Value of Pieces for "Infinite Chess"

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HorribleTomato

@CaptainTugwash is leaning towards 7/8 or even higher. I feel that it is only 5/6, but can still be a useful piece.

captaintugwash

I value it when developed early more than anything other than the chancellor and queen, so I suppose 7-8, but I recognise its value will decrease as pawns are exchanged, while the rook (the next best piece) will increase in value, so I expect in endgame the rook to be better.

 

The hawk is an interesting piece.

HorribleTomato

I do realize how it's important for hawks to get out early, but their points are slightly to high. BTW, I am arguing with the rook/chancellor. I refer to the useless space far away as "Nowhere" i.e. a space outside the board where queen only hits 1 piece. capitalized N. Q/R/C are the only ones who can effectively reach Nowhere, and it's there just for kicks. So, a rook can actually reach about 40 useful squares, and a chancellor can reach 48.

HorribleTomato

It's not often in infinite one goes Q(999999999999999999999999999999999999999999999999999999999999999,999999999999999999999999999999999999999999999999999999999) That space is "useless"

hitthepin
I agree that the rook rapidly increases in value in an endgame. However, it’s so much weaker in the opening/middle game that it kind of balances out. Time will tell.
hitthepin
I suppose the next step would be to quantify the values of the pieces throughout each phase of the game.
supware

Perhaps the value of a piece is some function on the number of moves..?

hitthepin
What do you mean?
vickalan

HGMuller made a formula to estimate piece value based on how many squares it attacks. But it is only valid for pure-jumpers (like knight), and he also said for "short-range" jumpers. The formula is:

  value (in centipawns) =33(N) + 0.6875(N)^2
  N = number of squares attacked.

For example, these pieces are jumpers, and their value is estimated as follows:

  knight: 8 squares, value = 308 (3 points)
  guard: 8 squares, value - 308 (3 points)
  hawk: 16 squares, value - 704 (7 points)

HorribleTomato

My hawks are jumping all over in my game v. Aiden. The only problem is it's jumps are slightly hard to control. That's why I traded one for his rook. tongue.png The thing is, a hawk covers infinity squares less than a rook, yet it's worth more! What?

hitthepin
Yes, I believe rooks are stronger in hawks in the endgame because there are more open files for it to travel along.
HorribleTomato

there are infinity files for it to travel along in the begining of the game... so, yeah.

HorribleTomato

Try to prove that a hawk is worth more than a rook. 

hitthepin
Yes, but at the beginning of a game, there are zero CENTRAL files for the rook to travel on. And of course the center is the most important part of the board.
supware
hitthepin wrote:
Yes, but at the beginning of a game, there are zero CENTRAL files for the rook to travel on. And of course the center is the most important part of the board.

There is only a centre at the beginning of the game in infinite chess (since there are no corners or edges).  Definitely evaluating a piece based on the number of squares it is currently attacking is the way to go

HorribleTomato

Central? There is no center in infinity... it goes on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on... and you get the point.

HorribleTomato

And don't forget to base it on the pieces it is defending also. tongue.png

captaintugwash

There is always a centre in infinite chess. It's where the pawns and king are.

HorribleTomato

There is no edge, therefore there can be no center. The thing about infinite is you don't even have to control the center... you can flank without developing a single piece, or develop backwards... and bringing the queen out early is sometimes a good idea!

captaintugwash

There's a centre because the pawns promote only in one region of the board, so that becomes the de facto centre.