By the way, you can give it a try from here to make up your mind (use Firefox or Chrome for full 3D, otherwise 2D works but it's harder to see the geometry).
Minimum material to checkmate at Raumschach ?
Sort:
waow, that's really impressive !!!
just a small comment: at raum schach, there is a unicorn, not a dragon, but the moves are correct though
my best guess: you can checkmate with K+Q vs K and not K+R vs K
it's hard to tell for minor pieces B N U
Yes, the game is still in dev so we used a dragon because we don't have a unicorn in our piece library yet.
In FIDE Chess you can only game draw in positions where no checkmates are possible by any conceivable sequence of moves. As opposed to not being able to force a mate against optimal defense.
If you mean the same here, then K+Q is certainly not a case of 'insufficient material'. There are mate positions, but I doubt they can be forced. I wouldn't be surprised if it is like KNNK in FIDE Chess. I am pretty sure that KQQK would be a general win in Raumschach, though. (Because you can make a 'pincer movement' from 3 directions, which is what you need in 3 dimensions.
The weaker sliders are pretty useless, as far as forcing a checkmate goes. their move patterns are extremely 'leaky', making it almost impossible to confine the very mobile King unless you have truly many of them. With K+2R checkmate positions do exist, though. (Corner and edge mates.) A King in opposition can confine the bare King to a single plane, next to a 'board face'. When this happens in a corner, there are 4 squares in that plane that should be attacked to inflict a mate. Besides the mentioned 2 Rooks, this could be done by 3 Bishops (when only one of them has the corner color) or 4 Unicorns (all of different 'meta-color'). With mixed pieces you would need R+2B, R+2U, 2B+U, R+B+U, B+2U. With the latter three there are color restrictions. I don't expect any of those to be forcible, they are just 'help mates'.
The easiest way to know which material combinations lead to a forced win would be to use an engine in self-play. It seems that there do exists Zillions-of-Games implementations of Raumschach.
Many thanks for those detailled explanations.
I think it makes more sense to decide a draw whenever there is no way to checkmate rather than when a mate can be forced against a perfect player.
By the way, our system acts as Zillions of Games, but for the web, so you're right we can make simulations here.
So to summarize, you can mate a lonely king with:
1Q, 2R, 1R+(2 of B|U), 1B+(2 of B|U), 4U
any idea for the N ? just asking if you had something in mind, but computer simulation (strong level vs random) should give us something as you suggested.
Thanks again.
It seems that K+2N is enough to have checkmate positions. (E.g. black: K Aa1, white K Cb1, N Cb2, N Ca2.) To deterine if mate positions exist computer simulations are not really needed. With the black King confined to the A pane by a white King in the C plane (Ca1, Ca2, Cb1 or Cb2) the other white pieces would have to attack Aa1, Aa2, Ab1 and Ab2 for it to be checkmate, i.e. 4 cells in a 2x2 pattern. A Unicorn can only attack one cell of such a 2x2 group, a Rook can attack 2 orthogonally adjacent, and Bishop and Knight 2 diagonally adjacent from the group. For the Rook there actually is a special case: when it is inside the group, it can attack two cells diagonally from each other (e.g. from Ab2 it would attack Ab1 and Aa2).
What you need to cover all four cells is 2 orthogonal pairs (only 2R), 2 diagonal pairs (2 of R,B,N in any combination, except 2B, as Bishops can only cover 2 squares along the long diagonal, Aa1-Ab2, but not Ab1 and Aa2 at once, and except R+B, because a diagonal + orthogonal pair would overlap, and the R could only cover the two squares on the short diagonal if it was on Aa1 (occupied by the black King) or on Ab2 (blocking the Bishop check)). Those are all possibilities with 2 pieces. If only one piece covers 2 squares, you need two other pieces to cover the other two, and any piece can cover a single square. So R,B or N + two of any (even U) can always do it. With only U you need 4 of them.
So the complete list:
Q, RR, RN, BN, NN, RBB, RBU, RUU, BBB, BBU, BUU, UUUU
or, more relevant, those that cannot:
R, B, U, RB, BB, RU, BU, NU, UU, UUU
or in short, if there is no Q: any single one, 3U, U+any, RB, BB. Furthermore, with B and U you have to worry about the colors. Note that on the standard Raumschach board (5x5x5) all corners have the same color! So in the usual case, when there haven't been any under-promotions, the Bishop that is not of the corner color (let's denote it by b) can never cover the two cells on the long diagonal. So it can cover at most 1 cell of the 2x2 group, like U, and b+any is also a no-no. BUU will be a no-no in practice even with the good Bishop, as for the mate the B would have to cover the long diagonal, and the U the squares Aa2 and Ab1, which are of the same color. But your starting U are of different color, and you must be pretty much out of your mind to ever under-promote to U. BBU will in practice be BbU, and will only work when the U is on the color of the b.
Sounds like an extra set of rules needed to play. Just what we need at chess.com. A way to see who really is good at chess.
I think the most confident way to know is to create endgame tablebase (just like nalimov). I'm pretty sure 3&4 pieces won't take much time/space, not sure about 5, but probably this could be affordable too.
Well, 4-men on a 125-cell board is already pretty tough. But on modern hardware it should indeed be doable. I could adapt my symmetry-less 4-men generator todo this rather easily.
But this would tell you what material you need to be able to force a checkmate, while the original question was when a server shold declare reglementary draw for lack of mating material.
I have a gut feeling, though, that generating the tablebases would not tell us anything we don't already suspect. All 4-men without Q will be draws. The only thing I am not completely sure of is KQK and KQQK.
Well even if it would take 5 time more space and time than regular chess, 5-men still will be affordable, taking less than 100GB and couple of days of calculating.
And you can know from tablebase that there is insufficient material if there is no won position within this pieces combination...
Yes, but that is a rather expensive method. KUUUK is already 5 men, and it is obvious that it is insufficient.
5-men for RaumSchach would be a lot more expensive than just a factor 5. Each man gives you nearly a factor 2, (125/64), so a 5-men is already a factor 32 more expensive than on 8x8.
A 4-men would need 244MB in my generator, which is RAM-based. So that would be doable. I have already done 4-men for Chu Shogi with it (12x12 board). When I have time, one of these days, I'll give it a try. I would have to redesign the helper board, however, mapping the 5x5x5 cube into a linear array so that there is sufficient guard space between the lines and planes that pieces cannot make unnatural moves wrapping around. The program uses tables to map contiguous square numbers as used for constructing the tablebase index to helper-board squares, so it is just a matter of initializing the that table differently. and it will be a bit tedious to type out the list of directions pieces move in, as the 3D pieces move in many more directions than their 2D counterparts...
I think symmetry could help a lot. There would be 18 squares for piece and 57 for pawns. Which is also about twice compared to regular chess(10 and 24). Although it is could be less if a board had even dimensions. It's the same for 6*6*6 board.
Because of unicorns you will have more different combinations of pieces, which also means more time/space. On the other hand, there will be a lot of drawn positions, which means bases would take less space. I'm not sure it's possible to mate with King and 3 light pieces.
KRRK has 97,272 wins (with the weak side to move), and KRNK has 39,048 wins. The longest KRRK win is mate in 10, though, while the longest KRNK win is mate in 16. I guess that in all cases the bare King has to start trapped in a corner, and that it is just more cumbersome to manoeuver the Knight for the kill. All this is 0.0% compared to the total number of 4-men positions, which is over 200 million.
A 5 men is 125 times bigger because the RaumSchach 'board' has 125 cells.
Is KRRK a draw? It sounds just counter-intuitive. I'm pretty sure that 3 light pieces is far away from checkmate, and maybe even 4 light pieces isn't enough with perfect play. 2 rooks + light piece might be enough in some situations (and even rook and 2 light pieces if you say that KRN can win sometimes).
Why 5 men is 125 times bigger?
Hmm, I see that my answer to your latest question actually replaced my original message above.
Just to summarize it: KQK is won, all 4-men without Q are general draws, although there sometimes is a negligible fraction of lengthy forced wins.
Bishops and Knights are not so light in this game. A Bishop moves in 12 directions, a Rook only in 6. a Rook has 15 moves max, a Knight and Bishop 24.
In FIDE chess board is 64 squares, but 5-men is more than 200 times larger than 4-men(7GB vs. 30mb)
Seems you are referring not to a single 4- or 5-men EGT, but to the total collection of all such EGTs for the different material signatures. The latter is not relevant: you generate them one at a time, and the memory requirement is determined by the one you are generating, no matter how many other there exist.
Hi,
We are working on an Raumschach, a 5x5x5 chess variant invented in 1907, web application and we need to know what the minimum material is to checkmate a lonely opponent king (so the program can declare a draw without having to wait for 50 moves).
Any idea or guessing anyone ?