Transposition Tables in Computer

Search algorithms are used in many game-playing programs. To enhance the strength of these programs additional heuristics and improvements are used. One of these improvements is the use of transposition tables. In these tables information concerning a position investigated can be stored in order to re-use this information when the same position is encountered again during the search process (a transposition). Amongst the information a transposition-table entry contains is the best move for that position and the score of that move. In order to estimate their contributions we have done experiments separating the eeects of using the transposition move and the transposition value. The transposition table is typically implemented as a large hash table. Even though this table is usually made as large as possible, subject to memory constraints , collisions occur frequently. When a collision occurs, a choice has to be made which position to store or keep in the table (using some replacement scheme). A second topic of our research is to compare the performance of several replacement schemes. The experiments are conducted on middle-game positions taken from chess games. Doubling the number of entries in the transposition table reduces the size of the search tree. This is an obvious result, since the more information in the table, the larger the chance that the information in the table can be re-used during search. Part of our research then is to quantify how much the size of the search tree is reduced when doubling the number of entries in the transposition table. It is known that the beneets of doubling the number of entries decrease at large table sizes. Therefore, it is interesting to examine other means of using much memory than increasing the number of entries in the transposition table. In particular, what additional information can be stored in a transposition-table entry to speed up the search? Preliminary results are given and some suggestions to be tested in the near future will be made.