Monday, 5 August 2019

Mating With B+N: The Stats

COULD you checkmate with bishop and knight against a lone king?
I ask because a Battersea club-mate, who has an ECF of 149, apparently converted the mate with a minimum of fuss in a London Summer League match last week.
When the subject of mating with bishop and knight comes up in conversation, I find many people are either adamant they could do it, or are equally adamant that they could not.
ChessBase's 2019 Mega database has 1,787 examples of the ending, with 368 finishing in a draw. That is a failure rate of 20.6%.
I instinctively felt the failure rate would be higher, but it should be remembered that games that make it into Mega19 are not a genuine cross-selection of all games played.
I have more than 3,600 games in my personal database, with the bishop-and-knight ending appearing only once.
Black to make his 64th move in Spanton (2008) - Michael Shepherd (2071), Isle Of Man 2002
64...Rxg3!? 65.Nxg3
Fifty moves to go.
65...Ke6 66.Ke4
As is well known, the first task of the player with the minor pieces is to force the enemy king to the back rank.
66...Kd6 67.Kd4 Kc6 68.Ba4+ Kd6 69.Bb3 Ke7
During the game, I thought voluntarily retreating like this was very strange. However, 69...Kc6 is no improvement as "back rank" in this ending actually means any edge of the board. So after 69...Kc6, play might proceed 70.Nf5 Kb5 71.Kc3 Kc5 72.Bc4 Kc6 73.Kd4 Kb6 74.Kd5, and Black is successfully being driven to the edge.
70.Ke5 Ke8
Or 70...Kd7 71.Nf5 Kc6 72.Kd4, transposing to the previous note.
71.Nf5 Kf8 72.Kd6 Ke8 73.Ke6 Kf8 74.Kf6 Ke8 75.Nd6+ Kf8
It is usually correct for the defender, once on the back rank, to head for the corner with a square of opposite-colour to the bishop. However, here it was better to leave the back rank with 75...Kd7, which does not save the game but means the mate will take longer.
76.Bc2 Kg8 77.Bg6 Kf8 78.Nf5 Kg8 79.Nh6+ Kf8 80.Bf5 Ke8 81.Be6 Kf8
81...Kd8 allows the black king to escape the back rank, and so prolong the mate.
82.Ng4 Ke8 83.Ne5 Kf8
This time ...Kd8 speeds the mate, viz 83...Kd8 84.Bd7 Kc7 85.Ke6 Kb6 86.Kd6 Ka5 87.Kc5, when the black king is corralled and will soon meet its end on a8.
84.Ng6+ Ke8 85.Ke5 Kd8 86.Kd6 Ke8 87.Bd5 Kd8 88.Bf7 Kc8 89.Ne7+ Kd8
89...Kb7 delays mate by two moves, but, despite my ropey technique, Black is doomed in either case.
90.Nc6+ Kc8 91.Na5 Kd8 92.Nb7+ Kc8 93.Nc5 Kd8 94.Ne6+ Kc8 95.Kc6 Kb8 96.Kb6 Kc8 97.Be8 Kb8 98.Bd7 Ka8 99.Nc7+ Kb8 100.Na6+ 1-0
100...Ka8 101.Bc6# would have meant I mated in 36 moves from the position after 65...Ke6. According to the Nalimov endgame tablebase, I should have been able to do it in 25 moves. I therefore took 44% longer than necessary, which I think shows there is a fair bit of leeway in this ending, so good technique is not always a must!

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