What is the Transposition Table" personality setting, and what value should I use here when creating my own personalities?"

The "Transposition Table" setting is used to tell the computer personality how much memory to allocate for its search data. The Transposition table is also widely known as the "Hash Table", named after the way that the data is organized. The purpose of the hash table is to speed up an chess engine's search, and the more search data that can be stored, the more likely subsequent parts of the search can be found and skipped.
However, this does NOT mean that you should use the maximum value under all circumstances. There are certain time control settings in which large values can actually make a computer player play WORSE. If you are going to be playing games that mainly use tournament time controls (such as 40 moves in 120 minutes), then a setting of 32MB is optimum, assuming your computer has enough RAM. If you are going to be playing mainly blitz or bullet games (10 minutes or less), then you don't need anything more than the default of 4MB for the transposition table. If you are going to be using Chessmaster mainly for lengthy analysis, then you should use as large a value as Chessmaster will let you -- 64MB is quite common for this purpose.

WARNING: You should always make sure that this setting is in no way near the amount of total RAM that is in your computer. If it approaches your computer's total RAM amount, then Windows will start moving parts of memory to your hard disk, causing lots of disk activity (also called "thrashing"), and degrading the overall performance of all programs that are currently running. So, for example, if your computer has 128 MB of memory, then a setting of 64 MB is the absolute TOTAL limit (because, of course, if you intend to use two computer players in the same game, then giving them both a 64 MB transposition table would cause severe thrashing).

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