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The αβ algorithm for two-player game-tree search has a notorious reputation as being a challenging algorithm for achieving reasonable parallel performance. MTD(f), a new αβ variant, has become the sequential algorithm of choice for practitioners. Unfortunately, MTD(f) inherits most of the parallel obstacles of αβ, as well as creating new performance hurdles. Transposition-table-driven scheduling (TDS) is a new parallel search algorithm that has proven to be effective in the single-agent (one-player) domain. This paper presents TDSAB, the first time TDS parallelism has been applied to two-player search (the MTD(f) algorithm). Results show that TDSAB gives comparable speedups to that achieved by conventional parallel αβ algorithms. However, since this is a parallelization of a superior sequential algorithm the results in fact are better. This paper shows that the TDS idea can be extended to more challenging search domains.