Description of the model

The more advanced model was a lot more successful in the Tony Jansen et al. paper and again so here. The approach uses more of the psychological aspects, such as looking at more position attributes, searching to a greater depth than one ply, but not to the depth some computers will go, and incorporating varying search depths. This model is still not the perfect reflection of the human psyche, as aspects such as adjusting attribute weights, depending on whether the game is in the opening, middle or end phase are not considered. However, it improves over the simple model and shows that this method can work well. Improvements such as considering what stage the player is in can improve the results of the inference, but only to a small extent as most of the work is accomplished in the middle game and some of the strategies will be common throughout the game [14].

The advanced model searches to a depth of at most four ply deep. This depth was settled upon for a number of reasons, a very important one being, that grandmasters do not search any deeper than novices or intermediate players, and hence gain no advantage, in their search depth, over a beginner [8] [5] [6]. However, novices do tend to react defensively, rather than anticipate the opponent's moves and act accordingly [26]. As people do not search as deeply as computers, it would be a very poor duplication of the way players behave, if this model were to go to a further search depth. Another reason being, the deeper the search depth, the greater the number of positions that needs to be searched. This reduces the speed of the programs, which run a lot slower, and finally, Jansen et al. only went to a depth of 4-ply [17][18]. This model uses a quiescent search strategy that is implemented as follows. Every possible position is generated for the current player at a base depth of one ply; further search is only done if a position is found to be non-quiescent. A non-quiescent position is defined as where a capture is possible, a promotion is possible, a check can be played, or the player is already in check [14]. The maximum search depth as stated before is four ply but this is only reached occasionally and mostly during the middle game period (although this phase is not explicitly catered for, the fact that, most of the non-quiescent positions are here, gives this part of the game a slightly different search strategy).

The moves are chosen probabilistically, again to keep in line with Jansen's work and for the reasons previously stated. The number of attributes is kept to only four to reduce the search space needed for inference of the weights. Humans and computers may look at more attributes, but it must be remembered that the aim is to show how this method works, not to find the perfect model. In addition, many attributes can be correlated and thus provide few new pieces of information; the ones chosen were because there was little connection between them. The attributes used are:

• the material balance of the position (where here, Queen = 9, Rook = 5, Bishop = Knight = 3, Pawn = 1), being the difference between the player's and opponent's total material;
• the mobility balance, i.e. the difference between the numbers of moves available to the player and the opponent.
• control of the centre 16 squares i.e. the difference between the number of squares controlled in the centre to that of the opponent.
• number of attacks where attacks to different pieces are worth different amounts, pieces of greater value are worth 1 and values less or equal are worth 0.1, a piece's value is determined as the value set in material balance, a king's value is set at infinity (you can't lose a king) so that all its attacks are weak (0.1) and all attacks against it are strong (1).