Is this positions drawn ??

[George Tsavdaris]

Neither Uri nor I have ever said we did not think it was a draw. Both of us agree that (almost certainly) it is. With Robin's Freezer analysis, the uncertainty is very, very low.

The distinction that is made here is between proof and acceptance.

Almost all mathematicians accept the Riemann hypothesis:
http://mathworld.wolfram.com/RiemannHypothesis.html
All known evidence and measurements support the hypothesis.
However, despite the fact that we believe it, it has never been proven.

This is completely different with our Chess case.
Why?
Because for Riemann's Hypothesis we need to check an infinite amount of numbers while on this Chess case a finite amount of positions.

And while in Riemann's case we have checked some trillions nontrivial zeros by now validating Riemann's hypothesis, we can never be sure for the rest infinite amount of numbers(zeros) beyond trillion....

In contrast in our Chess case, if we find for example some rules that only then the win can occur for the strong side and then search for all the possible positions with even applying restrictions for the movement of weak side, and yet we can't find a win, then the position is draw. Or not?
Since even if the code and the logic of the code has been verified to be flawless, who guarantees that the computer program+hardware that solved all these positions did this flawlessly?
Do we have to look at each position ourselves? Well this is a matter of taste of each person. Some will accept it, some will not.....


The famous four color theorem is the most famous for this kind of "confusion". To accept or not to accept its computer proof?

[Dann Corbit]

Neither Uri nor I have ever said we did not think it was a draw. Both of us agree that (almost certainly) it is. With Robin's Freezer analysis, the uncertainty is very, very low.

The distinction that is made here is between proof and acceptance.

Almost all mathematicians accept the Riemann hypothesis:
http://mathworld.wolfram.com/RiemannHypothesis.html
All known evidence and measurements support the hypothesis.
However, despite the fact that we believe it, it has never been proven.

This is completely different with our Chess case.
Why?
Because for Riemann's Hypothesis we need to check an infinite amount of numbers while on this Chess case a finite amount of positions.

And while in Riemann's case we have checked some trillions nontrivial zeros by now validating Riemann's hypothesis, we can never be sure for the rest infinite amount of numbers(zeros) beyond trillion....

In contrast in our Chess case, if we find for example some rules that only then the win can occur for the strong side and then search for all the possible positions with even applying restrictions for the movement of weak side, and yet we can't find a win, then the position is draw. Or not?
Since even if the code and the logic of the code has been verified to be flawless, who guarantees that the computer program+hardware that solved all these positions did this flawlessly?
Do we have to look at each position ourselves? Well this is a matter of taste of each person. Some will accept it, some will not.....


The famous four color theorem is the most famous for this kind of "confusion". To accept or not to accept its computer proof?

I agree that the Riemann hypothesis is probably more difficult. It is also possible that some fundamental new idea will render a simple solution.

In any case, the parallel I was drawing is that in both cases we believe the result, but it is not formally proven. In the case of the 4 color problem, I believe the result. Similarly, we know that EGTBs have formally solved endgames. I consider these proofs of 6 men or fewer on the chessboard.

It is always possible that a proof has a flaw. Andrew Wiles' proof of FLT originally had a bug in it, but it got ironed out. There can also be faulty proofs (either human or computerized) that have an error which does not get detected for a very long time.

At any rate, I do see a very clear distinction from something which is formally proven and something that looks like a lead-pipe cinch.

[Dann Corbit]

I agree that this is more convincing and can be used for what I consider as a real proof that I am lazy to construct(I still do not consider it as a proof inspite of the fact that it convinced me).

I think that black even does not need the quare a6 and can do fine even on 7*7 board with only c6 and b6

In order to construct a proof that I am too lazy to do we pracitcally need simply to divide the possible pair of squares of white king and white queen to 12 classes and give the corresponding squares of black king and rook in every class.

After this we need to prove that after white does a move in one of the classes black can capture the queen or make a move that goes to one of the classes.

Uri

Huh??

Robin gave proof, and it's quite simple

Page One.... http://www.talkchess.com/forum/viewtopi ... 72&start=0

Robin's post is convincing but I do not consider it as a proof.
I simply disagree with you about the meaning of the word proof.

Robin gave a strategy to draw the game.
A proof should prove that the strategy is really possible and that white cannot do something different that I did not imagine.

I am not sure if we practically need to do what I suggested and it is only one way to prove the draw.

Thinking about again it may be more simpler to prove that the strategy that Robin suggested is possible but it needs proof.

Here is part of the proof that you need to write in order to prove it based on my standards and not only in order to convince me(I added comments to Robin comments inside the ().

2) If the king is in check, move out of check to any one of the squares h7, g8, h8(possible but need proof because the queen may control all 3 squares from g7 and if the white king is at f8 white is winning
the white king can never go to f8 but in order to prove that black draw we need to mention the possible squares of the white king and prove that white cannot escape them in every one of the cases)

3) If the rook is not on f6 move the rook to f6(possible assuming the rook is not pinned but the rook cannot be pinned when the black king is at h7 g8 h8 and the rook is at f6 f2 c6 b6 a6).

Uri

Uri, George posted a link above, the utility you need for your final proof is
Freezer.

If this can't give a proof, then you'll have to run a hundred plys full width!

In ten years that might not be a problem

Terry

It will be a proof when freezer is run against the problem and verifies the result. Until then, it is only a very good hypothesis.

You have no confidence in players far better than yourself

That is definitely untrue. I have great respect for the many chess players who frequent this forum and are far better than I am. By the same token, every chess book written by GMs that includes a set of example positions has lots of mistakes in it.
WAC is full of mistakes
WCSAC is full of mistakes
BWTC is full of mistakes
as are all others.

My point here is that the best chess players (and the best chess engines) do not always get the answers write, even after very deep thinking or very long analysis.

It's a draw Dan, and a well known and understood draw.

I have never disputed that it is a draw. I have only disputed that the draw has been proven.

[Daniel Mehrmann]

Topalov vs. Mamedyrov

[d]3Q4/6pk/5r1p/4K2P/8/8/8/8 w - - 0 63


Topalov gave up trying to win and went for a draw ... but engines see a big plus for white. Is this position theoretically drawn ... or was Topalov too tired to find out if a win exists? Which engine also sees a draw ?

Yes, this position is a draw. It's a typical fortress !

But Homer can solve such "fortress" positions is a fast time:

Homer 2.01pre6 by Daniel Mehrmann, http://www.homer-chess.com, info@homer-chess.de

1/06 0:00 +5.29 1.Dd7 (132)
2/04 0:00 +5.33 1.Dd7 Tf8 (318) 19
3/06 0:00 +5.29 1.Dd3+ Kg8 2.Dd7 Tf8 (1.597) 99
4/08 0:00 +5.28 1.Dd7 Kg8 2.Kd5 Tf8 (5.843) 365
5/12 0:00 +5.13 1.Dd3+ Kg8 2.Dd7 Tf8 3.Kd4 Tf4+ 4.Kc5 (23.219) 494
6/13 0:00 +5.15 1.Dd3+ Kg8 2.Dd5+ Kh7 3.Db7 Tf1 4.Ke4 Kg8 (55.218) 587
7/14 0:00 +5.14 1.Dd7 Tf2 2.Ke4 Kg8 3.Kd3 Kf8 4.Ke4 (144.792) 664
8/14 0:00 +5.10 1.Dd7 Tf2 2.Ke4 Tf8 3.Kd3 Tf3+ 4.Kc4 Tf8 5.Dd3+ (175.161) 660
8/16 0:00 +5.10 1.Dd7 Tf2 2.Ke4 Tf8 3.Kd3 Tf3+ 4.Kc4 Tf8 5.Dd3+ (263.961) 626
9/14 0:00 +5.04 1.Dd7 Tf2 2.Ke4 Tf1 3.Ke3 Tf8 4.Dd3+ Kg8 5.Dc4+ Tf7 6.Dc8+ (312.147) 625
9/18 0:00 +5.04 1.Dd7 Tf2 2.Ke4 Tf1 3.Ke3 Tf8 4.Dd3+ Kg8 5.Dc4+ Tf7 6.Dc8+ (537.106) 604
10/18 0:01 +5.03 1.Dd7 Kg8 2.Ke4 Tf1 3.Dd5+ Kh7 4.Ke3 Tf8 5.De4+ Kg8 6.Ke2 Td8 (809.768) 558 TB:198
10/18 0:01 +5.03 1.Dd7 Kg8 2.Ke4 Tf1 3.Dd5+ Kh7 4.Ke3 Tf8 5.De4+ Kg8 6.Ke2 Td8 (992.585) 563 TB:198
11/18 0:02 +5.03 1.Dd7 Kg8 2.Ke4 Tf1 3.Dd5+ Kh7 4.Ke3 Tf8 5.De4+ Kg8 6.Ke2 Td8 7.De6+ (1.169.563) 551 TB:344
11/18 0:02 +5.03 1.Dd7 Kg8 2.Ke4 Tf1 3.Dd5+ Kh7 4.Ke3 Tf8 5.De4+ Kg8 6.Ke2 Td8 7.De6+ (1.452.658) 554 TB:344
12/20 0:03 +5.04 1.Dd7 Kg8 2.Kd4 Tf1 3.Dd5+ Kh7 4.Kc3 Tf4 5.Dd7 Tf8 6.Kb4 Ta8 7.Dd3+ (2.033.003) 515 TB:492
12/20 0:04 +5.04 1.Dd7 Kg8 2.Kd4 Tf1 3.Dd5+ Kh7 4.Kc3 Tf4 5.Dd7 Tf8 6.Kb4 Ta8 7.Dd3+ (2.302.840) 505 TB:736
13/21 0:07 +4.86 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Kg8 6.Kb3 Kf7 7.Dc7+ Kf8 8.Dc5+ Kf7 (3.612.503) 513 TB:968
13/24 0:15 +4.86 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Kg8 6.Kb3 Kf7 7.Dc7+ Kf8 8.Dc5+ Kf7 (7.043.634) 463 TB:2.227
14/24 0:18 +4.76 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Kg8 6.Kb4 Tc1 7.Db2 Tf1 8.Dc3 (8.587.061) 461 TB:2.855
14/24 0:25 +4.76 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Kg8 6.Kb4 Tc1 7.Db2 Tf1 8.Dc3 (11.208.397) 444 TB:3.861
15/25 0:30 +4.51 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Tf8 6.Kb4 Kg8 7.Ka5 Kh7 8.Db2 Ta8+ 9.Kb4 (13.531.811) 450 TB:4.736
15/27 0:41 +4.51 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Tf8 6.Kb4 Kg8 7.Ka5 Kh7 8.Db2 Ta8+ 9.Kb4 (17.710.176) 429 TB:6.701
16/24 0:44 +4.01-- 1.Dd7 (19.386.852) 434 TB:7.327
16/25 0:48 0.00 1.Dd7 Kg8 2.Kd4 Tf8 3.Dd5+ Kh7 4.De5 Tf1 5.Kc4 Tf2 6.Kb4 Tf8 7.Ka5 Kg8 8.Db2 Tf5+ 9.Kb4 Tf1 (20.777.528) 429 TB:7.887
16/25 0:50 +0.50++ 1.Da8 (21.137.413) 424 TB:8.595
16/38 3:05 +3.33 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Te1+ 4.Kf2 Te5 5.Df3 Kg8 6.Kf1 Kh7 7.Df7 Kh8 8.Da7 Kh7 9.Dg1 Txh5 (42.250.817) 227 TB:64.292
16/38 3:08 +3.83++ 1.Ke4 (43.674.221) 230 TB:65.049
16/38 3:21 +3.33 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Te1+ 4.Kf2 Te5 5.Df3 Kg8 6.Kf1 Kh7 7.Df7 Kh8 8.Da7 Kh7 9.Dg1 Txh5 (47.047.600) 233 TB:70.106
17/25 3:23 +2.83-- 1.Da8 (47.879.673) 235 TB:70.344
17/26 3:25 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (48.890.019) 237 TB:71.220
17/28 3:35 +0.50++ 1.Kd5 (51.513.650) 238 TB:75.118
17/32 4:34 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (59.614.073) 217 TB:107.889
18/26 4:36 +0.50++ 1.Da8 (60.285.774) 217 TB:109.441
18/28 4:46 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (63.751.997) 222 TB:112.032
18/28 4:46 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (63.751.997) 222 TB:112.032
19/28 4:51 +0.50++ 1.Da8 (65.061.029) 222 TB:114.796
19/28 4:53 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (65.444.083) 223 TB:116.083
19/28 4:53 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf7 4.De4+ Kg8 5.Ke2 Tf6 6.Ke1 Kh8 7.Dc2 Tf2 8.De4 Tf6 (65.444.083) 223 TB:116.083
20/28 4:57 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (66.276.875) 222 TB:117.688
20/30 5:06 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (68.853.536) 224 TB:122.096
21/28 5:08 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (69.583.559) 225 TB:123.321
21/32 5:19 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (72.502.509) 227 TB:131.123
22/30 5:25 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (73.865.861) 227 TB:134.485
22/34 6:04 0.00 1.Da8 Tf2 2.Ke4 Tf1 3.Ke3 Tf6 4.De4+ Kg8 5.Ke2 Tf8 6.Ke1 Kh8 7.Dc2 Tf6 8.De4 Kg8 9.Ke2 (85.620.494) 234 TB:163.513
Bester Zug: Dd8-a8 Zeit: 6:12.203 min K/s: 235.258 Knoten: 87.302.144 TB: 168.566


Best,
Daniel

ps: There is no trick, its just a Homer

[Dann Corbit]

I agree that this is more convincing and can be used for what I consider as a real proof that I am lazy to construct(I still do not consider it as a proof inspite of the fact that it convinced me).

I think that black even does not need the quare a6 and can do fine even on 7*7 board with only c6 and b6

In order to construct a proof that I am too lazy to do we pracitcally need simply to divide the possible pair of squares of white king and white queen to 12 classes and give the corresponding squares of black king and rook in every class.

After this we need to prove that after white does a move in one of the classes black can capture the queen or make a move that goes to one of the classes.

Uri

Huh??

Robin gave proof, and it's quite simple

Page One.... http://www.talkchess.com/forum/viewtopi ... 72&start=0

Robin's post is convincing but I do not consider it as a proof.
I simply disagree with you about the meaning of the word proof.

Robin gave a strategy to draw the game.
A proof should prove that the strategy is really possible and that white cannot do something different that I did not imagine.

I am not sure if we practically need to do what I suggested and it is only one way to prove the draw.

Thinking about again it may be more simpler to prove that the strategy that Robin suggested is possible but it needs proof.

Here is part of the proof that you need to write in order to prove it based on my standards and not only in order to convince me(I added comments to Robin comments inside the ().

2) If the king is in check, move out of check to any one of the squares h7, g8, h8(possible but need proof because the queen may control all 3 squares from g7 and if the white king is at f8 white is winning
the white king can never go to f8 but in order to prove that black draw we need to mention the possible squares of the white king and prove that white cannot escape them in every one of the cases)

3) If the rook is not on f6 move the rook to f6(possible assuming the rook is not pinned but the rook cannot be pinned when the black king is at h7 g8 h8 and the rook is at f6 f2 c6 b6 a6).

Uri

Uri, George posted a link above, the utility you need for your final proof is
Freezer.

If this can't give a proof, then you'll have to run a hundred plys full width!

In ten years that might not be a problem

Terry

It will be a proof when freezer is run against the problem and verifies the result. Until then, it is only a very good hypothesis.

Hi Dan,
Even Freezer will not generate a true proof, in the strict mathematical sense, which seems to be what you and Uri seek. This is not only because Freezer's source is not open, as Uri mentioned, but also because Freezer does not generate a full database of all possible relevant positions. In order to keep the computation size and eventual database size manageable, Freezer allows and often even requires users to define rules that will reduce the database computation to levels manageable by Freezer. In the specific position in question at least some rules are required by Freezer. Depending on what rules a user defines the _exact_ same position might result in an evaluation of "White wins", "Draw" or "Black wins", so clearly specifying these rules properly is essential. A savvy Freezer user will be good at defining rules which will result in an accurate conclusion, but this hardly constitutes a true proof in the mathematical sense, any more than my move generating algorithm did.

P.S. I ran Freezer on the position in question. The conclusion Freezer/I reached was "Draw". However I do not have a complete set of 6 man tablebases and I had to define several rules for Freezer to use in its database generation. The first of the rules I defined was "If White's queen is captured" = draw.

Robin, you improvised and even removed the Black h6 pawn and EGTBs returned a draw. What , more proof do Dan and Uri need??

http://www.shredderchess.com/online-che ... abase.html

It is possible for more pieces to be a hindrance and cause zugzwang. So removing a piece demonstrates nothing.

[D]8/8/8/8/8/NK1N4/6p1/k7 w - - bm Nb4; dm 2;
[D]8/8/8/8/8/NK1N4/8/k7 w - - c0 "pawn removed = stalemate, pawn there = loss";

[J. Prata]

"It is possible for more pieces to be a hindrance and cause zugzwang. So removing a piece demonstrates nothing."

Not in this case, as it is very easy to see.

From the M-W dictionary:

Main Entry: stub·born
Pronunciation: 'st&-b&rn
Function: adjective
Etymology: Middle English stibourne, stuborn
1 a (1) : unreasonably or perversely unyielding : MULISH (2) : justifiably unyielding : RESOLUTE b : suggestive or typical of a strong stubborn nature <a stubborn jaw>
2 : performed or carried on in an unyielding, obstinate, or persistent manner <stubborn effort>
3 : difficult to handle, manage, or treat <a stubborn cold>
4 : LASTING <stubborn facts>
synonym see OBSTINATE
- stub·born·ly adverb
- stub·born·ness /-b&r(n)-n&s/ noun

*

Main Entry: skep·ti·cism
Pronunciation: 'skep-t&-"si-z&m
Function: noun
1 : an attitude of doubt or a disposition to incredulity either in general or toward a particular object
2 a : the doctrine that true knowledge or knowledge in a particular area is uncertain b : the method of suspended judgment, systematic doubt, or criticism characteristic of skeptics
3 : doubt concerning basic religious principles (as immortality, providence, and revelation)
synonym see UNCERTAINTY

*

First one can be found in (almost?) all chordates.
Second one...

Oh, aw.

Long live them both for they made us what we are

[Dann Corbit]

I have never disagreed that the position is almost certainly drawn.
In fact, I think it is a draw myself.

However, your handwaving arguments about how easy it is to see it are not convincing to me.

The Freezer analysis is a reason to believe it, but even that is not totally certain. I would like to see the exact rules given to Freezer and the exact analysis provided in return.

The arguments put forth that explain why it is drawn are also convincing. But they are not proofs.

[smirobth]

I would like to see the exact rules given to Freezer and the exact analysis provided in return.

Rule1: If White's queen is captured = draw
Rule2: If White's pawn promotes = white win
Rule3: If Black's king leaves the 8 squares f8,g8,h8,f7,g7,h7,g6,h6 = white win
Rule4: If Black's rook leaves the squares b6, c6, f6, f2, h6 = white win
Rule5: If Black's pawns leave the squares g7, h6, g5 = white win
Rule6: If White's pawn advances = white win
Rule7: If Black's pawn promotes = white win
Rule8: If Black's rook is captured = white win unless the capturing piece can be recaptured = draw
Rule9: If a Black pawn is captured = white win unless the capturing piece can be captured = draw
Note that the vast majority of the rules favor White.

The output from position
[D] 3Q4/6pk/5r1p/4K2P/8/8/8/8

WTM all moves = draw
BTM Rf6-c6 or Rf6-f2 draw, all other moves lose.

All 3-4-5 tablebases present. Only some 6-man present.
All tablebases were checked to not be corrupted using Wilhelm, but only in the distant past, not immediately prior to running Freezer.

QED? I hope so, this is much further than I ever intended to go with such a trivial position.

[Terry McCracken]

I agree that this is more convincing and can be used for what I consider as a real proof that I am lazy to construct(I still do not consider it as a proof inspite of the fact that it convinced me).

I think that black even does not need the quare a6 and can do fine even on 7*7 board with only c6 and b6

In order to construct a proof that I am too lazy to do we pracitcally need simply to divide the possible pair of squares of white king and white queen to 12 classes and give the corresponding squares of black king and rook in every class.

After this we need to prove that after white does a move in one of the classes black can capture the queen or make a move that goes to one of the classes.

Uri

Huh??

Robin gave proof, and it's quite simple

Page One.... http://www.talkchess.com/forum/viewtopi ... 72&start=0

Robin's post is convincing but I do not consider it as a proof.
I simply disagree with you about the meaning of the word proof.

Robin gave a strategy to draw the game.
A proof should prove that the strategy is really possible and that white cannot do something different that I did not imagine.

I am not sure if we practically need to do what I suggested and it is only one way to prove the draw.

Thinking about again it may be more simpler to prove that the strategy that Robin suggested is possible but it needs proof.

Here is part of the proof that you need to write in order to prove it based on my standards and not only in order to convince me(I added comments to Robin comments inside the ().

2) If the king is in check, move out of check to any one of the squares h7, g8, h8(possible but need proof because the queen may control all 3 squares from g7 and if the white king is at f8 white is winning
the white king can never go to f8 but in order to prove that black draw we need to mention the possible squares of the white king and prove that white cannot escape them in every one of the cases)

3) If the rook is not on f6 move the rook to f6(possible assuming the rook is not pinned but the rook cannot be pinned when the black king is at h7 g8 h8 and the rook is at f6 f2 c6 b6 a6).

Uri

Uri, George posted a link above, the utility you need for your final proof is
Freezer.

If this can't give a proof, then you'll have to run a hundred plys full width!

In ten years that might not be a problem

Terry

It will be a proof when freezer is run against the problem and verifies the result. Until then, it is only a very good hypothesis.

Hi Dan,
Even Freezer will not generate a true proof, in the strict mathematical sense, which seems to be what you and Uri seek. This is not only because Freezer's source is not open, as Uri mentioned, but also because Freezer does not generate a full database of all possible relevant positions. In order to keep the computation size and eventual database size manageable, Freezer allows and often even requires users to define rules that will reduce the database computation to levels manageable by Freezer. In the specific position in question at least some rules are required by Freezer. Depending on what rules a user defines the _exact_ same position might result in an evaluation of "White wins", "Draw" or "Black wins", so clearly specifying these rules properly is essential. A savvy Freezer user will be good at defining rules which will result in an accurate conclusion, but this hardly constitutes a true proof in the mathematical sense, any more than my move generating algorithm did.

P.S. I ran Freezer on the position in question. The conclusion Freezer/I reached was "Draw". However I do not have a complete set of 6 man tablebases and I had to define several rules for Freezer to use in its database generation. The first of the rules I defined was "If White's queen is captured" = draw.

Robin, you improvised and even removed the Black h6 pawn and EGTBs returned a draw. What , more proof do Dan and Uri need??

http://www.shredderchess.com/online-che ... abase.html

It is possible for more pieces to be a hindrance and cause zugzwang. So removing a piece demonstrates nothing.

[D]8/8/8/8/8/NK1N4/6p1/k7 w - - bm Nb4; dm 2;
[D]8/8/8/8/8/NK1N4/8/k7 w - - c0 "pawn removed = stalemate, pawn there = loss";

I was going to remove myself from this debate, but after such an insult, it's not so easy!!

I don't need to be instructed in Chess Fundamentals!

It further annoys me as you think you can prove something to me with these "ABC's".....

Your proof to me...*sigh*

[Terry McCracken]

I would like to see the exact rules given to Freezer and the exact analysis provided in return.

Rule1: If White's queen is captured = draw
Rule2: If White's pawn promotes = white win
Rule3: If Black's king leaves the 8 squares f8,g8,h8,f7,g7,h7,g6,h6 = white win
Rule4: If Black's rook leaves the squares b6, c6, f6, f2, h6 = white win
Rule5: If Black's pawns leave the squares g7, h6, g5 = white win
Rule6: If White's pawn advances = white win
Rule7: If Black's pawn promotes = white win
Rule8: If Black's rook is captured = white win unless the capturing piece can be recaptured = draw
Rule9: If a Black pawn is captured = white win unless the capturing piece can be captured = draw
Note that the vast majority of the rules favor White.

The output from position
[D] 3Q4/6pk/5r1p/4K2P/8/8/8/8

WTM all moves = draw
BTM Rf6-c6 or Rf6-f2 draw, all other moves lose.

All 3-4-5 tablebases present. Only some 6-man present.
All tablebases were checked to not be corrupted using Wilhelm, but only in the distant past, not immediately prior to running Freezer.

QED? I hope so, this is much further than I ever intended to go with such a trivial position.

It's ludicrous, to have to go to such measures to appease a few skeptics.

Robin, you are a far more patient man than I.

Terry