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

@zacharydaiquiri said in #1:
>
> 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?

Let's do some very rough calculations.

First, we calculate an upper bound of the number of positions with all pieces on the board. We have 16 pieces on 32 fields, giving us 32!/16! = 12576278705767096320000 possibilities. But since pawns are interchangeable, and there's one axis of symmetry, there are at most 10916908598756160000 positions of interest. (This includes many positions which are illegal, or unreachable, but we're doing an upper bound approximation).

Stockfish can process about 70 million positions/second on decent enough hardware. That's on a regular chess board. With half a board, it can likely process many more positions, but let's keep the 70 million positions/second. That means processing all positions of interest with all 16 pieces on the board takes less than 5000 stockfish years.

What about positions with less pieces? A very rough upper bound on that is to take each of the positions calculated above, and remove every subset of pieces. This would multiply the number of positions to be inspected by 2^16 == 65536. (Far, far less in practice as we will generate every position with less than 16 pieces multiple times). Multiplying 2^16 with 5000 stockfish years gets us 327680000 stockfish years, or less than 328 million stockfish years. And that's a very rough upper bound.

328 million stockfish years seems feasible. Altough there will be major hurdles in exchanging data between nodes calculating positions.

@Abigail-III said in #11:
> Let's do some very rough calculations.
>
> First, we calculate an upper bound of the number of positions with all pieces on the board. We have 16 pieces on 32 fields, giving us 32!/16! = 12576278705767096320000 possibilities. But since pawns are interchangeable, and there's one axis of symmetry, there are at most 10916908598756160000 positions of interest. (This includes many positions which are illegal, or unreachable, but we're doing an upper bound approximation).
>
> Stockfish can process about 70 million positions/second on decent enough hardware. That's on a regular chess board. With half a board, it can likely process many more positions, but let's keep the 70 million positions/second. That means processing all positions of interest with all 16 pieces on the board takes less than 5000 stockfish years.
>
> What about positions with less pieces? A very rough upper bound on that is to take each of the positions calculated above, and remove every subset of pieces. This would multiply the number of positions to be inspected by 2^16 == 65536. (Far, far less in practice as we will generate every position with less than 16 pieces multiple times). Multiplying 2^16 with 5000 stockfish years gets us 327680000 stockfish years, or less than 328 million stockfish years. And that's a very rough upper bound.
>
> 328 million stockfish years seems feasible. Although there will be major hurdles in exchanging data between nodes calculating positions.

Wow, thanks, this problem makes more sense now :) I guess this means if all the laptops in the world got grinding, it would be solved in at most few weeks, using this method of analysing all positions.

@zacharydaiquiri said in #12:
> Wow, thanks, this problem makes more sense now :) I guess this means if all the laptops in the world got grinding, it would be solved in at most few weeks, using this method of analysing all positions.

No. While all the laptops in the world combined may have the required CPU, they don't have the bandwidth to perform such a task. Unless distributed projects like cracking RC5 messages, or finding OGRs, this task requires massive exchange of data. Nodes cannot work on a position and calculate all possibilities all to the end -- they basically need to know a significant fraction of the work done by all other nodes.

You need clusters of supercomputers, each with thousands of cores, with the clusters connected with short, fat pipes. (And then you probably still need years, not weeks).

After all, I said feasible, not cheap or fast.

If the pawns have gone all positions can be mirrored on two axes. This also lessens the positions.

@Sarg0n said in #14:
> If the pawns have gone all positions can be mirrored on two axes. This also lessens the positions.

Sure. But the amount of pawnless positions is way less than the amount of positions with at least one pawn. It won't make much of a difference in the back of an envelop calculations above.