6 pawns and 7 pawns seem to be good enough guides. Enough to know you wouldn’t give up your hawk for a rook.
Feb 5, 2018
0
#69
A sudden thought occurred to me: in infinite chess, a knight always attacks eight squares. However, in classical, the knight doesn’t always hit eight squares, due to the edges of the board. Does that mean the knight increases in value in infinite?
Feb 5, 2018
0
#70
So, because I was bored in class, I calculated that on average, a Knight in classical chess is only attacking 5 or 6 squares on average (actual number: 5.5625. But someone should check me), compared to eight in infinite. So if the Knight is worth 3 in classical, maybe it’s worth 3*8/5, or 4.8 in infinite?! I don’t know.
Not a bad concept, but when switching to an infinite board I think all pieces get more attacking ability (except maybe pawns?). So this means adjusting the value of all pieces. The knight has more power, but how does that compare to the power gained by the bishop? The diagram here helps show what 's going on, but doesn't solve anything. Too much work for me to figure all this out.😥
Feb 5, 2018
0
#72
Well, true. Maybe sliding pieces should get a bigger boost than one point.
hitthepin wrote:
So, because I was bored in class, I calculated that on average, a Knight in classical chess is only attacking 5 or 6 squares on average (actual number: 5.5625. But someone should check me).
I make it 5.75, but I'm not double checking.
My calculation is 368/64
Yours is 356/64
I double checked, it was bugging me.
16*8 = 128
16*6 = 96
20*4 = 80
8*3 = 24
4*2 = 8
total squares attacked... 336
336/64 = 5.25
We were both wrong.
My values:
Pawn 1
Knight 3
Bishop 4
Guard 4 Just because the guard isn't mobile doesn't mean it's not strong- it's defensive capabilities are OP
Hawk 5 most agree this should be 6, but the tempi spent to get this guy in the game affects score and also it's likeness to a rook, but weaker, may even make this piece a 4!
Rook 6
Chancellor 9 Due to easy development and therefore ability to rush develop for attack, this piece may be considered 10 points also
Queen 10
King 2.5 The labor to defend the king! Honestly.
Feb 5, 2018
0
#78
2.5 is not accurate for the king. He’s either the most valuable piece (game), or the same as a guard. Although I agree that a guard’s defensive capabilities are strong, it’s not worth 4. 3 or maybe 3.5 maximum.
Feb 5, 2018
0
#79
Also, the issue with chancellors is the fact that they are valuable. They only really seem to come into power towards the endgame. There haven’t been many infinite games that reached the endgame yet. :( I so want to see one.