There are several techniques, which can greatly improve the performance of search trees in terms of both speed and memory. Pruning techniques such as alpha–beta pruning, Principal Variation Search, and MTD-f can reduce the effective branching factor without loss of strength. In tactical areas such as life and death, Go is particularly amenable to caching techniques such as transposition tables. These can reduce the amount of repeated effort, especially when combined with an iterative deepening approach. In order to quickly store a full-sized Go board in a transposition table, a hashing technique for mathematically summarizing is generally necessary. Zobrist hashing is very popular in Go programs because it has low collision rates, and can be iteratively updated at each move with just two XORs, rather than being calculated from scratch. Even using these performance-enhancing techniques, full tree searches on a full-sized board are still prohibitively slow. Searches can be sped up by using large amounts of domain specific pruning techniques, such as not considering moves where your opponent is already strong, and selective extensions like always considering moves next to groups of stones which are about to be captured. However, both of these options introduce a significant risk of not considering a vital move which would have changed the course of the game.