6781097117

EPIA'2011

ISBN: 978-989-95618-4-7

Since the freąuencies are relatwe. the sum of the freąuencies of pre-flop or post-flop has to be 1 (Pre CO + Pre_C 1 + Pre_C2 + Pre_C3 + Pre_C4 + Pre_C5 = 1 and PostCO + PostCl + Post_C2 + Post_C3 + Post_C4 =1). Afler applying the Expectation Maximization algoritlun on this data. the resulting clusters were the follow.
Feature	Cluster#0 13%	Cluster# 1 3%	Cluster#2 21%	Cluster#3 15%	Cluster#4 33%	Cluster#5 10%	Cluster#6 5%
Pre cO	0.3345	0.1007	0.4626	0.0093	0.2281	0.0019	0.0212
Pre c2	0.2167	0.1909	0	0.7364	0.3157	0.0404	0.0104
Pre c3	0.0201	0.174	0	0	0.0075	0.0094	0.0535
Pre c4	0.1971	0.1836	0.0051	0.1504	0.1009	0.6254	0.0261
Pre c5	0.2316	0.3508	0.5322	0.1039	0.3477	0.3228	0.8889
Post cO	0.1091	0.2132	0	0.3059	0.0807	0.1022	0.0666
Post cl	0.2033	0.0572	0	0.4297	0.2511	0.8755	0.0765
Post c2	0.1378	0.7045	0.0578	0.1536	0.0172	0.0222	0.1722
Post c3	0.2674	0.0126	01564	0.0604	0.1194	0	0.2684
Post c4	0.2824	0.0125	0.7858	0.0504	0.5315	0,0002	0.4163

Sonie notes about this results. The namc feature was removed bccausc it was just a label: it has no influence on the clustering. Anotlier feature that was removed was Pre Cl which was removed by the RemoveUseless filter from Weka.

Post_Cl	Numeric [0,1]	Relative freąuency of actions in Post-Flop of the tvpe of cluster 1.
Post_C2	Numeric [0.1]	Relathe freąuency of actions in Post-Flop of the type of cluster 2.
Post_C3	Numeric [0.1]	Relathe freąuency of actions in Post-Flop of the tvpe of cluster 3.
Post_C4	Numeric [0.1]	Relative freąuency of actions in Post-Flop of the type of cluster 4.

7 different tactics were clustered from the database. For instance. for cluster#2 players. about half of their aclions in Pre-Flop are of type 0 and the other half of type 5. In Post-Flop most of the actions from these players are of type 4. and some are of type 3.

Using this table it is possible to predict the opponents' behavior. If we storę and analyze the opponents' actions during the gamę. we can detennine its tactics and thereforc predict possible ne\t moves from those players.

To use this opponent modeling methodology. the agents inust save the historical actions of the advcrsaries throughout the gamę. saving the features present on Tables 3 and 4 for each action. Using the Euclidian distance formula (eąuation 4), it is possible to determine the current strateg}- cluster of the opponents. This way, by knowing the strateg} cluster of the opponent. it might be possible to predict some opponents" actions. with the freąuency of the action in the cluster being the probability of occurrence of that action.

8 Conclusions

The analysis of actions in a Poker gamę presents a very suitable problem to be solved by clustering algorithms. The definition of groups of actions might help the poker