in the sequence is solved the same way . Given this is so , the crux must surely be how the attacker forces the defender into one of the starting positions to begin with , which may be easier or harder to do depending on whether or not the defender realises the danger in the first place . In my defence in the game I opted to run near to a corner without voluntarily entering the corner itself – looking back through the final 20-odd moves of the game , Welling never achieved either of the starting positions against me , though that was more by luck than judgement on my part . Rory reckoned that it would be best for the defending King to stay in the middle of the board for as long as possible until forced towards the corner by the attacker . The only caveat here I can see is to avoid straying too close to the blockading Knight from where it could passively influence the position . We didn ’ t draw any conclusions on what other viable starting positions existed in addition to the two we found . Nor did we look at which is the best location for the defending King to run to – in the game I opted for the vicinity of a1 , but it would be interesting to see how running to the vicinity of either a8 or h1 would change the solution . To try and shed some light on this , the final part of this discussion describes what I found out when I ran the position through the Nalimov Tablebases . Those whose interest has been piqued by the above can also check out two articles by GM Karsten Mueller [ 5,6 ] that give more theory and a lot more examples of solutions to Troitzky Endgames from different positions .
The Nalimov Tablebases give the solutions for all chess endings with three to five men and for some with six men . The one drawback with them is that they do not currently take account of the 50 move rule .
There are several implementations available on-line , the nicest of which is probably at the K4IT website [ 7 ]. The outcome of the exercise was illuminating to say the least . Some of the general points which emerged can be summarised as follows : - 1 . From the starting position after 68 … Nxg7 the win , on best play takes 90 moves ; 2 . If it were Black ’ s move in the same position , the win would only take 31 moves on best play ; 3 . On worst play by the defender , best by the attacker , it ’ s over very quickly – 69 . Kh4 Kf4 70 . Kh3 Kf3 71 . Kh2 Kf2 72 . Kh1 Ng4 73 . h6 Nf5 74 . h7 Ng3 #. 3 . On worst play by the defender , best by the attacker , it ’ s over very quickly – 69 . Kh4 Kf4 70 . Kh3 Kf3 71 . Kh2 Kf2 72 . Kh1 Ng4 73 . h6 Nf5 74 . h7 Ng3 #. 4 . The win on best play does not respect the 50 move rule , so the position for all theoretical , if not practical purposes , is a draw . Initially I thought otherwise , since mid-way through the solution , the Knight blockading on h6 moves away allowing h5-h6 , before the other Knight moves in to renew the blockade on h7 . However if the purpose of this finesse is to zero the 50 move clock then it ends up being futile as the pawn advance h5-h6 occurs on move 101 and it is 55 moves later before it advances any further . Probably the purpose is to set up the possibility of Stamma ’ s mate ( see 7 below ); 5 . The forcing line drives the defending King around the whole board clockwise , before finally delivering mate in the vicinity of h1 ; 6 . There are at least six instances where the attacker has to find the only move , the point being that otherwise the defending King will be able to temporarily escape , entailing threefold repetition as it is being rounded up again , before mate can be delivered ;
7 . The crux of the solution is where the defending King is driven close to the blockading Knight , so that it has fewer flight squares . This Knight then has to be left en prise , the point being that if the defending King captures , Stamma ’ s mate follows . Since the Knight is poisoned , the King has to move away and gets trapped on the h1-h5 file , which directly leads to the final mating sequence . The forced win is as follows – it ’ s not a unique line – there are some transpositions possible along the way : - 69 . Kf3 Ke5 70 . Ke3 Kd5 71 . Kd3 Ne8 72 . Kc3 Ke4 73 . Kc2 Kd4 74 . Kd2 Nd6 75 . Ke2 Nc4 76 . Kf2 Kd3 77 . Kf3 Ne5 + 78 . Kf4 Kd4 79 . Kg5 Neg4 80 . Kf4 Kd5 81 . Kf3 Ke5 82 . Ke2 Ke4 83 . Kd2 Kd4 84 . Kc2 Ne5 85 . Kb3 Nd3 86 . Ka4 Kc4 87 . Ka5 Ne5 88 . Kb6 Kb4 89 . Kb7 Kb5 90 . Kc7 Kc5 91 . Kb7 Nd7 92 . Ka7 Kb5 93 . Kb7 Nf6 94 . Kc7 Kc5 95 . Kb7 Nf7 96 . Ka6 Kb4 97 . Kb6 Ne5 98 . Ka6 Nc4 99 . Kb7 Kc5 100 . Kc7 Kd5 101 . h6 the pawn moves 101 … Nh7 102 . Kd7 Nb6 + 103 . Kc7 Kc5 104 . Kb7 Nd5 105 . Ka7 Kc6 106 . Ka6 Nb6 107 . Ka5 Kc5ο 108 . Ka6 Nc4 109 . Ka7 Kd6 110 . Kb7 Kd7 111 . Ka7 Kc7 112 . Ka6 Kc6ο 113 . Ka7 Nd6 114 . Kb8 Kb6 115 . Ka8 Kc7 116 . Ka7 Nb7 117 . Ka6 Kc6ο 118 . Ka7 Nc5 119 . Kb8 Kd7 120 . Ka8 Kc8 121 . Ka7 Kc7 122 . Ka8 Kb6 123 . Kb8 Nd7 + 124 . Kc8 Kc6 125 . Kd8 Nb6 126 . Ke8 Kd5 127 . Ke7 Ke5 128 . Ke8 Ke6 129 . Kd8 Kd6 130 . Ke8 Nc8 131 . Kd8 Na7 132 . Ke8 Nc6 133 . Kf7 Kd7 134 . Kg7 Ke7 !
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27 | P a g e I r i s h C h e s s J o u r n a l