I didn't cover the Mind Sports event in Beijing much for the blog, but I did follow it to some degree on my own. One game really caught my eye, and I will share it with you in a moment. The game was an unlikely candidate as an attention-getting: a rapid game that reached a drawn rook and pawn vs. rook endagme after 64 moves and that ended, appropriately enough, in a draw 68 moves later. The defender was never lost, and the drawing methods used have long been known to endgame theory.
What caught my eye was something "mathematical" or "philosophical": it seemed to me at one point that Teimour Radjabov, who had the extra pawn, had managed with a brilliant idea to eliminate the independent significance of one drawing method by showing that he could force the defender (Wang Yue) to switch to a different drawing method, one which is a bit more complicated in practice. Specifically, it seemed for a while that Radjabov had shown that the strong side could force the defender to go from the Karstedt Maneuver to the Last Rank Defense. That doesn't change the objective evaluation of the ending, but such a reduction would be of real theoretical significance.
Upon closer examination, it turns out not to be the case. No doubt tired and short of time, Wang Yue may have gotten befuddled and tricked into a Last Rank Defense, while I, well-rested and in the leisure of my study, was temporarily tricked as well. After patient examination, I realized that this was not the case, and Wang Yue could have returned to the Karstedt after all. Still, Radjabov's concept was truly ingenious, and a very nice practical idea we should all incorporate into our endgame repertoires.
Curious? Have a look here. There are four fragments there. The first three demonstrate basic defensive ideas in rook and pawn vs. rook endings, going from easiest (Philidor's Method) to slightly less easy (the Karstedt Maneuver) to more difficult (the Last Rank Defense). After laying the basic theoretical groundwork we turn to the Radjabov-Wang Yue game, with an emphasis on the point where the former's great practical idea forces Black out of the cookbook Karstedt and makes him find his bearings.