By Edmar Mednis

In an article in the February-March 1981 issue of CHESS I discussed the important developments up to then for the Q + RP vs. Q endgame .. Of all the Q + P vs. Q endgames, the case with a RP is the most important one for the practical player. This is because it is the one that occurs most frequently and the reason for this is also quite understandable: the RP is the pawn least likely to have been exchanged off in earlier play. In the above article I made the recommendation that a major chess computer program be used to do the work in analyzing the Q + P vs. Q endgame. The small number of pieces remaining on the board. makes this endgame quite analyzable for the programs with lots of "brute force". On the other hand, the extreme tediousness of such endgames makes them very unpleasant for a human analyst. In 1985 my wish was answered: the former World Champion computer chess program BELLE spent the better half of its time that year in undertaking a definitive study of this endgame. In the process BELLE has generated a "truckload" of information. Unfortunately, the very extensivness of it makes the gob of a human in tackling it still very hard. Because I had published work on the Q + RP vs. Q endgame, I decided to take advantage of BELLE's "expertise" and calculating ability in this area. I selected the six endgames from recent tournament play that seemed to me to be the most important ones theoretically and asked BELLE to comment on them, thus providing both evaluations and analysis to us humans. This article is based on the results from BELLE's work. I am greatly indebted to Ken Thompson, the chief "brain" behind BELLE and to International Master Mike Valvo for their help and cooperation in fulfilling my request and explaining BELLE's "thinking". An important aspect of the latter is that because of its 1985 work, BELLE has developed an extensive database of positions which are won and drawn. Because it believes in playing "objective chess" BELLE refuses to play out for a win those positions which, according to its program, are theoretical draws. Therefore for such positions we can not learn what the best winning tries are. My method will consist of presenting the endgames as BELLE sees them. I will explain why the moves played are good and bad and will compare BELLLE's conclusions with those of noted human analysts. As will be seen, the humans are wrong a lot. The reason is that - as I indicated earlier - this is the most difficult endgame for us to analyze. Implicit in my presentation is my belief that there is no reason to doubt BELLE's analysis. I will discuss here two of the endgames: first where the humans play the worst and then the best played one. At the end of the column I will summarize the major results from the study of all six of the endgames.