Reproduction of past results

In the past papers by Tony Jansen et al., the inference of chess player strategy was made through a statistical approach [17][18]. The evaluation functions used are probabilistic logistic functions of linear combinations of attributes for a position. The process works by attaching weights to a set of attributes. These weights are the parts of the opponent's strategy that were examined. They signify the importance of these attributes to the playing style of the opponent being analysed. The measure of the success of this inference is an adaptation of the compression work compiled by Althöfer [1], who discusses in his 1990 paper the use of a chess program to predict the most likely move to be played by a Grandmaster in a given position. The predictive ability is measured by the compression of the data of chess games played, although Althöfer seemed simply interested in compression. In Althöfer's work, he is more concerned in things like the short notation of Correspondence Chess. The correspondence chess archives use the method of having bits represent that of the initial and final squares, resulting in twelve bits per move and allowing for quick decoding. The method that Althöfer put forward is that chess moves can be ranked by a particular program, by using the likelihood that a move would be played. A code can then be given to each possible move, with the three best probabilities being given codes of lengths two, three and three. The rest of the codes are all of size 1+log₂(n-3), irrespective of the probability of them occurring.

The basic idea is that the best proposals will be the most common ones found and will have the smallest storage size, hence the whole database will be smaller as most of the moves that occur match the ones that are predicted with the highest probability, so that the overall size of the database must get smaller. A further extension, that he mentioned, is to have every move ranked and then have the moves encoded through Huffman coding. This would produce the best codes for this style of compression. The reason that this study is important is that it gives a way to measure the predictive ability of a chess program. The compression achieved on a given game, as a result, will show how well the inference was accomplished [10]. Jansen et al. investigated the problem of inferring, from records of chess matches, some piece of the strategy utilised to play the game. He started by generating game records from self-play by two simple chess programs, one of which looks ahead one move (a one-ply search), while the other looks ahead one move further (with a limit of four moves), every time a piece can be taken (a four-ply quiescent search). The approach is then to try to infer, entirely from these records, precise estimates of the weights used in the evaluation function. Once this succeeded, they then applied the same technique to grandmaster games, to see how well a strategy could be inferred from a grandmaster. It was acknowledged that the programs used were simplifications of the true strategy used. Despite this, they were able, with some success, to predict the moves made by the players.

This was measured by using the idea Althöfer had about compression, only that here it is used as a measure of the effectiveness of the prediction produced by the program. The inference was first made on generated data and then finally on the games that have been played by chess masters. Both were successful in that compression was achieved by both of these studies.

The evaluation functions are found by using predefined evaluation routines and then placing weights on each different one. The weights dictate how important a particular attribute is, from no relationship to a decision, to fully relying on an attribute to make a decision. These weights are then what are inferred, and hence the actual importance of an attribute can be inferred. This technique is not perfect however, as it does not allow for the changing importance of an attribute throughout a game, for instance in the opening, middle or end phase and the variation in strategy because of a different opponent. However, these changes in strategy could be subtle enough for it not to matter from this statistical way of inferring the strategy. The approach does result in very accurate estimates of the actual weights, but they are only estimates, as they can never truly be known. A property of the approach taken by Jansen et al. is that it uses probabilistic choice, which can simulate humans better [17][18]. Humans do not make the same move every time they encounter the same position. This also allowed for the use of statistical inference to find the values of the weights. The inference performed on the simplest of the models studied, using Maximum Likelihood inference, was moderately successful with a small amount of compression. The inference achieved with the higher-level search strategy, was significantly improved with the results showing at most a 26% reduction in the size of the database for a grandmaster and up to 78% reduction on games that had been generated by a computer. This result demonstrates that this technique was successful in being able to infer something about the strategies used in chess play. This also shows that the behaviour and psychology behind grandmaster games is a lot more complex than the simple attributes that were analysed in the study. The description of the chess program is in Appendix 3 in Section 12.