Value of Pieces for "Infinite Chess"

I'll be out for most of today, but I thought I'd give my quick opinion on the value of some pieces when played on an infinite board. (This is just my speculation, and I don't think anything is really known for sure):

First, for normal chess (or variants on 8 x 8 board) we know these values:

Pawn: 1 (the unit to value all other pieces)

Bishop: 3

Knight: 3

Guard: 3 (same moves as king)

Rook: 5

A queen is a rook plus bishop (5 + 3 = 8). But the queen is known to have a value closer to 9, so this bonus can be considered a "synergistic" benefit. (So queen is known to be around 9).

Now, lets put these pieces on the infinite board. This is a very "large" board, so give sliding pieces a bonus of 1:

Bishop: 3 + 1 = 4

Rook: 5 + 1 = 6

Knight: 3

Guard: 3

Now we can calculate the value of other pieces:

Queen: (rook + bishop) = 6 + 4 = 10
Chancellor: (rook + knight): 6 + 3 = 9
Hawk: (attacks twice the squares as a knight, so twice the value): 2 x 3 = 6

Other opinions and comments are welcome.

Also, there is an interesting YouTube video about Infinite Chess. But it doesn't really look at the game how we play chess normally. This video is more related to math and game theory, but it's still interesting for people who enjoy games and "infinity".

Guard should lose value due to the largeness of the board.

You can watch the video by clicking on "play" in the picture above. If that doesn't work then go here: (YouTube - infinite chess).

is this homestuck

No, the YouTube video works fine for me from both post 2 and 9. Are you watching it from your cellphone or PC? If you're in a library maybe they have a filter so you can't watch YouTube. If at home tell your friends to stop hogging all the bandwidth with the World of Warcraft. You have a chess game to play!

It's very hard to place values on the pieces, and I think they will fluctuate dramatically. Some will start strong and get weaker, others will start weak and get stronger.

"The larger the board, the weaker the pieces are, always."

This is not something I agree with. I understand the point that the bigger the board, the lower the ratio of squares a given piece controls. But piece power is not about board size, it's about how they compare to other pieces.

And in the case of the queen, the lack of boundries makes her more powerful, not less. She can exploit the extra space better than all the other pieces, which means her power is reduced less dramatically than other pieces due to the large board size. So her relative power compared to other pieces is increased.

I think the queen is worth a lot more than a chancellor. If the C is 9, I put the Q at 15.

I'd also place the hawk's value higher than twice that of the knight, at least to begin with, because although the hawk controls twice the squares, it also has greater forking potential. It can hit from a square further away, which is worth at least a pawn for me. It can also support the queen in attacks better than a knight. Hawk is probably worth 7 when developed early, decreasing as pawns are removed.

Chancellors are probably weaker to beging with and increase in value as the game develops. They're too strong to be used for positonal trading in the centre. Even a bishop is too strong for this, but a chancellor fighting in the centre is easy to attack.

The bishops are interesting pieces. I think while they have a counterpart, they are less powerful. But in my recent game with hitthepin, he lost his black squared bishop quickly. I felt that increased the value of my bsb substantially, since he no longer was able to challenge the diagonals the bishop controls. I think a bishop without an enemy counterpart is worth a rook, while a bishop that is matched is still much better than a knight.

The knights are weak, but their strength will be control of the centre in openings. They will be the easiest piece to sacrifice. 3 points is probably a fair value.

Guard will be really strong in a pawn endgame, but they're defensive pieces in the middlegame and are probably worth roughly the same as a knight. They will almost certainly outperform a knight in an otherwise matched endgame though. The knight still can't lose a tempo.

Consider the knight attacks 8 squares. Well, when it comes to forking potential, actually it attacks 7, since it originated from the 8th square.

So there's obviously one arrangement of pieces where the knight forks 7 pieces. There is no empty square.

How many different arrangements can 6 pieces find themselves in whilst being attacked by a single knight? There's one empty square, and it can be in seven places. So 7.

What about 5 pieces? It's getting harder to calculate here, but I'm pretty sure that despite the hawk only attacking twice the squares a knight does, there will be singnificantly more than twice the different ways (in terms of piece arrangement) a hawk can fork.

Calculating piece values is a minefield.

There's a different way to compare knight and hawk... forking potential.

Consider the different ways pieces can be arranged in order for a single knight or hawk to fork them.

A knight can't deliver an 8-way fork because the knight must originate from the 8th square, so let's look at a 7-way fork. There is only one arrangemtn of pieces where the knight can do this... the only empty square is the knight's origin, so an enemy piece can't occupy it and for all intents and purposes is not empty. So there's one arrangement of pieces where the knight can fork 7 pieces.

If it's six pieces, there's now an empty square that can be in any of 7 different places, so there's 7 arrangements where the knight forks 6 pieces.

Without getting into the deep dirty maths of it all, there are hundreds of different forking arrangements that a knight can execute.

The hawk is an entirely different beast altogether. I think we're talking tens of millions. I'm not joking. The arrangement potential for an 7 piece fork I think is 15^6.

So, I think the hawk is massively stronger when it comes to the ability to deliver forks.

Haha nicely timed post, you got this in before I made that point myself!

Oh I didn't notice I posted that other one about knight forks, I thought I deleted it and started again. Jeez I smoke too much when I have the day off.

I mgiht be wrong and it's actually a great deal simpler than I think. My brain works in weird ways sometimes.