WO2006019337A2

WO2006019337A2 - Method for computer evaluation of a game position

Info

Publication number: WO2006019337A2
Application number: PCT/RU2005/000424
Authority: WO
Inventors: Vladimir Aleksandrovich Bazenov
Original assignee: Bazenov Vladimir Aleksandrovic
Priority date: 2004-08-12
Filing date: 2005-08-12
Publication date: 2006-02-23
Also published as: RU2004124505A; WO2006019337A3

Abstract

The invention relates to mind game-theory problems, more specifically to methods for evaluating game positions in terms of a possible chance of success of parties in a subsequent game and a probabilistic forecasting of the result thereof. The game positions are defined as sports and recreative games such as, for example chess, various types of checks, go, sports card games (bridge etc) and any game situations as a the air controller operation, military game, commercial games and the like. The inventive method for computer evaluation of a game position, mainly for games in which the participating parties make moves resulting in the change of a game position, for example for chess, consists in storing the examined position and the order of the moves in the computer memory, afterwards in carrying out a computer generation and evaluation of the positions occurred in the variants of a further game positions, whose number is limited by technical capabilities of computer means. The method also consists in determining the valuation function value for at lest one part of said positions and in subsequently processing the array of obtained valuation functions.

Description

METHOD FOR COMPUTER EVALUATION OF THE GAME POSITION

Technical field

The invention relates to the field of intelligent gaming tasks, specifically, to methods for evaluating gaming positions in terms of the parties' possible chances in a future game and probabilistic prediction of its outcome.

At the same time, game positions here are understood not only as game situations in the traditional, everyday sense, i.e. situations that arise in games of a sports or entertainment nature, such as, for example, chess, drafts of various varieties, go, sports card games (bridge, etc.), but also any game situations, in the broad, logical and mathematical sense of the word, in which parties must find the optimal strategy and make moves that lead, after each move, to a change in the game situation.

Examples of such a wider understanding of the gaming position include air traffic control, war games, commercial games, and the like.

The prior art. Closest to the technical nature of the proposed method is a computer-based evaluation of the game position, mainly for games in which the parties involved in the game make moves leading to a change in the game position, including setting the position to be studied and the order of the moves in the computer’s memory, followed by a computer the generation and evaluation of positions arising in the variants of the further game, the number of which is limited only by the technical capabilities of computer tools, with the determination of the estimated values functions, at least for a part of these positions, and processing an array of values of the obtained evaluation functions (see, for example, E. Geek computer clocks, M., Agency FAIR, 1997, pp. 8-11). / 1 / In the known method, when enumerating options, a so-called “tree of options) is built)), i.e. each variant has branches at least in part of the moves, and the evaluation function is determined for all or for some branches of those variants whose final positions allow such a definition. The fundamental disadvantage of this method is the avalanche-like growth of branches in the tree of options and, in this regard, the extremely limited depth of options, which is associated with the limited capabilities of modern, even the most high-speed computers. In this regard, the accuracy of the assessment of the game position is also limited, since, as you know, this accuracy is higher, the greater the depth of enumeration of options.

Disclosure of the invention.

The objective of the invention is to increase the accuracy of the assessment of the gaming position, in the expression of this assessment in the form of a numerical value.

This problem is solved by the fact that in the method of computer evaluation of the game position, mainly for games in which the parties involved in the game make moves that lead to a change in the game position, including setting the position to be studied and the order of the moves in the computer’s memory, subsequent computer generation and assessment of the positions arising in the variants of the further game, the number of which is limited only by the technical capabilities of computer tools, with the determination of the values of the evaluation function, at least for parts of these positions, and processing the array of values of the obtained evaluation functions, according to the invention, the options are generated in the form of non-branching chains of moves of the sides, each chain is formed by randomly choosing the moves of the sides in each of the positions successively appearing in the variant, and the assessment of the position under study is given in the form, at least one numerical value, determined by statistical processing of the array of values of the obtained evaluation functions, taking into account their size or other characteristics and the comparative frequency occurrences in the array.

In addition, the evaluation functions in the variants are obtained in numerical and / or logical form.

In addition, an assessment of the position under study is given taking into account only those evaluation functions obtained during the generation that are determined.

In addition, the deterministic evaluation function is determined in numerical form.

In addition, evaluation functions defined in numerical form are grouped according to specified ranges before statistical processing of the array.

In addition, the deterministic evaluation function is determined in a logical form.

In addition, in relation to chess, a deterministic evaluation function in a logical form can take the following meanings: “mat on one side”, “mat on another side”, “pa”.

In addition, the evaluation function is determined using a separate computer program.

In addition, set the maximum number of moves in the chain. In addition, the set number of moves in the chain exceeds the average number of moves in the game. The invention consists in the following.

Variant of use of the invention. If, in the known method, the computer in the initial (investigated) position goes through all possible options (i.e., it looks through all the first moves of that side, which is the turn of the move, then all possible return moves in each variant, etc.), then it is clear that the number of moves viewed in this enumeration increases rapidly, like an avalanche.

If, for example, in the starting position, the number of possible moves of the side beyond which the turn is equal to 20, then the number of reciprocal moves will be of the order of 20 square, i.e. about 400.

For each return move, the first side again has about 20 possible moves, i.e. the number of second moves of the first side approaches 8000, etc. Such a rapid increase in the number of branches in variants, since the performance of even the most modern computers is limited, as a result, limits the depth (i.e., the number of consecutive moves viewed) of variants.

It is clear that the accuracy of the assessment of the game position, in the general case, is directly related to this depth, i.e. range of calculation options.

With a reasonable time limit, modern chess computers, for example, are capable, in the general case (if we are not talking about “fixed” options, that is, options where the parties make forced, compulsory moves), to ensure that options are viewed to a depth of 6-7 moves.

On the contrary, in the proposed method according to the invention, the generation of options from the initial position is done by random the choice of moves of both sides in each of the successively occurring positions, so that each option has the form of a non-branching chain of moves.

This allows you to dramatically increase the depth of options at the same computer speed. This is also facilitated by the fact that with a random choice of moves, the time spent on choosing a move is significantly reduced, since the definition of evaluation functions at each move is excluded from the procedure.

The random choice of moves, of course, cannot adequately reflect the possible course of the further game. But here the law of large numbers comes into effect. With a very large number of scanned options among random outcomes of the game, in a sufficiently large number of them there will also be regular outcomes characterized by sufficiently defined evaluation functions. The evaluation function is usually a certain number attributed to the estimated position based on a number of criteria. The wider the set of these criteria, the more it takes into account position factors, the more accurately the OB characterizes the odds of the parties. However, the evaluation function in the process of enumeration or generation characterizes the positions arising during the virtual game, as a rule, these are the final positions arising at the end of the variant.

In order to proceed to the assessment of the initial, investigated position, a procedure for processing the resulting array of values of the evaluation function is necessary.

In the known method, this procedure (called minimax) leads to the choice of optimal evaluation functions and, as consequence, to the selection and recommendation of the course from which the option begins corresponding to this optimal evaluation function.

The objective of this invention does not include the recommendation of the best move (or a series of best moves) in the position being studied, but only its assessment in terms of the ratio of the odds of the parties in the further game.

Therefore, the processing of the array of the obtained values of the evaluation function of the options is carried out in a fundamentally different way. This array is processed statistically, grouping the values of the estimated function that are of the same type or close in magnitude (for example, located in certain specified ranges), and then, based on this processing, the final numerical estimate of the initial position is derived, for example, as the weighted average of the obtained estimated values function options.

With such statistical processing of a large array of values of the evaluation function, the randomness factor (not regularities) arising in the final positions variants is leveled, and the odds of the parties are estimated more accurately than when using the known method.

The evaluation function can be expressed not only in numerical, but also in a logical form.

Evaluation functions may also be approximate or deterministic.

In relation to chess, for example, examples of deterministic logical evaluation functions can be: “mat black”, “pat”, “mat white”. Another example: in a game situation related to the work of an air traffic controller, a deterministic logical evaluation function may look like this: a plane collision)).

Such evaluation functions can be taken into account during statistical processing of the array of values of the evaluation function of variants, along with numerical evaluation functions of variants, which are also deterministic.

Examples of approximate logical evaluation functions, as applied to chess, are, for example, such as: “y white is a little better)),“ y black is an advantage)), etc.

Mathematical, including statistical processing of such estimation functions is difficult, if at all possible, therefore it is preferable to exclude them from the array during such processing, i.e. when processing, consider only that part of the array that contains the values of deterministic evaluation functions. To enable statistical processing of the array of numerical values of the evaluation functions, it is advisable to group them according to the given ranges of values, so as to then take into account their number in each range. As for the evaluation functions, expressed in logical form, there are usually relatively few of them, and there is no need to group them by ranges.

It is possible to agree, for example, to give such functions a certain numerical value in order to simplify the mathematical processing of the resulting array of values of the evaluation functions.

Issues related to the determination of the value of evaluation functions for a certain game position, as applied, for example, to chess, are rather deeply developed / 1 /. There are many special computer programs for determining the value of the evaluation function, therefore, these issues will not be considered here.

The depth of options (length of chains) should be limited. In each game, there is an average number of moves, this number of moves can be used as an initial parameter when setting the length of chains, which should be at least no less than this average number of moves.

This depth significantly exceeds the corresponding depth of options for existing methods of assessment, which, obviously, leads to an increase in the accuracy of the assessment.

The invention is further illustrated by a specific use case for a chess game.

Any chess position can be correlated with a certain evaluation function, the value of which is obtained by one of the developed methods.

If chess pieces are given a certain value (for example, if, as is customary, the value of a pawn is considered to be 1, then the value of a knight will be 3, an elephant - 3.5, a rook - 5 and a queen - 9), then the primary and simplest criterion for evaluating a chess position there may be a comparative assessment of the total costs of the material of the parties.

This component of the evaluation of a chess position can be called material. However, of course, this cannot be the only assessment of the chess position, because there are many purely positional criteria that more or less significantly affect the odds of the parties.

These include, for example, the degree of development of the figures (in the opening or middlegame), the activity of the king (in the endgame), mutual security of pieces, the presence of possible moves, the presence of open lines, the pawn structure, for example, the presence of passed or double pawns, the presence of forced moves with threats to the king, openness or, conversely, the safe shelter of the king and many others.

These criteria for evaluating a position can be conditionally called positional.

Finally, the position assessment can be further substantially refined if we consider a certain number of possible options for the development of the further game and evaluate the positions obtained at the end of these options in the manner described above, and then process these estimates using a specific technique.

The combination of all the criteria inherent in the selected evaluation methodology allows you to determine the resulting value of the evaluation for the chess position under study. This can be either a numerical characteristic (expressing the probability of a particular outcome of the game during the continuation of the game, starting from this position), or a logical characteristic of the type: “mat black” or “pat”).

So, the proposed method involves setting the studied position in the computer’s memory (if it is already recorded there, for example, during the game, then you just need to fix it in the computer’s memory as the initial task — an object for evaluation).

Next, we carry out a computer procedure for generating options for further games in each of the resulting positions (including the initial one), choosing a random move on each side, and forming a set of non-branching chains of moves, resulting in each chain to a certain position, which be compared the value of the evaluation functions. It is important that the number of moves in the resulting chains is many times greater, with the same technical capabilities of computer tools, the number of moves obtained when constructing a tree of variants according to the known method. That is, in other words, the depth of viewing options in the described method is significantly greater than in the known.

In fact, this depth can significantly exceed the average length of a chess game. This means that viewing options for the described method is carried out almost to the end of the party. It is clear that this is directly related to improving the accuracy of the assessment of the position under study.

The resulting array of values of the evaluation functions obtained as a result of the described procedure - all or in some part of it, omitting those values that clearly fall out of the accepted rating scale or are not determinate (for example: “black is a slight advantage))), and also omitting those positions, which the computer could not match the value of the evaluation functions, is then subjected to statistical processing.

Two cases are possible here. In the first case, if when evaluating the positions at the end of the variant chains, the numerical values of the evaluation functions were operated on, then the procedure for processing the array of the obtained evaluation functions may look as follows.

Group the values of the evaluation functions, placing them at predetermined intervals. For example, 19,500 obtained PF values from 0.1 to 0.2 are placed in one interval, 30,600 PF values from 0.2 to 0.3 are placed in the next interval, etc.

Then calculate the resulting value and take it as an assessment of the investigated position. Various techniques are possible here. For example, you can calculate the resulting value as the weighted average value of the evaluation function, and calculate it, for example, by the formula:

O _cp . = (0.15 m + 0.25 n + ...) / (m + n + ...), ^where: t, n ... - respectively, the number of RP values in each interval, in our case it is 19500 , 30600 ...

0, 15; 0, 25 ... are the average OF values in each interval. The resulting evaluation value will be the desired one. The second case involves the use of logical evaluation functions

In a chess game (as in other games, including logical and mathematical ones), not only numerical values of the evaluation functions are possible, but also logical evaluation functions. In chess, for example, the following can be assigned:

"Mat Black."

In order to take into account such estimates in statistical processing of an array of evaluation functions, identical logical evaluation functions are also grouped, the number of evaluation functions in each group is calculated, and then the odds of the parties are evaluated in accordance with the ratio of these amounts.

Industrial applicability.

In one of the tested cases, this ratio of logical OFs (respectively “mat black)),“ mat white)))) and “pat”) amounted to 112000: 45000: 16000.

From here it is easy to derive numerical probabilistic characteristics of various outcomes of the game, they will comprise an assessment of the initial position. In principle, the case of the combined use of numerical and logical evaluation functions is also possible.

In this case, the easiest way is to give logical evaluation functions numerical values as well, for example, a numerical value of 100 can be assigned to the evaluation function “black”.

There are other possible ways of accounting for logical evaluation functions.

A detailed description of all possible methods of processing the array, the values of the resulting evaluation functions, is the know-how of the invention. Non-deterministic evaluation functions such as “y whites are slightly better” are used in well-known methods for evaluating chess positions, however, it is very difficult to formalize and subject, along with the rest of the array, further statistical processing, therefore, when using the described method, it is recommended to avoid using such methods for obtaining evaluation functions in which such non-deterministic valuation functions are provided.

The know-how of the invention includes the development of such computer programs that determine only the deterministic values of the evaluation function.

The technical result of the invention is to increase the accuracy of assessing the chances of the parties in the playing position, and therefore, the possibility of a more informed choice of the optimal strategy for the further game. The described method is tested, the obtained results confirmed the achievement of the specified technical result.

Claims

CLAIM.

1. A method of computer assessment of the game position, mainly for games in which the parties involved in the game make moves leading to a change in the game position, including setting the position to be studied and the order of the moves in the computer’s memory, subsequent computer generation and evaluation of the options that arise game positions, the number of which is limited only by the technical capabilities of computer tools, with the determination of the values of the estimated

Функции functions, at least for a part of these positions, and processing an array of values of the obtained evaluation functions, characterized in that the variants are generated in the form of non-branching chains of moves of the sides, each chain is formed by randomly choosing the moves of the sides in each of the successively occurring variants

15 positions, and the assessment of the studied position is given in the form of at least one numerical value, determined by statistical processing of the array of values of the obtained evaluation functions, taking into account their size or other characteristics and the comparative frequency of occurrence in the array. 0 2. The method of computer assessment of a game position according to claim 1, characterized in that the evaluation functions in the variants are obtained in numerical and / or logical form.

3. A method for computer-based evaluation of a game position according to claim 1, characterized in that the evaluation of the position being studied is given taking into account5 only those evaluation functions that are determined during generation.

4. A method for computer-based evaluation of a game position according to claim 3, characterized in that the deterministic evaluation function is determined in numerical form.

5. A method for computer-based evaluation of a game position according to claim 4, characterized in that the evaluation functions defined in numerical form are grouped according to predetermined ranges before statistical processing of the array.

6. A method for computer-based evaluation of a gaming position according to claim 3, characterized in that the deterministic evaluation function is determined in a logical form.

7. A method for computer-based evaluation of a game position according to claim 6, characterized in that, as applied to chess, a deterministic evaluation function in logical form can take the following values: “mat one way”, “mat another way”, “pat”.

8. The method of computer assessment of the gaming position according to claim 1, characterized in that the evaluation function is determined using a separate computer program.

9. A method for computer-based evaluation of a gaming position according to claim I _5, characterized in that the maximum number of moves in the chain is set.

10. The method of computer evaluation of the game position according to claim 1, characterized in that the set number of moves in the chain exceeds the average statistical number of moves in the game.