Value of Pieces for "Infinite Chess"

@captaintugwash

Sorry, that was a typo. I meant to say that pawns should be the base value you judge by and should be assigned the value of 1 (for humans.)

As you point out, values change on board position and games state, requiring reevaluation. A computer is likely to want to assign a value per piece and temporally (for example to assign a value to a pawn based on its potential future value because it's a passed pawn nearing promotion.) 

I typed hastily, sorry for that.

I think using a pawn as a value of 1 always makes sense, but to be more specific (same as normal chess) it should be assumed that it is a normal pawn in the starting position, with other pawns still next to it.

Pawns can change value in a game. A pawn on the 7th rank is often valued about the same as a rook. Isolated pawns lose value. And in infinite chess I think the hawk's pawns are worth much less at the start. But for general discussion, I think it is almost always assumed that a normal pawn has a value of "one".

(fyi: some programmers use centipawns, i.e. 1 pawn = 100 centipawns).

Centipawns help programs, they don't help humans.

Speaking of "infinity", this video is somewhat related to the concept of infinity:

I've noticed that in a few games, players are testing the strategy of using one or both of the hawks in opening development (Captain "Tug" is one player doing this).

While nobody should talk about specific moves of a game in progress, it's alway ok to discuss playing theory in general. I decided to do a little study on this strategy.

The first thing to say is that a hawk attacks twice the squares of a knight, so is probably worth about twice the value (diagram here):

This means that developing both hawks to the central fighting area would be like having FOUR extra knights! And like knights, all moves are jumps - so this could be used for amazing striking power especially when the board is crowded. Although in my games I have not started with a hawk move, if my opponent moved one toward the center, I would almost for sure do the same.

The next think to think about is how deadly can a hawk actually be? It can jump three squares which is more than a knight. How much trouble can this cause in an opening? To answer this, I produced the following diagram:

It shows the possible striking points a hawk can have after four moves (per hawk). A hawk can move in position safely away from the opponent's pawns in their starting positions, and yet be able to attack the first rank pieces (including chancellors, queen and king)!

Is there any position that the hawk can move where two valuable pieces are "forked", creating deadly attacks in the opening? By checking each forking possibility (and assuming no opponent pieces have moved), neither hawk can fork two (or more) undefended pieces which are worth more than the hawk itself. In the worst case, a hawk can create a "check" where the king will need to move to one of three safe squares.

So while the hawk can create dangerous playing opportunities, it appears that in a well-played game, defending against hawks is possible. So (like so much in chess) using the hawks as an opening strategy appears to be sound strategy, but it's unknown if it is truly in the repertoire of the very best openings. Time will tell!😈

Good point - when the hawks leave the jäger units the pawns don't do well.

Time will tell if those pawns are important. I am happy to abandon those pawns in favour of development until I'm beaten.

It depends what you get in compensation. In both my games, I left those pawns because I felt that development is more important... it's a gambit, essentially, but those pawns could be worth something like 0.5 of the 2nd rank pawn, while the developed hawk might be worth a whole pawn more than an undeveloped hawk. Of course, these numbers are pure speculation, it'll take many games before we can even begin to get an idea, but I wouldn't call those pawns endgame "insurance". I would imagine that overall pawn structure will be a more important endgame factor than simply how many pawns one has.

Well yes, but the hawk's pawns are less relevant than the king's pawns in this regard since it takes twice as long to push them to promotion.  For example, who do you think wins an endgame where white has all his hawk's pawns and no others, while black has the two pawns in front of the rooks? Assume kings are both in starting position. I'm not 100% sure, but I think that's black's endgame. That's 10 pawns vs 2. Certainly it's close, and if you remove the leading pawns from the hawk's pawns, then it's certainly black's. That's still 8 vs 2. So those hawk's pawns are not so important as the others.

That said, I suppose you're right if both players have an otherwise perfectly matched middlegame, and exchange all the pieces. Then the hawk's pawns will be relevant. But really, how often do you expect that to happen? It's not so risky abandoning them imo, the rewards so far have vastly outweighed the risk.

Actually it's not black's because the lone queen can't checkmate, but still you can see how worthless those hawk's pawns are compared to the main armada. Black is the one queening, not white, and black can grab all the pawns to draw an endgame with a 6 pawn deficit.

How many total games of Infinite Chess have been played (and recorded) in total? What does an endgame look like? I suspect the current list of games is ending in novelty mates that one side simply didn't see because there aren't enough games played yet.

I believe there's been about 10 games played, but a few were no-shows by one opponent, and there's a few others played with other (usually stronger) pieces. In my opinion, two of the better games played are this one:

(cobra91-vickalan) (but I lost)

and the current championship game is good: (supersam1-vickalan)

I agree that there could be a lot of novely mates that no one has anticipated yet. There may also be interesting situations where the king tries to walk away to "infinity" while knights or other pieces chase him (or pawns try to promote). But usually if there are a few sliders (rooks, queens, chancellors) then forming a "wall" around the opponent king would usually be a sensible strategy (assuming there is enough material).

fyi: Regarding the game in progress, I'm sure everyone knows, but please don't make detailed comments about it because it's still in play.