Value of Pieces for "Infinite Chess"

The queen benefits from board expansion more than any other piece. And I'm not giving up a hawk for a rook.

Of course not.

Well in theory defending the king is costly- especially when attacked from all sides! So it can't stray into the heat of battle, but the guard can.

Chancellors must be used as a flank and back attacker- there isn't much use in the heat of battle and can be used to cut off king escape routes.

True, true.

Trying again:

Pawn: 1
Knight: 3
Guard: 3
Bishop: 4
Rook: 6
Hawk: 7
Chancellor: 9
Queen: 11

Explanation:

Knight: Matmatically compared to a pawn, a knight’s value is around 5.8, but in practice, this is balanced out by the sheer size of the board.

Bishop: It’s definitely stronger than it is in classical, which is 3, but a little weaker than it is in 4-player, which is 5. So 4 seems to be a good value.

Guard: I feel like the guard might be worth only 2 in the opening, but it obviously goes up in value towards the endgame. 3 seems like a good average.

Rook: Rooks are definitely stronger in infinite compared to classical, but are weaker than hawks.

Hawks: I feel like one hawk is superior to two knights. Two knights together don’t really seem to have the same synergy as a hawk does.

Chancellor: Rook+Knight

Queen: A rook and a bishop is 10. However, as it has been mentioned by @vickalan, its synergistic bonus of one point is given because there is only one queen, but two rooks, two bishops, etc.

What do you guys think?

Put the queen at 15 thanks to her astonishing tempo potential and I like those values.

I'll try to explain why the queen is so powerful...

 

Consider the following position -  (hitthepin vs captaintugwash)

 

White to move. For the sake of discussion, let's assume white plays 1. B(7,5)... it's not a good development move but let's consider it so we can see how the queen is well developed on (4,24)...

 

1. B(7,5)... Q(23,5)

 

The queen now attacks the bishop along the 5th rank, while at the same time threatening Q(5,-13), which forks king and hawk. White cannot defend both threats.

(I can see the bishop is protected by the knight, but imagine if it wasn't. The point is purely to demonstrate that the queen has subtle attacking potential.)

 

So... from (4,24), the queen is controlling the fifth rank, at least while white has an unprotected hawk and an exposed king.

 

This is just the tip of the iceberg. The queen exerts immense pressure from afar, no other piece can touch this power.

It's difficult to visualise the queen's path because it goes off the board, but imagine a huge traingle with the three corners at the following squares... where she currently is, (4,24)... to the right of the board along the 5th rank (23,5), to underneath the white king (5,-13). This bottom corner of the traingle is the square the attacks both the white king and his black squared hawk.

 

When you can see what I'm getting at here, you'll understand the queen is a vastly powerful piece. If the enemy queen is developed (and yes in this example the queen is most certainly developed), then you should try to ensure you have as few unprotected pieces as possible, and your king is not exposed.

As for the bishop, I think it's important to distinguish between two types of bishop...

- a "matched" bishop (that is, one where the enemy has a direct counterpart),

- an "unmatched" bishop (that is, one where the enemy does not have a direct counterpart).

 

I feel the unmatched bishop is as powerful as a rook, since the rook cannot challenge the attacking bishop. It can block checks, but will be pinned.

 

I would not be so quick to snap up a rook for my bishop since it leaves the enemy with a more powerful bishop.

Also, the pawn value of 1 would refer to the king's pawns, not the hawk's pawns. Those Jager units, as Vick likes to call them, are worth half a pawn or less at the start, to the point where development of the hawk is preferable to maintaining protection, at least in my opinion.

If you note in the position above, the queen is only able to take that triangular path because white took the pawn on (13,15), opening up the diagonal. This for me demonstrates that development is worth more than the hawk's pawns. White has to move his rook twice, once to grab the pawn, and once to retreat after I attack, while I develop my queen to a surprisingly nice square in one move.

This is tempo, and this is why the queen is so awesome, and why the hawk's pawns are largely unimportant in the opening stages.

About the bishop: I agree an unmatched bishop is very strong. However, these values are averages for all kinds of bishops: good, bad, matched, unmatched. I feel that that average is 4.

And I don’t feel as though the queen is worth 15. Maybe 13 or so, but 15 feels to high. Who knows, though, time will tell!

Yeah in terms of the queen's value, I'm practically pulling a number out of my behind. I just feel she is a lot stronger than the next best piece, which must be the chancellor. I doubt the queen is worth two chancellors though, but she must be better than two rooks. She's worth approximately a little less than two rooks in classical chess, but here the queen benefits from no boundry a lot more than the rooks do.

 

And yeah you're right about averages, but I do think the unmatched bishop is either as powerful, or very close to, that of a rook. It's important to consider this when deciding if it's good or bad to trade bishop for rook... how strong will the matching enemy bishop be? Will you eventually need to give up a rook to remove it?

When it comes to the queen's value, I talk exclusively about middlegame. Obviously in endgame it's a different matter, probably two rooks can match her then, especially considering the two rooks can mate (probably by force) but the queen can't.

 

But as a supporting piece, the queen is truly immense.

I'm almost certain the two rooks can force checkmate against a lone king. Consider that in classical chess, one does not need to corner the king with the rook, merely driving him to the edge will suffice. One rook can create the "edge", while the other, along with the king, set about the classical R+K vs K endgame.

We will see. I agree that in infinite the queen is stronger than two rooks in the middle game. So 13 maybe.

Hawks are so overrated- I sacrificed a queen for a hawk and it was considered an even trade!