Alpha - Beta - Conspiracy Search ( Draft of Oct

We introduce a variant of-search in which each node is associated with two depths rather than one. The purpose of-search is to nd strategies for each player that together establish a value for the root position. A max strategy establishes a lower bound and the min strategy establishes an upper bound. It has long been observed that forced moves should be searched more deeply. Here we make the observation that in the max strategy we are only concerned with the forcedness of max moves and in the min strategy we are only concerned with the forcedness of min moves. This leads to two measures of depth | one for each strategy | and to a two depth variant of-called ABC search. The two depth approach can be formally derived from conspiracy theory and the structure of the ABC procedure is justiied by two theorems relating ABC search and conspiracy numbers.