Would a 4x8 chess setup which uses the kingside of the normal setup be solvable?

So me and my dad invented this variant of chess, played on a 4x8 board, where the starting position would be the entire kingside of the board. The starting FEN would be like this: kbnr/pppp/4/4/4/4/PPPP/KBNR. Pawns can only promote to a rook, as there is no queen to start with.

The question that I ask is this: Would this game be solvable using all of the biggest supercomputers in the world, just by searching through every possible position using brute force? Or is this new chess variant yet another game on the list of those yet to be solved?

Regards, zacharydaiquiri

Hi!

I really have no clue yet, but I think this is a very interesting question. I feel like it should be solvable, since the number of possible moves is extremely reduced because of the lack of any queen ever and the restricted size. I have some ideas:

• If i am correct, trying to solve for all games starts with solving all the endgames. It would be interesting to see what changes there.
• It would be interesting to compare the number of possible first n moves of 4x8 chess to regular chess and see how much the numbers diverge
• If someone could reprogram stockfish to solve?
• It feels like playing perfectly, all games should be a draw. what is your experience? how draw-ish are the games you've played so far?

thanks for your cool idea!

Katha

PS: check out this wiki page, https://en.wikipedia.org/wiki/Minichess, your version is apparently called "Demi-Chess" and seems to also appear as playable in some Chess Variants Game

16 piecex/32 squares, no Q. Could be solved "strong/hard" probably IMHO.

Solved mathematically: Pretty certainly not. "Solving" a position boils down to tablebases (https://en.wikipedia.org/wiki/Endgame_tablebase) which in regular chess already requires terabytes of size for at most 7 pieces. In your variant the board is smaller, and I'd be hard pressed to estimate how that affects the complexity, but I'd guess that in this case number of pieces is more influential; the space requirement for such a calculation would then be unrealistically high. Can someone back me up?

@Lokapit said in #5:

Solved mathematically: Pretty certainly not. "Solving" a position boils down to tablebases (en.wikipedia.org/wiki/Endgame_tablebase) which in regular chess already requires terabytes of size for at most 7 pieces. In your variant the board is smaller, and I'd be hard pressed to estimate how that affects the complexity, but I'd guess that in this case number of pieces is more influential; the space requirement for such a calculation would then be unrealistically high. Can someone back me up?

There are different ways of "solving" a game. Strongly solved means being able to determine the outcome (given perfect play from either side) from any position which may appear on the board. Weakly solved implies you have an algorithm in which one of the players can force a win (or that both players can force a draw). Ultra-weak solved implies knowing what the outcome of the game will be with perfect play, but it does not imply you know what the perfect play will be.

It's extremely unlikely tablebases are required to solve a game weakly, or ultra weakly. Are endgame tablebases needed to solve chess strongly? Probably not. Although if in the next decade or so, we will create a device which plays chess perfectly, it's likely it will make use of tablebases. But that's more because most computer chess implementation currently use tablebases, not because it's fundamental to chess.

if you are geeky enough to code the limited playing field into a chess engine, it should be easy to analyze. with so little material and space you might even be able to solve it on your own just by gathering experience in the miniature format.

solving it definitely like a tablebase should also be possible, since you only have half the material in a 4 lane playing field with half the amount of squares. the number of possible moves you can make is much lower because of the narrow playing field. if you can do 7piece tablebases for 64 squares it should be "easy" compared to that, because they solved material like KQRBvsKQN on 64 squares where there are just so many more squares available for the pieces (less blocking and a gazillion more quiet moves but also checks, its amazing how long you can drag out an open position sometimes with less material, cf. https://lichess.org/blog/W3WeMyQAACQAdfAL/7-piece-syzygy-tablebases-are-complete).

if you solve it with a computer, you kinda take away the essence of the miniature imo. the miniature is played to have an easier time calculating, but still take away important lessons applicable to the bigger board (and to have something new and fun ofc).

Not sure, but I have experience with this so here's what I do know. 7 piece endgame tables would be easy to generate on a decent home computer, since each table would be roughly 1/128th as large as for chess, and there would be significantly less tables since there are none with Queens. 8 piece endgame tables would be a little easier to generate than 7 piece chess tables, since each table would be around 1/4 the size, but there would be more tables. A computer with 256GIG of ram would be reasonable for generating these. 9 piece tables would require high end workstations, with 8TB of ram, and would take a fair while to do with just one workstation, but if you had a million dollars to spend on hardware and electricity should take less than a year. 10 piece tables would need supercomputers, with around 256TB of ram each, and I hate to think how much storage, but with "all the supercomputers on earth" you should be able to do it in under a year.
So with those resources, you just need to trade off 6 pieces and you can look up the resulting position's value.
Looking at it from the other end, the open has a lot less possible moves per ply than chess, but with the bishops on opposite colors, there would be a huge chance any quick tradeoffs would result in draws. So proving it a win would depend on there being some faintly forcing line(millions of lines being needed is fine for this size of solving attempt) that results in trading down to won 10 piece "endgames" in all cases. Proving a draw would require that both white and black can find a forcing line that results in non-lost 10 piece "endgames"

@katharinaellador said in #2:

Hi!

I really have no clue yet, but I think this is a very interesting question. I feel like it should be solvable, since the number of possible moves is extremely reduced because of the lack of any queen ever and the restricted size. I have some ideas:

• If i am correct, trying to solve for all games starts with solving all the endgames. It would be interesting to see what changes there.
• It would be interesting to compare the number of possible first n moves of 4x8 chess to regular chess and see how much the numbers diverge
• If someone could reprogram stockfish to solve?
• It feels like playing perfectly, all games should be a draw. what is your experience? how draw-ish are the games you've played so far?

thanks for your cool idea!

Katha

We've played probably about 8 games or so far, and after a few games, we have begun rarely to get a winning player. Usually, we will push a few pawns at the beginning, both trying to put the other player under lots of pressure with our pawns. Because we always push all our pawns very early, we end up with a very closed position that is seemingly impossible to win for either player. This makes me feel as if perfect play might be a draw, but neither me or my dad is by no means "perfect".

oh wow, didnt think it would be completely impossible. ty angrim for your insights