Likelihood function

A single position is evaluated in the same way as before in Section 3. Each attribute is given a weighting ($\lambda$ value) as before. The advanced model is again a probabilistic model and the probabilities of the one ply are the same as the basic model but the evaluation is somewhat different. The value of a position is now derived from the sum of the future moves multiplied by their corresponding probabilities of being played.

To determine the values and probabilities of root positions, a backup of the higher levels is needed and this was done through a probabilistic variation of the minimax algorithm. Appendix 1 holds the likelihood function for the advanced model, as the complexity of this model is too great to state here.

The inference is made in the same way as before using ML as the measure of fit to the data. The hill climbing is accomplished in the same fashion as before using a data file that recorded the evaluation of each attribute at each ply for any given position. This can mean numbers of 1,500,000 or more positions that must be backed up to the root node and can be moderately time consuming, taking a few minutes for a complete run through the data of a given move (assuming it is 4 ply deep and on average 35 moves per ply).