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Deriving Concepts and Strategies from Chess Tablebases. Matej Guid, Martin Možina, Aleksander Sadikov, and Ivan Bratko. Faculty of Computer and Information Science University of Ljubljana, Slovenia May 200 9. Introduction. - PowerPoint PPT Presentation
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Deriving Concepts and Strategies from Chess Tablebases
Matej Guid, Martin Možina, Aleksander Sadikov, and Ivan Bratko
Faculty of Computer and Information ScienceUniversity of Ljubljana, Slovenia
May 2009
Introduction
Chess tablebases contain a wealth of knowledge, however, mining for this knowledge, manually or automatically, proved as extremely difficult.
RESEARCH QUESTION
How to produce human-understandable models and use them to generate instructions suitable for teaching humans?
RESEARCH QUESTION
How to produce human-understandable models and use them to generate instructions suitable for teaching humans?
Machine learning from tablebases did not yield much success…
• relatively small domains (such as KRK endgame in chess)
• resulting models are hardly intelligible to human experts (novices,
beginners…)
IF ... THEN ...IF ... THEN ......
ABML
hierarchical goal-based rules
textbook instructions games with instructions
Obtaining Knowledge from Domain Expert
Computer (to the expert):
“What goal would you suggest for white in this position?
What are the reasons for this goal to apply in this position?”
The expert (a FIDE master):
“Black king is quite close to the edge of the board, but the king is not constrained by white pieces. Therefore I would suggest White to constrain black king.“
A new attribute king_constrained was introduced.The argument was used to induce a new rule.
Strategic Goal-Based Rules
Hierarchical model of an ordered set of rules of the following form:
IF preconditions THEN goal
Preconditions and goals are both expressed by using the features that resulted from the knowledge elicitation process.
IF edist < 3 AND king_constrained = falseTHEN king_constrained = true AND edist should not increase
added by computer
induced from expert’s argument
preconditions: conjunction of particular conditionsgoal: conjuction of particular subgoals
The expert may add, modify, and/or remove any of the preconditions and subgoals.
It is important to rely on common knowledge about the domain!
The expert may add, modify, and/or remove any of the preconditions and subgoals.
It is important to rely on common knowledge about the domain!
Strategic Goal-Based Rules
Hierarchical model of an ordered set of rules of the following form:
IF preconditions THEN goal
Preconditions and goals are both expressed by using the features that resulted from the knowledge elicitation process.
IF edist < 3 AND king_constrained = falseTHEN king_constrained = true AND edist should not increase
added by computer
induced from expert’s argument
A subgoal can specify:
desired value of an attribute: true/false, <, >, …
its optimization: minimize, maximize
qualitative changes: decrease, increase, not decrease, not
increase
A subgoal can specify:
desired value of an attribute: true/false, <, >, …
its optimization: minimize, maximize
qualitative changes: decrease, increase, not decrease, not
increase
F|5
F|--
T|6 F|7
F|--
F|--
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
iterative deepening
goal achievable: player MAX can force its execution
desirable: distance to mate decreases at given
search depth
allowing non-optimal play, but aiming towards final goal: delivering checkmate
7
?|?
?|?
T|7 F|6
?|? ?|?
?|?
T|5T|4 F|4 F|6
?|?
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
the student can sometimes achieve the goal in several ways
do they all decrease distance to mate?
7
T|5
?|?
T|7 F|6
T|6 T|8
?|?
T|5T|4 F|4 F|6
?|?
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
the student can sometimes achieve the goal in several ways
do they all decrease distance to mate?
7
T|5
T|6
T|7 F|6
T|6 T|8
T|9
T|5T|4 F|4 F|6
?|?
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
the student can sometimes achieve the goal in several ways
do they all decrease distance to mate?
7
T|5
T|6
T|7 F|6
T|6 T|8
T|9
T|5T|4 F|4 F|6
T|10
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
the student can sometimes achieve the goal in several ways
do they all decrease distance to mate?
7
T|5
T|6
T|7 F|6
T|6 T|8
T|9
T|5T|4 F|4 F|6
T|10
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
7
goal achievable dtm decreases
goal achievable dtm does not decrease
T|5
T|6
T|7 F|6
T|6 T|8
T|9
T|5T|4 F|4 F|6
T|10
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
7
max search depth
Counter example: goal can be achieved, but resulting play does NOT decrease distance to
mate
T|5
T|6
T|7 F|6
T|6 T|8
T|9
T|5T|4 F|4 F|6
T|10
goal achievable distance to mate
Achievability of Goals
search depth
MAX
MIN
MAX
7
max search depth
Among counter examples, the position with highest distance to mate is chosen as the key counter example.
Key counter example
Computer (to the expert):
“Would you admonish a student if he or she played 1.Rd1-c1 in this position?"
1.Ke7-d7 is optimal move according to tablebases:achieves mate in 6 moves (after 1...Kb7-b6 2.Rd1-d5!)
1.Rd1-c1 is the worst possible execution of suggested goal (“constrain king…”)achieves mate in 11 moves -> much worse!
Key counter example
Computer (to the expert):
“Would you admonish a student if he or she played 1.Rd1-c1 in this position?"
Human players typically choose a longer path to win by systematically achieving intermediate goals.
The resulting play in counter examples should lead to overall progress towards achieving the final goal of delivering checkmate.
Key counter example
Computer (to the expert):
“Would you admonish a student if he or she played 1.Rd1-c1 in this position?"
The expert found this execution of the goal to be perfectly acceptable.
The ruleIF edist < 3 AND king constrained = falseTHEN king constrained = true AND edist should not increase
was therefore accepted.
Hierarchy of Goals
goal is achievable also when goals can be executed regardless of the defender's play (optimal or non-optimal)
the student is instructed to always try to execute the highest achievable goal
typical of a human way of thinking
It would be redundant to express goals in the following way:
“Constrain black king or deliver a checkmate,if the opponent plays badly and allows it."
It would be redundant to express goals in the following way:
“Constrain black king or deliver a checkmate,if the opponent plays badly and allows it."
Constructing Human-Friendly Instructions
instructions are obtained by stating only the progressive subgoal
IF king_constrained = false … THEN king constrained = true …
IF … THEN edist should decrease
IF edist>0 … THEN edist=0
the exception is the last, default goal
IF edist < 1
THEN edist should not increase
AND knight_on_edge = false
AND wrong_corner_way should decrease
AND wrong_corner_way minimize
AND white_king_more_central = true
derived instruction: “Block the way to the wrong corner."
Obtaining Diagrams and Variations
desirable to provide most useful representation of the goals and concepts
simulations of delivering checkmate
• randomly chosen initial positions
• the program used hierarchy of goals as a heuristic
• execution of goals in these simulations was optimal (quickest
play)For each goal…
Position that occurred most frequently is presented by a diagram.
When several positions occurred equally frequently, more diagrams were usedand variation (sequence of moves) given.
For each goal…
Position that occurred most frequently is presented by a diagram.
When several positions occurred equally frequently, more diagrams were usedand variation (sequence of moves) given.
The Bishop and Knight Checkmate (KBNK)
regarded as the most difficult of the elementary mates
general strategy:
• driving the opposing king to the edge of the board
• forcing the king to the appropriate corner
• delivering a checkmate
only knowing this basic strategy hardly suffices for delivering
checkmateFor example, grandmaster Epishin (Kempinski-Epishin, Bundesliga 2001) failed to force the defending king to the appropriate corner and the game ended in a draw.For example, grandmaster Epishin (Kempinski-Epishin, Bundesliga 2001) failed to force the defending king to the appropriate corner and the game ended in a draw.
No formalized models for KBNK endgame suitable for teaching purposes were derived by any machine-learning programs.
Derived Strategy, Concepts, and Example Games
1. (highest) goal: Deliver checkmate. 2. goal: Prepare the knight for checkmate. 3. goal: Restrain black to a minimal area beside the right corner. 4. goal: Build a barrier and squeeze black king's area. 5. goal: Approach black from the center. 6. goal: Block the way to the wrong corner. 7. goal: Push black towards the right corner. 8. goal: Push black towards the edge. 9. goal: Approach with the king.10. goal: Bring the knight closer to black king. default goal: Keep the kings close.
A strategy is an ordered list of goals:
The rule-based model for KBNK, description of the attributes and example games containing automatically generated instructions can be found in a web appendix at http://www.ailab.si/matej/KBNK/
Evaluation
Three chess teachers (among them a selectors of Slovenian women's and youth squad) all agreed on the usefulness of the presented concepts and found the derived strategy suitable for educational purposes.
Among the reasons to support this assessment was that the instructions “clearly demonstrate the intermediate subgoals of delivering checkmate.” The rules by using them as a heuristic function for 6-ply minimax search to play 100 randomly chosen KBNK positions (at least 28 moves to mate with optimal play) against perfect defender:
• quickest play: average game length was 32 moves, 100% checkmate
• slowest play: average game length was 38 moves, 100% checkmate Four strong grandmasters were asked to express their assessment for each game to what degree (1 to 10) they find KRK play to be human-like:
our program 4.1 7.1 8.2 7.3
tablebases 2.2 3.1 1.8 2.0
Conclusions
We developed a procedure
• for semi-automatic synthesis of textbook instructions for
teaching the difficult KBNK endgame,
• accompanied by example games containing generated instructions. Derived strategy includes concepts and key positions from
KBNK that help the human learner to easily understand main principles of this strategy:
• detected automatically from simulated games
• goals enable correct play also against sub-optimal defence Positive assessment of derived textbook instructions by chess coaches We explained:
• guidelines for interaction between the machine and the expert to obtain a human-understandable rule-based model for playing a chess endgame
• how the instructions, including illustrative diagrams, could be derived semi-automatically from such a model.
![Deriving Concepts and Strategies from Chess Tablebases · PDF fileand knight versus the lone king endgame. 1 Introduction Chess tablebases ... study specialist John Roycroft [3] and](https://img.pdfslide.net/doc/110x75/5a86caf47f8b9a001c8d502f/deriving-concepts-and-strategies-from-chess-tablebases-knight-versus-the-lone-king.jpg)
