[joelangeway]

One example that just occurred to me: The base 2 log of the number of legal positions of a 9x9 go game is about 126.3, which means if I use a good hash of board positions yielding twice that number of bits, I have a better than 50/50 chance of having no collisions. That is very good to know if you've got anything like a transposition table in a Go playing program.

[Someone]

You don't really need that precise an estimate.

  81 * 2log3 ~= 128.38

So, the number of legal positions is only a factor of about 5 down from the number of positions disregarding life.

[cstoner]

Generally, a Zobrist hashing system is used (which is a specific type of transpositon table) for Go. It's also probably used for chess, but I don't follow chess AIs as closely.