How could Checkers be solved in 2007 when .............

[Chessqueen]

Hello:

Sorry I do NOT have a graphical interface for Checkers, and I do NOT know where there is a Talkcheckers forum similar to this Talkchess forum. I am a terrible Chess player but I recently beat a Checker player rated 2150 playing Black. Since I do NOT have ant Checkers interface I am using Arena for chess. See if you can find the winning combination for Black to play and win ? I will give you the solution in 1 hour if you can NOT find it. This was playing the American checkers, NOT the British Checkers version.
[d]8/K5p1/1p5P/2P1k3/8/8/8/K1p1p1K1 b - - 1 1

Since in Checker which is different than Chess if you force your opponent to take your Stone your opponent is obligated to take on his next move , this is the force win with Black to move and win.
1. Cb2 Ka1c3 2. Ef2 Kge3 3. Kd6 Ce7 4. Gf8=K Kac5 5. Kdb4 Kbd2 6. Kdf4

Sorry for posting this here, I just found a great Checkers GUI, but NOT a Checker Forum similar to Talkchess Forum https://3dkingdoms.com/checkers.htm

Ratings are relative, not absolute. The important thing is the rating difference between players, not the number itself. 2150 out of context could be an average player in a site where ratings are inflated. For example, top human players at Lichess are rated 3100+ in bullet games, and there are more blunders there than in 2700+ Elo FIDE human games at classical time controls. Sure, the longer time control improves the quality of the games and reduces the amount of blunders, despite the seemingly lower ratings.

AFAIK, American checkers and English draughts are exactly the same regarding the rules of play. There might be small differences of style like black pieces in England being red in USA; and the colours of the squares.

First of all, here is a comparison since chess and checkers have different notations:

Code: Select all

In chess, white starts the game and it is shown in the bottom half of the chessboard.
In American checkers / English draughts, black starts the game and it is shown in the bottom half of the checkerboard.

                  CHESS                            AMERICAN CHECKERS / ENGLISH DRAUGHTS

                  Black                                            White
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a8 | b8 | c8 | d8 | e8 | f8 | g8 | h8 |        |    | 32 |    | 31 |    | 30 |    | 29 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a7 | b7 | c7 | d7 | e7 | f7 | g7 | h7 |        | 28 |    | 27 |    | 26 |    | 25 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a6 | b6 | c6 | d6 | e6 | f6 | g6 | h6 |        |    | 24 |    | 23 |    | 22 |    | 21 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a5 | b5 | c5 | d5 | e5 | f5 | g5 | h5 |        | 20 |    | 19 |    | 18 |    | 17 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a4 | b4 | c4 | d4 | e4 | f4 | g4 | h4 |        |    | 16 |    | 15 |    | 14 |    | 13 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a3 | b3 | c3 | d3 | e3 | f3 | g3 | h3 |        | 12 |    | 11 |    | 10 |    |  9 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a2 | b2 | c2 | d2 | e2 | f2 | g2 | h2 |        |    |  8 |    |  7 |    |  6 |    |  5 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a1 | b1 | c1 | d1 | e1 | f1 | g1 | h1 |        |  4 |    |  3 |    |  2 |    |  1 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
                  White                                          Red / Black

The checkers notation might seem weird or strange, but if you flip the board to show white in the bottom half of the checkerboard, you get:

Code: Select all

   AMERICAN CHECKERS / ENGLISH DRAUGHTS

                Red / Black
+----+----+----+----+----+----+----+----+
|    |  1 |    |  2 |    |  3 |    |  4 |
+----+----+----+----+----+----+----+----+
|  5 |    |  6 |    |  7 |    |  8 |    |
+----+----+----+----+----+----+----+----+
|    |  9 |    | 10 |    | 11 |    | 12 |
+----+----+----+----+----+----+----+----+
| 13 |    | 14 |    | 15 |    | 16 |    |
+----+----+----+----+----+----+----+----+
|    | 17 |    | 18 |    | 19 |    | 20 |
+----+----+----+----+----+----+----+----+
| 21 |    | 22 |    | 23 |    | 24 |    |
+----+----+----+----+----+----+----+----+
|    | 25 |    | 26 |    | 27 |    | 28 |
+----+----+----+----+----+----+----+----+
| 29 |    | 30 |    | 31 |    | 32 |    |
+----+----+----+----+----+----+----+----+ 
                  White

Which is more user-friendly for left-to-right, top-to-bottom readers.

------------------------

I have the CheckerBoard GUI. If I set up the position and analyze with KingsRow 1.19b (which is not the latest version) and 8-man EGDB:

A first search with Multi-PV enabled at low depths retrieved than only 18-14 (e5-f4) would be a probable win for black (evals around 66, where 100 is a man and usually enough to win), but higher depths output drawish scores:

Code: Select all

depth 33,  1046.2s,  18-14,1  18-22,1  24-27,1  18-15,1  3-7,-1  2-7,-1  25-30,-1  25-29,-1  3-8,-2668  2-6,-2670  18-23,-3900

Positive scores are better for black and negative scores are better for white. The range of evaluations goes between -4000 and 4000 (-3999 means a mate in 1 ply for white).

------------------------

A second search with Multi-PV disabled also outputs a draw:

Code: Select all

value>1,  depth 37/5.0/5, 124.2s,  5006 kN/s,  pv 18-15 19x10 2-6 28x19 6x24

Such low values of selective search and mean depth values denote that EGDB positions are found. In this case, the mainline quickly goes down to a 3 vs 3 endgame (6 pieces after 4 captures: e5-d4 c5xe3, e1-f2 a7xc5, f2xd4xb6), thus covered by the 8-man EGDB.

------------------------

It is possible to post Checkers diagrams, but I had to resort to off-site images for the stones. And of course the Diagram's AI won't work, as it is not aware that capturing is mandatory.

theme=MV firstRank=1 graphicsDir=*/graphics.dir/alfaerieSVG/
graphicsType=svg
whitePrefix=b
blackPrefix=w
promoChoice=K
symmetry=none
checker::fmFfcafm(afcafm)F::c1,e1,b6,g7,,c5,h6
king::mFcafm(acafm)F:checkerking:e5,,a1,g1,a7

BTW, the WinBoard Alien Edition does support Checkers.

Well done! The pieces are not shown to me, unfortunately, neither in the quote of your post, nor if I copy and paste your post without quoting. OTOH, I can see the pieces in your original post.

Regards from Spain.

Ajedrecista.

NOTE: Eureka I just found the best Checker Forum for Beginner player like myself, since I tried hard to become good at Chess and could never achieved it, I am having a better chance at Checker http://playground.usacheckers.com/forum/index.php

Also a great site to play American Checkers online and practice to become better https://cardgames.io/checkers/

[Chessqueen]

Hello:

Sorry I do NOT have a graphical interface for Checkers, and I do NOT know where there is a Talkcheckers forum similar to this Talkchess forum. I am a terrible Chess player but I recently beat a Checker player rated 2150 playing Black. Since I do NOT have ant Checkers interface I am using Arena for chess. See if you can find the winning combination for Black to play and win ? I will give you the solution in 1 hour if you can NOT find it. This was playing the American checkers, NOT the British Checkers version.
[d]8/K5p1/1p5P/2P1k3/8/8/8/K1p1p1K1 b - - 1 1

Since in Checker which is different than Chess if you force your opponent to take your Stone your opponent is obligated to take on his next move , this is the force win with Black to move and win.
1. Cb2 Ka1c3 2. Ef2 Kge3 3. Kd6 Ce7 4. Gf8=K Kac5 5. Kdb4 Kbd2 6. Kdf4

Sorry for posting this here, I just found a great Checkers GUI, but NOT a Checker Forum similar to Talkchess Forum https://3dkingdoms.com/checkers.htm

Ratings are relative, not absolute. The important thing is the rating difference between players, not the number itself. 2150 out of context could be an average player in a site where ratings are inflated. For example, top human players at Lichess are rated 3100+ in bullet games, and there are more blunders there than in 2700+ Elo FIDE human games at classical time controls. Sure, the longer time control improves the quality of the games and reduces the amount of blunders, despite the seemingly lower ratings.

AFAIK, American checkers and English draughts are exactly the same regarding the rules of play. There might be small differences of style like black pieces in England being red in USA; and the colours of the squares.

First of all, here is a comparison since chess and checkers have different notations:

Code: Select all

In chess, white starts the game and it is shown in the bottom half of the chessboard.
In American checkers / English draughts, black starts the game and it is shown in the bottom half of the checkerboard.

                  CHESS                            AMERICAN CHECKERS / ENGLISH DRAUGHTS

                  Black                                            White
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a8 | b8 | c8 | d8 | e8 | f8 | g8 | h8 |        |    | 32 |    | 31 |    | 30 |    | 29 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a7 | b7 | c7 | d7 | e7 | f7 | g7 | h7 |        | 28 |    | 27 |    | 26 |    | 25 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a6 | b6 | c6 | d6 | e6 | f6 | g6 | h6 |        |    | 24 |    | 23 |    | 22 |    | 21 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a5 | b5 | c5 | d5 | e5 | f5 | g5 | h5 |        | 20 |    | 19 |    | 18 |    | 17 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a4 | b4 | c4 | d4 | e4 | f4 | g4 | h4 |        |    | 16 |    | 15 |    | 14 |    | 13 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a3 | b3 | c3 | d3 | e3 | f3 | g3 | h3 |        | 12 |    | 11 |    | 10 |    |  9 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a2 | b2 | c2 | d2 | e2 | f2 | g2 | h2 |        |    |  8 |    |  7 |    |  6 |    |  5 |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
| a1 | b1 | c1 | d1 | e1 | f1 | g1 | h1 |        |  4 |    |  3 |    |  2 |    |  1 |    |
+----+----+----+----+----+----+----+----+        +----+----+----+----+----+----+----+----+
                  White                                          Red / Black

The checkers notation might seem weird or strange, but if you flip the board to show white in the bottom half of the checkerboard, you get:

Code: Select all

   AMERICAN CHECKERS / ENGLISH DRAUGHTS

                Red / Black
+----+----+----+----+----+----+----+----+
|    |  1 |    |  2 |    |  3 |    |  4 |
+----+----+----+----+----+----+----+----+
|  5 |    |  6 |    |  7 |    |  8 |    |
+----+----+----+----+----+----+----+----+
|    |  9 |    | 10 |    | 11 |    | 12 |
+----+----+----+----+----+----+----+----+
| 13 |    | 14 |    | 15 |    | 16 |    |
+----+----+----+----+----+----+----+----+
|    | 17 |    | 18 |    | 19 |    | 20 |
+----+----+----+----+----+----+----+----+
| 21 |    | 22 |    | 23 |    | 24 |    |
+----+----+----+----+----+----+----+----+
|    | 25 |    | 26 |    | 27 |    | 28 |
+----+----+----+----+----+----+----+----+
| 29 |    | 30 |    | 31 |    | 32 |    |
+----+----+----+----+----+----+----+----+ 
                  White

Which is more user-friendly for left-to-right, top-to-bottom readers.

------------------------

I have the CheckerBoard GUI. If I set up the position and analyze with KingsRow 1.19b (which is not the latest version) and 8-man EGDB:

A first search with Multi-PV enabled at low depths retrieved than only 18-14 (e5-f4) would be a probable win for black (evals around 66, where 100 is a man and usually enough to win), but higher depths output drawish scores:

Code: Select all

depth 33,  1046.2s,  18-14,1  18-22,1  24-27,1  18-15,1  3-7,-1  2-7,-1  25-30,-1  25-29,-1  3-8,-2668  2-6,-2670  18-23,-3900

Positive scores are better for black and negative scores are better for white. The range of evaluations goes between -4000 and 4000 (-3999 means a mate in 1 ply for white).

------------------------

A second search with Multi-PV disabled also outputs a draw:

Code: Select all

value>1,  depth 37/5.0/5, 124.2s,  5006 kN/s,  pv 18-15 19x10 2-6 28x19 6x24

Such low values of selective search and mean depth values denote that EGDB positions are found. In this case, the mainline quickly goes down to a 3 vs 3 endgame (6 pieces after 4 captures: e5-d4 c5xe3, e1-f2 a7xc5, f2xd4xb6), thus covered by the 8-man EGDB.

------------------------

It is possible to post Checkers diagrams, but I had to resort to off-site images for the stones. And of course the Diagram's AI won't work, as it is not aware that capturing is mandatory.

theme=MV firstRank=1 graphicsDir=*/graphics.dir/alfaerieSVG/
graphicsType=svg
whitePrefix=b
blackPrefix=w
promoChoice=K
symmetry=none
checker::fmFfcafm(afcafm)F::c1,e1,b6,g7,,c5,h6
king::mFcafm(acafm)F:checkerking:e5,,a1,g1,a7

BTW, the WinBoard Alien Edition does support Checkers.

Well done! The pieces are not shown to me, unfortunately, neither in the quote of your post, nor if I copy and paste your post without quoting. OTOH, I can see the pieces in your original post.

Regards from Spain.

Ajedrecista.

NOTE: Eureka I just found the best Checker Forum for Beginner player like myself, since I tried hard to become good at Chess and could never achieved it, I am having a better chance at Checker http://playground.usacheckers.com/forum/index.php

Also a great site to play American Checkers online and practice to become better https://cardgames.io/checkers/

Chinook is NOT unbeatable, by human I believe that GM Tinsley would have won if he did NOT get sick during his match

[Ajedrecista]

Hello:

Chinook is NOT unbeatable, by human I believe that GM Tinsley would have won if he did NOT get sick during his match

The web version of Chinook is known to not be the full, stronger, best version of Chinook. Furthermore, the version of 2007 that claimed to weak solved the game was stronger than the versions that played two matches against Tinsley in the '90s. What about the last match if Tinsley did not got sick? We will never know.

Regarding the game of the video, it is a Single Corner (11-15, 22-18), probably the oldest way to start a game. There are many lines with their names, just like in chess. However, I could not find the name of this line. There is an online checkers opening explorer with a few games and 4.- ..., 19-16 is not there.

There is something called PP (published play) that is very important in checkers. I even did not find 3.- ..., 24-19 in the famous book Duffy's Single Corner of 1934, the closest being the variation 103 (off 60, trunk)... or I do not know how to search in this nightmare of variations and transpositions, which is also possible. I also did not found the line of the video in Anderson's The game of draughts of 1852. I looked into Lees' Guide to the game of draughts of 1893 (one of many Lees' guides), also without success. But I am sure that some to many moves of the game are already PP, God knows where.

Finally, KingsRow opening book already thinks that 5.- ..., 29-25 is suboptimal to say the least, with 4.- ..., 26-22 being the way to go. KingsRow also did not like 10.- ..., 25-21 (10.- ..., 25-22 preferred). The next move by black reduces a good part of its previous advantage, with another blunder at 13th white move and so on. That game was of poor quality by both sides under KingsRow standards. For example, KingsRow gives drawish evals after 16.- 1-6 (9:18 in the video), just with other big blunder in the next white move (both 16.- ..., 23-18 and 16.- ..., 26-22 would have saved the draw).

Regards from Spain.

Ajedrecista.

[towforce]

To solve a game you need to search until you reach a tablebase position. Which then gives you an exact score (distance to win, or a draw). So you won't need the heuristic evaluation of the engine. Under conditions where the search cannot be deep enough to reach the tablebases, the quality of play is determined by the heuristic evaluation, though.

It is wrong to rule out the possibility of solving chess without a comprehensive search of the entire game tree.

In terms of working out how to construct such a proof, it would probably be a good idea to start with checkers, though: I'm guessing that most checkers positions could be resolved to a high degree of accuracy with today's computers, which would help in terms of looking for patterns and testing ideas (mathematical progress usually entails getting the answer first, then working out why it works).

[Chessqueen]

Hello:

Did Kingsrow reached the level of Chinook in Checkers?


NOTE: Eureka I just found the best Checker Forum for Beginner player like myself, since I tried hard to become good at Chess and could never achieved it, I am having a better chance at Checker http://playground.usacheckers.com/forum/index.php

AFAIK, the 2007 solution of checkers was a weak solving in the sense that Chinook was unbeatable if playing from the starting position with the standard, official rules. It is different than being a 24-piece DTM EGDB (distance-to-mate end game database) at any given position. It is true that both KingsRow and Cake improved a lot, to the point that there was a time that the challenge was not to lose any game —which was trivial—, but to reduce the time to not to lose any game. For example, a big difference would be if one engine needed 1 second/move to not lose while the other needed 10 seconds/move.

Furthermore, the thumbnail of the video shows a 10×10 checkerboard of International draughts with flying kings and men can capture backwards, which is a different variant than the 8×8 American checkers / British draughts without flying kings and men can not capture backwards that was weakly solved in 2007. The search space complexity of the game of nxn checkers was already a subject at TalkChess in 2016 and later confirmed outside TalkChess in 2017. You can see the difference of the search space complexity between an 8×8 checkerboard with 24 pieces (an upper bound of circa 5*10^20) and a 10×10 checkerboard with 40 pieces (an upper bound of circa 2.3*10^33).

There is an equivalent forum to TalkChess dedicated to 10×10 International draughts (and sometimes to other variants) here. The USA Checkers forum posted by you is the well-known forum of ACF (American Checkers Federation), that is, one of the 8×8 variants.

Thanks Müller for allowing a checkers thread once in a blue moon.

Regards from Spain.

Ajedrecista.
[/quote]

This is well explained on this video ===>

[Chessqueen]

Human are stiil beating computer in Checkers (KingsRow), and we are NOT even talking about the Checker World Champion.

[Krzysztof Grzelak]

I think it is worth mentioning one more important program - Nemesis Professional Draughts.

[Ajedrecista]

Hello:

Human are stiil beating computer in Checkers (KingsRow), and we are NOT even talking about the Checker World Champion.

This is not a real time game, it is a finished game loaded in the GUI and replayed with the 'Forward' button. Having said that, it is true that KingsRow opening book evaluates the last opening move 12.- ..., 32x23 (b8xd6) (1:05 in the video) as 0 (draw), but changes its mind immediately when out of the book, so it must be a mistake when building the book and a very difficult, good find by whoever discovered it among a few million lines contained in the book.

Eval by KingsRow 1.19b:

Code: Select all

value=121,  depth 41/34.4/61,  539.2s,  6213 kN/s,  pv 2-7 31-27 9-14 18x9 5x14 22-17 7-10 17-13 1-6 30-26 11-16
value>125,  depth 43/38.6/64,  741.7s,  5977 kN/s,  pv 2-7 31-27 9-14 18x9 5x14 22-17 7-10 17-13 1-6 30-26 11-16
value>129,  depth 43/37.3/64,  933.9s,  6123 kN/s,  pv 2-7 21-17 15-19 23x16 11x20 25-21 8-11 17-13 9-14 18x9 5x14
value>128,  depth 43/37.2/64,  1003.8s,  6217 kN/s,  pv 2-7 21-17 15-19 23x16 11x20 25-21 8-11 17-13 9-14 18x9 5x14
value=125,  depth 43/37.0/64,  1141.2s,  6309 kN/s,  pv 2-7 21-17 15-19 23x16 11x20 25-21 8-11 17-13 9-14 18x9 5x14

Which should be won by very good players.

When switching the book off, black/red obtains an early, slight to moderate advantage, but KingsRow does not like 7.- ..., 29-25 (h8-g7) at all (0:40 in the video), so this is a problem in the opening book. Welcome to checkers: a slight inaccuracy even in the opening and the game is over! There are surely safest ways to play with white, for example 3.- ..., 18-14 (e5-f4) instead 3.- ..., 24-19 (b6-c5).

This game started in the same way that the other game you posted against the web version of Chinook. Both games exploited the dust hole [square 12 (a3) for white and 21 (h6) for black]. Other bad spot uses to be the dog hole [square 5 (h2) for white and 28 (a7) for black] IIRC.

Regards from Spain.

Ajedrecista.

[jefk]

tf wrote
It is wrong to rule out the possibility of solving chess without a comprehensive search of the entire game tree.

correct; but, i'm not going to dwell on this further here, even for checkers;
the topic of checkers (weakly solved (*) ) is already a digression, and
game theory would be a futher digression.

What i would propose is another subtopic, besides 'kindergarten and tournaments,
a subtopic 'Game Theory' (mainly applied to chess, ofcourse, but as first
start maybe also to checkers, and draughts (**)). In relation to ICGA research etc.
(not sure how these people communicate, besides academic and yearly conferences
https://icga.org/.

(*) there's no reason to doubt the validity of the weak solution for checkers,
https://www.researchgate.net/publicatio ... _Is_Solved
Done some futher reading, and found that this solution was was for the
unrestricted form regarding the checkers openings. Nowadays
there often are checkers games/tourns with a restricted set of openings
(chosen via ballots) and then with (probably unbalanced or even slightly unsound)
openings (similar as TCEC) you can get odd results of course.
Note, already in 1934 a draw problem for checkers was recognized and then the first
restricted (opening) varations started to occur.
(**) there certainly are other methods to discuss besides number-crunching (brute force
tree 'solving') in this regard, besides graph theory, there's also topology
(applied to game theory)