New Results in Deep-Search Behaviour

Factors Affecting Diminishing Returns for Searching Deeper1

“…However, none had such a large set of test positions at his/her disposal as we have (over 40,000 positions). Steenhuisen (2005) observed deep-search behaviour of CRAFTY on different test sets and reported different best-change rates and best-change rate decreases for different test sets. This and the following section will show that bestchange rates strongly depend on the values of the positions included in a test set.…”

“…In each case, we suggest that a dataset used for such an investigation should be representative for the whole game of chess, as it was probably the case with our large dataset of real-game positions. Steenhuisen (2005) was the first to point out that the chance of new best moves being discovered at higher depth decreases faster for positions closer to the end of the game. However, having in mind that deep-search behaviour depends on the values of positions in a test set, it seems worthwhile to check whether his results were just the consequence of dealing with positions with a decisive advantage (at least on average) in a later phase of the game.…”

“…For the measurements done in the go-deep experiments we use the same definitions as provided by Heinz (1998) and Steenhuisen (2005). Let B(d) denote the best move after a search to depth d, then the following best-move properties were defined.…”

“…For confidence bounds on the values for best-change rates we use the 95%-level of confidence (λ = 1.96). Moreover, we use the equation given by Steenhuisen (2005) (in Equation 3: m represents the number of successes in a sample size of n observations). Our hypothesis is the following: best-move changes depend on the value of a given position.…”

“…A remarkable follow-up on the previous work done on deep-search behaviour using chess programs was published by Steenhuisen (2005) who used CRAFTY to repeat the go-deep experiment on positions taken from previous experiments to push the search horizon to 20 plies. He used the same experimental setup to search, among others, a set of 4,500 positions, from the opening phase, to a depth of 18 plies.…”