
## 6. References

by one ply upon a fail-high report. Unfortunately, the size of the resulting search tree exceeded the size of the tree constructed by standard R = 2. Still, another variant was to reduce the depth by one ply upon fail-high reports, and to reduce the depth by two plies upon fail-high reports in that node's subtree, rather than cutting off.

Our empirical studies showed that cutting off the search at the subtree of a fail-high reported node does not decrease tactical strength. Indeed, this is the verified null-move pruning version that we studied in this article. In contrast to the standard approach which advocates the use of immediate cutoff, the novel approach taken here uses depth reduction, and delays cutting off the search until further verification. This yields greater tactical strength and a smaller search tree.

Beal, D.F. (1989). Experiments with the null move. *Advances in Computer Chess 5*, (Ed. D.F. Beal) , pp. 65–79. Elsevier Science Publishers, Amsterdam, The Netherlands. ISBN 0-444-87-159-4.

Berliner, H.J. (1974). *Chess as Problem Solving: The Development of a Tactics Analyzer*. Ph.D. thesis, CarnegieMellon University, Pittsburgh, PA.

Berliner, H.J. (1987). Some innovations introduced by HITECH. *ICCA Journal*, Vol. 10, No. 3, pp. 111–117. Berliner, H.J. and Ebeling, C. (1990). HITECH. *Computers, Chess and Cognition* (Eds. T.A. Marsland and J. Schaeffer), pp. 79–109. Springer-Verlag, New York, N.Y. ISBN 0-387-97415-6/3-540-97415-6. Birmingham, J.A. and Kent, P. (1977). Tree-searching and tree-pruning techniques. *Advances in Computer Chess* 1, (Ed. M.R.B. Clarke), pp. 89–107. Edinburgh University Press, Edinburgh. ISBN 0-852-24292-1.

Campbell, M.S. and Marsland, T.A. (1983). A comparison of minimax tree search algorithms. *Artificial Intelligence*, Vol. 20, No. 4, pp. 347–367. ISSN 0004-3702.

Condon, J.H. and Thompson, K. (1983a). BELLE. *Chess Skill in Man and Machine*, (Ed. P.W. Frey), pp. 201–210. Springer-Verlag, New York, N.Y., 2nd ed., ISBN 0-387-90790-4/3-540-90790-4.

Condon, J.H. and Thompson, K. (1983b), BELLE chess hardware. *Advances in Computer Chess 3*, (Ed. M.R.B. Clarke), pp. 45–54. Pergamon Press, Oxford, ISBN 0-080-26898-6.

Donninger, C. (1993). Null move and deep search: Selective search heuristics for obtuse chess programs. *ICCA*
Journal, Vol. 16, No. 3, pp. 137–143.

Ebeling, C. (1986). *All the Right Moves: A VLSI Architecture for Chess*. MIT Press, Cambridge, MA., ISBN
0-262-05035-8.

Feist, M. (1999). The 9th World Computer-Chess Championship: Report on the tournament. *ICCA Journal*, Vol. 22, No. 3, pp. 155–164.

Goetsch, G. and Campbell, M.S. (1990). Experiments with the null-move heuristic. *Computers, Chess, and Cognition*, (Eds. T.A. Marsland and J. Schaeffer), pp. 159–168. Springer-Verlag, New York, N.Y., ISBN 0-387-974156/3-540-97415-6. Gillogly, J.J. (1972). The technology chess program. *Artificial Intelligence*, Vol. 3, No. 1-3, pp. 145–163. ISSN 0004-3702. Hammilton, S. and Garber, L. (1997). DEEP BLUE's hardware-software synergy. *IEEE Computer*, Vol. 30, No. 10, pp. 29–35. Heinz, E.A. (1999). Adaptive null-move pruning, *ICCA Journal*, Vol. 22, No. 3, pp. 123–132.

Herik, H.J. van den and Herschberg, I.S. (1992). The 7th World Computer-Chess Championship: Report on the tournament. *ICCA Journal*, Vol. 15, No. 4, pp. 208–209.

Hsu, F.-h. (1999). IBM's DEEP BLUE chess grandmaster chips. *IEEE Micro*, Vol. 19, No. 2, pp. 70–80.