Chess problems and studies

[Brian-E]

Since you know how to force the opposing king along the edge from one corner to another, you know that there's a key moment in the standard manoeuvre when it looks as if the defending king is escaping but then the beautifully co-ordinated knight and bishop prevent that. From the first diagram below we have 1.Ba2 Kd1 2.Nd4 Ke1 3.Kd3 Kf2 4.Ne2 Kf3 (escaping?) 5.Be6 (second diagram, and no, the king is still caught! - 5...Kf2 6.Bd5). And Ushenina kept playing the latter moves of this standard manoeuvre wrong, as you saw, even though as far as I know the game was played at normal tournament time controls.

Well, this carefully constructed co-ordination between bishop and knight, aided by the king, is also just what is needed to drive the king into a corner in the first place. That is not a standard manoeuvre so much as a bit of technique which is worth practising against a computer.

This game shows GM Alexander Grishuk successfully winning this ending from a position with the defending king in the middle of the board, and at blitz time controls to boot!
http://www.chessgames.com/perl/chessgame?gid=1705983

[LaurV]

Thanks for the link. From a fast skimming, black was helped in the beginning by a very convenient position (having the opposition and well placed other wood). Of course, one can argue that the grand master created that position himself, that is why is a grand master, and that is why I say that learning the part of how to bring the king to the side is somehow futile for a real match, you either can do it, or can not. I would also argue that the "blitz time" is "visible" (now that you told me ) because the "sliding the enemy king on the side of the board" part is far away from being optimal. I would say that black had in mind that he has to push the other king to the black corner (because of black-square bishop) and white has in mind that he has to stay on the white corner, with all the effort and consequences. And this can be seen. First, black plays with the bishop on the other side. Second, white helped him (making mistakes). For example, at move 89, white move back Kc8, when Ke8 should have been a far-better move (extend the final with at least 5-6 moves, black has now to guard e6, f6, g6, and to bring the white king back to the (repeated) position in d8, but with the bishop in the right side. Etc.

I don't argue with you, don't get me wrong. I really appreciate the efforts that you (and other people) put into learning and playing this wonderful game, and I like this puzzles, but for me they are just that: "puzzles". You solve them (or not?) and forget. I never "learned" this things. Same as openings, I never learned them. My strength when I play is the "combinatorix" part, doing zillions of combinations in my head. If I am enough lucky to get "not very crumpled" from the opening part, I can sustain a very good face-to-face game. But the most games I lost (against masters and friends too) were lost because I made stupid mistakes (most of them in the opening phase, but during whole game too). One would argue that this is the only way we all lose, because if nobody makes mistakes, it would be a perfect play, hehe...

[edit: yes, about those ladies' game, you are totally right there is a moment when the opponent moves along with you, and you are tempted to follow with the king, but if you follow with your king, his king goes back and the position repeats, then you the you stop yor hand and think "if I move the king here, he will go back, and I didn't realize any progress", then you move the horse, and the enemy gets lost. The whole key is the fact that, if your bishop is well placed, the right move is to follow with your king, and his king can't go back, because you mate him in one move. And don't touch that horse! [edit 2: see the moves 89..91 in the Grischuk's game you linked] And this trick I didn't find out by myself, I had to learn it from the web, of course!]

[Brian-E]

Yes, you're right about the poor quality of play in the Karjakin-Grischuk endgame. 89.Ke8 would indeed have been better, requiring the accuracy of the standard manoeuvre to avoid letting the white king escape - and hoping that Grischuk might "do an Ushenina" and not know how to finish the manoeuvre off. It rather looks like it was all one huge time scramble, doesn't it? Perhaps I should have looked for a better-played example. But the problem is, this endgame KBN vs K occurs extremely rarely. It has never once occurred in any of my own games, and they number more than ten thousand.

I know you have a strong analytical mind (combinatorix as you call it) and solve problems from first principles very well indeed. You've shown that here many times. My mind is anything but the same, and I play chess using vague heuristics which come from experience. I would be utterly hopeless at it if the rules of play were altered.

[gd_barnes]

I haven't seen all of the variations clearly spelled out from the last puzzle. With help from Rybka and then help from Batalov's 6-man endgame database, here appear to be the best variations:

1. h8(Q) Nc5
2. Qxh6 Nd7++
(forced mate in 2)

1. h8(R) Nc5
2. Rxh6 Nd7++
(forced mate in 2)

1. h8(N) Ng5
2. Nf7+ Nxf7
3. Kg8 Bc4
4. Kh7 Bd3+
5. Kg8 Ng5
6. Kf8 Kd7
7. Kg8 Bc4+
8. Kh8 Ke7
9. Nf5+ Kf8
10. Nxh6 Bd3
11. Nf5 Nf7+
12. Kh7 Bxf5++
(forced mate in 12)

In the 1. h8(B) variation, after 1...Bg4 I feel like the key is for white to delay the capture of a piece as long as he can because once we're at a 6-piece game the endgame database usually comes up with a mate in < 40 moves from that point forward. With that idea I kind of had to "encourage" Rybka to avoid lines that lost a piece or swapped pieces while at the same allowing it to make moves that appeared to be nearly the best for each side on each move. Here is the best line that I could come up with.

1. h8(B) Bg4
2. Kf7 Nd6+
3. Kf6 Kd7
4. Kg6 Bc1
5. Nh5 Bf5+
6. Kg7 Ke7
7. Kg8 Bg4
8. Ng3 Bf4
9. Nh1 Be6+
10. Kg7 Be5+
11. Kg6 Bxh8
From here, the 6-piece database shows it as a mate in 14 moves, which would make the original position a mate in 25 moves. This seems low so perhaps my methodology of having white avoid a capture was not optimal. Regardless, I am fairly confident that the original position is a mate in less than the originally stated 70 moves.

Using Batalov's 6-piece endgame database site, on the right side, you can find a link to "7-man Lomonosov Tablebases". It costs $29.95 for a one-year "license". I don't care for such licenses that expire. I would want permanent access to the DB so I'm not willing to pay for it.

If anyone is willing to shell out $29.95 for a year's license to a 7-piece endgame database, I would be curious to find out how close the above analysis is to the optimum play by both sides.

[LaurV]

Can't SF solve it? I mean, 25 moves are not much of a depth for him, if you give it the position after 1. h8(B), and let it for a day or so?

[gd_barnes]

Originally Posted by LaurV

Can't SF solve it? I mean, 25 moves are not much of a depth for him, if you give it the position after 1. h8(B), and let it for a day or so?

I don't know. I haven't downloaded it. After thinking for a day, Rybka could not even determine that the original position was a forced mate. I think it gave the position a valuation of -70 or -80 or something like that.

I suspect that this type of position is difficult for programs. It's best for endgame databases.

[gd_barnes]

Originally Posted by LaurV

Careful! KBN against K is draw according with the current rules (in the general position, you may need more than 50 moves to mate). Can you mate him here in less than 50 moves, considering that the king is cornered? This is in itself, another puzzle. And if so, how? (edit, remark that you are in the opposite-color corner, for the bishop)

I think the longest mate in a KBN vs. K end game position is 33 moves. See http://www.gilith.com/chess/endgames/kbn_k.html. Batalov's endgame database confirms it. (I think Brian mentioned 32.) It's generally better for the losing side to have his towards the middle and then head for the "wrong" corner. This takes more moves than being in the "wrong" corner to begin with.

Of course few people could force mate in 33 moves or less over-the-board with this ending.

BTW, in correspondance play in today's day-and-age, usually the 50-move draw rule is removed. But if one side can demonstrate that a position is drawn using an end-game database, he can claim a draw. This avoids games that are 100s of moves.

[MooMoo2]

Originally Posted by gd_barnes

In the 1. h8(B) variation, after 1...Bg4 I feel like the key is for white to delay the capture of a piece as long as he can because once we're at a 6-piece game the endgame database usually comes up with a mate in < 40 moves from that point forward. With that idea I kind of had to "encourage" Rybka to avoid lines that lost a piece or swapped pieces while at the same allowing it to make moves that appeared to be nearly the best for each side on each move. Here is the best line that I could come up with.

1. h8(B) Bg4
2. Kf7 Nd6+
3. Kf6 Kd7
4. Kg6 Bc1
5. Nh5 Bf5+
6. Kg7 Ke7
7. Kg8 Bg4
8. Ng3 Bf4
9. Nh1 Be6+
10. Kg7 Be5+
11. Kg6 Bxh8
From here, the 6-piece database shows it as a mate in 14 moves, which would make the original position a mate in 25 moves. This seems low so perhaps my methodology of having white avoid a capture was not optimal. Regardless, I am fairly confident that the original position is a mate in less than the originally stated 70 moves.

Originally Posted by LaurV

Can't SF solve it? I mean, 25 moves are not much of a depth for him, if you give it the position after 1. h8(B), and let it for a day or so?

Originally Posted by gd_barnes

I don't know. I haven't downloaded it. After thinking for a day, Rybka could not even determine that the original position was a forced mate. I think it gave the position a valuation of -70 or -80 or something like that.

According to SF, the original position is not a mate in 25 moves (50 ply) or less, or even 30 moves (60 ply) or less. See attached screenshot for reference.

I'll let it run a bit longer and see what it comes up with.

[gd_barnes]

Originally Posted by MooMoo2

According to SF, the original position is not a mate in 25 moves (50 ply) or less, or even 30 moves (60 ply) or less. See attached screenshot for reference.

I'll let it run a bit longer and see what it comes up with.

I fail to believe that. I would be willing to make a gentlemen's wager that it is a mate in 30 moves or less. I suspect that SF as well as other programs have tremendous difficulty analyzing such positions. I do not believe that SF has looked at ALL variations of 60-ply. I believe that because of what I have seen with Rybka. In known mating positions where a mate is known in a certain number of moves, Rybka frequently had to look well beyond the required ply-level to find the mate. I was able to prove this by comparing it to the 6-piece endgame database. It would find the mate in the correct number of moves but had to look far more plies than should have been necessary to do so. I suspect that you letting it run for several more hours or a day will not give you any additional information.

To test this, find some positions that are known mates in 15-20 moves. Then plug them into SF and see if it finds the mate within the requisite 30-40 plies. I suspect that you will be surprised. I do not have an explanation for this. It's either: (1) Bugs in the program -or- (2) A feature whereby it is showing the ply-level that it has searched for some of (what it believes to be) the strongest positions but not all searching has been done to that ply level.

The only way to know for sure is for someone to buy access to a 7-man endgame database. This is all very interesting to me. I may finally decide to buy that one-year license.

Edit: By the way, in looking at the analysis scores of Rybka at each ply for several possible response for each move, it became clear to me that the first two moves by each side (4-ply) are forced; that is 1. h8(B) Bg4 2. Kf7 Nd6+. After determining that, I put the position prior to white's move 3 into Rybka. After a day of thinking it could still not find a mate. In looking at your SF line, it is confirming this. The 3rd move by white is the first interesting move. It's about an even choice between Kf6 and Kg6. In looking at the analysis scores and pushing the pieces around a bit myself, I had concluded that 3. Kf6 was slightly better. But after letting Rybka think for several more hours, I'm thinking that 3. Kg6 may be better for white. The lines do not appear to transpose to one another. They result in completely different positions.

[axn]

Originally Posted by gd_barnes

I do not have an explanation for this. It's either: (1) Bugs in the program -or- (2) A feature whereby it is showing the ply-level that it has searched for some of (what it believes to be) the strongest positions but not all searching has been done to that ply level.

You're kidding, right? Of course, it is #2. Try to calculate how many gazillions of positions it must evaluate to reach a depth of just 10-ply if you have to search exhaustively. The strength of the modern chess engine is that they have strong heuristics that allow them to aggressively prune the search tree. SF is particularly good at this (compared to other chess engines). This works great in practical play, but is not really good in these study-like positions.

[Batalov]

Interesting. This position shows that there is something off with the latest released SF-7.
Instead, try the latest experimental build. I tried the 160302 version. This one sees Bg4 right away, but SF-5 or SF-7 doesn't (well, sometimes does; its behaviour seems stochastic).