Extended Null-Move Reductions

In this paper we review the conventional versions of nullmove pruning, and present our enhancements which allow for a deeper search with greater accuracy. While the conventional versions of nullmove pruning use reduction values of R ≤ 3, we use an aggressive reduction value of R = 4 within a verified adaptive configuration which maximizes the benefit from the more aggressive pruning, while limiting its tactical liabilities. Our experimental results using our grandmasterlevel chess program, Falcon, show that our null-move reductions (NMR) outperform the conventional methods, with the tactical benefits of the deeper search dominating the deficiencies. Moreover, unlike standard null-move pruning, which fails badly in zugzwang positions, NMR is impervious to zugzwangs. Finally, the implementation of NMR in any program already using null-move pruning requires a modification of only a few lines of code.