Comments/Ratings for a Single Item

Ok, I understand :)!

This game is really sweet for a quite large (12x12) variant, and as advertised it has a small learning curve. Lots of fun!

I'm not quite clear on Fergus' statement on this game's page: "While it is possible for a King and Champion to checkmate a lone King, this will usually require cooperation, which may make the Champion as ineffective as a minor piece in the endgame."

Has this assertion (to paraphrase, mating with K + Ch possible, but not always forced) been previously confirmed somewhere? If it is true, is it as stated not the most normal case that mate can be forced on any reasonable sized square/rectangular board?

Yes, I can confirm that (from end-game tables). Champion can force mate only on boards up to 10x10.

Short-range leapers (i.e. up to distance 2) that cannot force mate without King help must in general lose their mating potential when the board is made sufficiently large. For pieces like WFDN it would not be a problem, and even WFvDvN could force mate on any size board. (But not on an infinite quarter plane, as it cannot catch up with a King running sideways.) But less powerful pieces cannot hinder the King enough to allow the other King to catch up with it.

Thank you H.G.

Now I can rest assured that for a 10x8 variant idea I'm toying with, a Champion can always force mate, while for Gross Chess' 12x12 board it cannot.

Are you sure?  It does not make sense to me why a mate could be forced on 10x10 but not on 12x12.  Both sizes are much, much larger than the max range of either piece (range 2).

When programming is involved one can never be completely sure. But it is what the EGT generator says, and that same generator gives exactly the right statistics for the conventional pieces (where other EGT exist to compare against). The number of positions at each DTM then is exactly the same.

What I am sure of is that the argument you give is not relevant. What is relevant is whether the bare King can outrun the 'posse' that tries to drive it in the direction where it doesn't want to go, and run circles around it. If the mobility of the exclusion zone created by the attacking pieces is larger than the speed of a King, the latter is effectively trapped on one side of it. The point is that the board has edges. So it is enough if your posse can keep up with the King when it stays running in the same direction. Because eventually it will be blocked by an edge, and will have to reverse. Which takes some extra moves before you have to start keeping up with it, which can be used to make progress. E.g. King + Bishop + something vs King: King + Bishop can confine a King in a triangle at a corner, because the attacking King can plug the hole where the bare King could slip through the Bishop diagonal. But is just moves fast enough to keep doing that. But when the bare King has to reverse because it hits the edge, it now needs two moves before it threatens to escape, so you have one spare move to approach your third piece. Eventually it will then join the posse, and force the bare King to step back rather than just reversing, at an edge. This will work on a board of any size.

But when the speed of the posse is lower than that of the bare King, you can no longer confine the latter when the number of moves it needs to gain the width of the posse is smaller than what the posse needs to cross the entire board.

P.S. The entry form throws away long stretches of text again. Luckily I has moved this one to the clipboard before pressing 'Preview'....

This is interesting, but I don't understand what the word pose means in this context.

I'm guessing H.G. actually meant to spell the word 'posse' instead, i.e. use one more 's'.

> I'm guessing H.G. actually meant to spell the word 'posse' instead, i.e. use one more 's'.

Ah yes, I am sorry. It is a word I only know from watching westerns, and I had never seen it written down. Of course I should have known that 'pose' according to English pronounciation rules would sound different, and actually is an existing word. I corrected the spelling now in my original posting, thanks.

Okay, I'm not much into westerns, but I guess it means in this context, the group of pieces trying to checkmate the King.

@ H.G.: I'm not 100% clear on whether champion+K cannot always force mate on a 12x8 board (which might be called bigger than 10x10 due to the greater width, though 10x10 has more squares in total). Might you happen to know?

Also, I noticed on the Omega Chess commercial page somewhere that champion+K cannot [always] force mate in that variant, but no doubt that's because of the 4 extra squares added to the board edges, at the corners. It's also noted there, as I long ago figured out, that R+K cannot always force mate, either, though it's often possible I suppose.

Usually it is the narrowest dimension that counts, although the largest dimension will then affect how long it takes. When you can push the bare King towards the small edge, you can just repeat doing that as often as is necessary. (For symmetric pieces. With asymmetric pieces it is more complex.)

Just to be sure I checked it out, and the WAD on 12x8 can force mate in maximally 37 moves. Even its weaker cousin the WD can force mate there (43 moves).

Thanks H.G.

If I think I can use my (12x8) Wide Nightrider Chess and (10x10) WAD Chess variant ideas after all (see the diagram testing thread) then the info you've provided about the WAD's mating potential on these size boards will nicely be of assistance.

Today I was toying with the thought of what if this variant were played on a 12x10 board, but then I couldn't conceive of an arguably nice setup where the Vaos are not peering into the enemy camp beyond the pawn-line. Thus it seems 12x12 is a good board size fit for the selected armies of this variant.

Sufficient Checkmate material: 

Fergus said that Cannon could checkmate with any other minor piece. I have tested this myself and confirm that K+C+N and K+C+B could indeed force checkmate. How do you force a checkmate with two cannons? I tried it out; and although I could trap the king in the corner, checkmate could not be forced so I'm curious how you did that.

Fergus also said that checkmate could be done by two knights. It is well known in FIDE chess that checkmate could not be forced. Is there some additional rules in this variant that I'm missing?

Also how do you guys value Cannon comparing to Knight and Bishop? In Chess P-N-B-R-Q is valued 1-3-3.5-5.5-10 and in Chinese chess P-N-C-R is valued 2-4-4.5-9 but these are some what different scales. 

Thanks!

It looks like you're right about the Cannons. I have been running Zillions-of-Games with a King and two Cannons for White and only a King for Black. Having finished something else I was working on, I just remembered I had it running, and it is has gone for nearly 600 moves without checkmating the King, which is well over the 50-moves limit.

I have been letting Zillions-of-Games run with two Knights and a King for White against a lone King for Black, and it has played over 200 moves so far without a checkmate. So, it's not looking good for this combination of pieces either.

I left Zillions-of-Games running again, this time with a Knight, a Vao, and a King for White against a lone black King. I then forgot about it until I was ready to turn the computer off for the night. I just stopped it on turn #1986. So, clearly, a Knight and a Vao are not sufficient mating material.

I based my original judgments on whether I could conceive of checkmates that used the pieces in question. For example, if the Black King were on a12, the White Vao was on the diagonal for that space, say at h6, and the White Knight moved to c10, that would be checkmate. The difficulty is in getting the lone King to stay in a corner where it can be easily checkmated in this way. I'll have to run more trials with Zillions-of-Games to see what combinations of material can actually force checkmate.

Although I believe it is correct that those combinations cannot force mate, testing with Zillions means little.  It's skill level is very low.

Is Chessv stronger?

Yes, by a large margin.  Zillions is so universal that it has basically no specialized chess knowledge.  It also hasn't been updated in about 15 years and chess programming techniques have improved a lot in that time.

Interesting questions. I hacked my 4-men EGT generator to also handle hoppers. It indeed says that in KVNK, KCCK and KNNK mate can in general not be forced. For the latter this always hold: there are no forced mate-in-2 position on boards of any size. KCCK in addition has some forced mate-in-2 positions (when the bare King already starts in a corner, pushed against the edge by the other King). For KVNK there are some longer forced mates, of up to 16 moves, but the positions that are lost for the side to move make up only 0.2% of all positions on 8x8, and less than 0.05% on 12x12.

KCNK and KCBK are generally won, though. (Max DTM 50 and 39 moves on 12x12, respectively.) For comparison, KBNK takes at most 64 moves on 12x12.

I had no easy way to check if the results are correct, as the program only produces statistics (number of mate-in-N and mated-in-N for each N), and does not contain code to probe the DTM or best move for a specific position. The hack seemed simple enough, though. (Just skip to the first occupied square in the applicable direction before starting to generate captures in the normal way.)

When you get into 5-6 pieces pawnless endings it probably get really tricky :)!