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[Event "FIDE World Championship 2023"] [Site "Astana KAZ"] [Date "2023.04.16"] [Round "6"] [White "Liren, Ding"] [Black "Nepomniachtchi, Ian"] [Result "1-0"] [WhiteElo "2788"] [BlackElo "2795"] [TimeControl "40/7200:20/3600:900+30"] [Variant "From Position"] [ECO "?"] [Opening "?"] [Annotator "https://lichess.org/@/chessentialsBLOG"] [FEN "5r1k/R3N1p1/5p1p/7P/3P4/p1P3Q1/5PPK/1bq5 w - - 0 41"] [SetUp "1"] [Source "https://lichess.org/study/S98rQMrO/ghY4hHAN"] [Orientation "white"] { In the very likely case that you didn't get any of what I wrote in the Introduction, let me demonstrate the use of the Method of Comparison with a few concrete examples. The first position is taken from game seven of the 2023 World Chess Championship between Ding Liren and Ian Nepomniachtchi (which is currently ongoing as I write these lines). This game was my inspiration for this study/article/video because it featured an incredibly deep move 41, whose point I didn't grasp at all at first glance - but only after I used the method of comparison to unravel its hidden points. } 41. d5 { This is not the only winning move in this position, but it is an effective one. However, at first glance it seems very random - why should White spend a full tempo on placing a pawn on d5? Well, it turns out that there are quite a few variations where the fact White now controls the e6 square is crucial due to checkmating ideas against the Black king. } (41. Qc7 { When I first saw this position, I wondered - why exactly does White need the move d5? So, I decided to use the method of comparison and see the variation with immediate Qc7 - a move played in the game - but with the White pawns still on d4 and a3. It turns out that there is an important difference if we compare these two variations. } 41... Kh7 42. Ng6 Rg8 { And here, White can no longer play Qf7 as in the game precisely because the e6 square is not under the control. } 43. Qf7 (43. Qg3 { It has to be said that the engine thinks that White is still winning, but that is now beside the point }) 43... Qg5 { And here, it turns out that White can't really capture on g8 because it does not lead to mate. } 44. Qxg8+ Kxg8 45. Ra8+ Kf7 46. Rf8+ { And now the king has the e6 square available. } 46... Ke6 { This wouldn't have been possible with the pawn on d5. }) 41... a2 42. Qc7 { Only now that we have placed the pawn on d5 can we go for this - as now it works. } 42... Kh7 43. Ng6 Rg8 44. Qf7 { And here Black resigned as mate can be delayed, but not avoided. Note, btw., that the method of comparison is somewhat iterative, as here you have to go back to the line with 41.Qc7 and ask yourself - but why exactly doesn't the move Qg5 - which was saving Black there - work here? } 44... Qg5 45. Qxg8+ { This is the point - with the pawns on d5 and a2 this leads to mate (as opposed to the position with the pawns on d4 and a3). } 45... Kxg8 46. Ra8+ Kf7 47. Rf8# 1-0