Modelling of a Chessmaster

The inference of a player's evaluation function is only significant if it holds for more than one game. This is where the inference of a chessmaster is tested. The past paper of Jansen et al. showed that the inference of Fischer could be applied to that of both Fischer and Kasparov. Here this same study is analysed but the reason for the greater predictive accuracy of Kasparov with Fischer's weights is explained. The training data for this experiment is again that of the eleven games by Fischer in the 1963 USA Championships. The weights inferred from this are then used on the four games of Kasparov-Karpov, Kamsky-Kasparov, Fischer-Taimanov and Sherwin-Fischer. The results in both Jansen et al.'s and this paper show that Kasparov is compressed greater than that of Fischer. This may seem counter intuitive, as one may suspect that the Fischer game would be compressed better than that of Kasparov as it is Fischer's own style that is being used. The reason for this difference is easily found however, by simply using Training data from Kasparov. The results show that the compression achieved using Kasparov's training data is similar to that of using Fischer's training data. Because Kasparov's games are more compressed than Fischer's is, it can be said that he is more inherently compressible than Fischer, is by this method. This does not imply that Kasparov has a simple style, but rather his characteristics are more closely matched to this method than that of Fischer. An example of how this works, can be demonstrated by assuming that the tosses of a biased coin towards heads were to be encoded. Should the actual result for the number of tosses be 80% and the prior for the encoding is 60%, the message length will still be quite short as the number of heads coming up is large and thus the shorter codes occur more often. If the actual percentage is lower, then the total message length becomes longer, because each instance uses a larger code to describe the event. The results for both cases were similar apart from small changes either up or down. One explanation could be the uneven search space for $\lambda$ values. With only one game, this space becomes more uneven and jagged than if there were more games.

 

Table 5: Inference results using the advanced model with Fischer's 1963 USA Championship as training data.

	No.
Player	Moves	I-Random	I-Inferred	Comp(%)	I-Training	Comp (%)
Kasparov	86 (W)	357.298	292.091	$81.7\%$	301.831	$84.5\%$
Kasparov	107 (B)	498.60	438.11	$87.8\%$	439.034	$88.1\%$
Fischer	89(W)	385.881	340.31	$88.1\%$	350.559	$90.8\%$
Fischer	100(B)	421.211	376.724	$89.3\%$	404.874	$96.1\%$

 

Table 6: Inference results using the advanced model with the Kasparov 11 games as training data.

	No.
Player	Moves	I-Random	I-Inferred	Comp(%)	I-Training	Comp (%)
Kasparov	86 (W)	357.298	292.091	$81.7\%$	300.171	$84.0\%$
Kasparov	107 (B)	498.60	438.11	$87.8\%$	440.654	$88.4\%$
Fischer	89(W)	385.881	340.31	$88.1\%$	344.716	$89.3\%$
Fischer	100(B)	421.211	376.724	$89.3\%$	404.329	$96.0\%$