{"id":3168,"date":"2014-09-30T19:53:59","date_gmt":"2014-10-01T03:53:59","guid":{"rendered":"http:\/\/www.danamackenzie.com\/blog\/?p=3168"},"modified":"2014-09-30T20:07:45","modified_gmt":"2014-10-01T04:07:45","slug":"mind-blowing-endgame","status":"publish","type":"post","link":"https:\/\/danamackenzie.com\/blog\/?p=3168","title":{"rendered":"Mind-Blowing Endgame"},"content":{"rendered":"<p>I know that games played against my computer aren&#8217;t the most interesting topic in the world, but recently I had an endgame against Shredder that blew my mind. I learned something new and I think you will, too.<\/p>\n<p>Let&#8217;s start on move 88, when the computer played a move that totally shocked me. (Parenthetical remark &#8212; the computer&#8217;s strength was set at 2114, not at full strength.)<\/p>\n<p><a href=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3169 aligncenter\" alt=\"qb1\" src=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb1.jpg\" width=\"434\" height=\"434\" srcset=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb1.jpg 482w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb1-150x150.jpg 150w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb1-300x300.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/a>FEN: Q7\/P6p\/2K3p1\/8\/8\/3kb3\/5p2\/8 b &#8211; &#8211; 0 88<\/p>\n<p><em>Position after 88. Kc6. Black to move.<\/em><\/p>\n<p>Here I was expecting Black to play 88. &#8230; f1Q 89. Qd8+ Kc2 90. a1Q Qc4+, which I thought was likely to lead to a draw. But I guess the computer saw some way for me to escape the checks (maybe 91. Kd6, planning to run to the kingside?). Instead it played <strong>88. &#8230; Bxa7!?!?<\/strong><\/p>\n<p>When I saw this move, I thought, &#8220;Oh damn, the computer hoodwinked me again.&#8221; Of course I saw that 89. Qxa7 f1Q?? 90. Qa6+ would lose for Black. But the real question is what happens after <strong>89. Qxa7 Ke2<\/strong> (diagram 2).<\/p>\n<p><a href=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb6.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3171 aligncenter\" alt=\"qb6\" src=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb6.jpg\" width=\"434\" height=\"434\" srcset=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb6.jpg 482w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb6-150x150.jpg 150w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb6-300x300.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/a>FEN: 8\/Q6p\/2K3p1\/8\/8\/8\/4kp2\/8 w &#8211; &#8211; 0 90<\/p>\n<p><em>Position after 89. &#8230; Ke2 (analysis). White to move.<\/em><\/p>\n<p>Here, unfortunately, my analysis was totally superficial. I thought, &#8220;Queen against an f-pawn on the seventh rank. Draw.&#8221;<\/p>\n<p>Which it would be, if Black didn&#8217;t have the g- and h-pawns. But he does! And that changes everything. His standard drawing resource in such endgames is to move the king to h1 (if necessary) and set up a stalemate after Qxf2. But because he has other pawns on the board, it won&#8217;t be stalemate here!<\/p>\n<p>This is why it&#8217;s so important in chess not to just memorize formulas like &#8220;queen against an f-pawn on the seventh rank is a draw.&#8221; You&#8217;ve got to think about <em>why<\/em> it&#8217;s a draw.<\/p>\n<p>In fact, it&#8217;s pretty easy to work out that White wins in diagram 2 after <strong>90. Qa2+ Kf3<\/strong> (I&#8217;ll let you work out 90. &#8230; Ke1, but in my opinion Black&#8217;s best defense is to head for g2) <strong>91. Qc4!<\/strong> (Shredder&#8217;s nice move. If Black lets the queen get to f1, White is definitely winning.) <strong>Kg2 92. Qg4+<\/strong>. And here it is. If Black steps in front of the pawn with &#8230; Kf1, White can start moving his king closer. If Black goes to the h-file with <strong>92. &#8230; Kh2 93. Qf3 Kg1 94. Qg3+<\/strong>, we get the classic position where <strong>94. &#8230; Kh1 95. Qxf2<\/strong> would be stalemate. Except here it&#8217;s not, and White wins.<\/p>\n<p>This morning I started wondering how far advanced Black&#8217;s pawns would have to be in order to make the game a draw. That&#8217;s the sort of question the Nalimov tablebase (which gives perfect play for both sides in positions with 6 or fewer pieces) is meant for.<\/p>\n<p>I was quite surprised at the answer. Black&#8217;s pawns don&#8217;t have to be far advanced at all. In fact, if Black&#8217;s pawn were at h5 instead of h7, it would be a draw. (Maybe that&#8217;s not such a big surprise, because at h5 the pawn takes away the key move 92. Qg4+ in the above line.) Or if Black&#8217;s pawn were at g5 instead of g6, it would be a draw. Or &#8212; get this &#8212; if the g-pawn were<em> off the board<\/em> instead of at g6, it would be a draw!<\/p>\n<p>I know you won&#8217;t believe this, so here&#8217;s a sample line to give you the idea.\u00a0 (Obviously I can&#8217;t show you all the variations.) Take the g-pawn off the board in diagram 2. Then after 1. Qa2+ Kf3 2. Qc4 Kg2! 3. Qg4+ Kf1! 4. Kd5 h5!! Black draws. If White takes the pawn it&#8217;s the regular book draw. If 5. Qf3 h4! 6. Ke4 Kg1 7. Qg4+ Kh2 White is reluctantly forced to take the h-pawn: 8. Qxh4+ Kg1, and we&#8217;re back in the book draw. Notice that if Black still had a pawn at g6, it would not be a draw! That&#8217;s why removing Black&#8217;s g-pawn made such a difference.<\/p>\n<p>Pretty amazing stuff. But that&#8217;s not the end of this fascinating endgame!<\/p>\n<p>Because I was determined not to get hoodwinked, I declined the bishop on a7, which meant that I <em>did<\/em> get hoodwinked. The game went on with some mistakes for both sides until we got to this position.<\/p>\n<p><a href=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3172 aligncenter\" alt=\"qb3\" src=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb3.jpg\" width=\"434\" height=\"434\" srcset=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb3.jpg 482w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb3-150x150.jpg 150w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb3-300x300.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/a>FEN: 8\/8\/3b4\/1k6\/8\/6pQ\/5pK1\/8 w &#8211; &#8211; 0 109<\/p>\n<p><em>Position after 108. &#8230; Bd6. White to move.<\/em><\/p>\n<p>You will look in vain for an endgame like this in Reuben Fine&#8217;s <em>Basic Chess Endings<\/em>. At this point I thought it was a dead draw, because I couldn&#8217;t imagine how White could make progress. How can I ever chase the bishop away from the defense of the g3 pawn? How can I possibly use both my king and my queen for a mating attack when one or the other has to constantly watch out for the advance of the g- or f-pawns?<\/p>\n<p>I was surprised to see, though, that the computer rated the position at 2.2 pawns in my favor &#8212; a winning advantage. What the heck, I thought. Let&#8217;s forget about playing the game, and let&#8217;s see why the computer thinks that White can win. The next eight moves were basically Shredder versus Shredder.<\/p>\n<p><strong>109. Qf5+ Kc4 110. Qe6+ Kc5 111. Qe4 Kb6 112. Qd5 Kc7 113. Qb5 Kd8 114. Qb7 Bc7 115. Qc6 Kc8 116. Kf1 &#8230;<\/strong><\/p>\n<p><a href=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3173 aligncenter\" alt=\"qb4\" src=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb4.jpg\" width=\"434\" height=\"434\" srcset=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb4.jpg 482w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb4-150x150.jpg 150w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb4-300x300.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/a>FEN: 2k5\/2b5\/2Q5\/8\/8\/6p1\/5p2\/5K2 b &#8211; &#8211; 0 116<\/p>\n<p><em>Position after 116. Kf1. Black to move.<\/em><\/p>\n<p>First, let me say that I was amazed that the queen by itself could chase the king and bishop to the edge of the board. The Black king and bishop just can&#8217;t help getting in each other&#8217;s way. Over and over we get positions where the king and bishop are on adjacent dark squares. All I have to do is post my queen on the light square which is a knight&#8217;s move from each of them, and one of the two will have to retreat. That happened on moves 111 and 113, and it will happen on the next move, too.<\/p>\n<p>Already I&#8217;ve learned something! I&#8217;ve never studied Q vs. B endings before (who has?) so I simply didn&#8217;t know that the queen can herd the king and bishop in this way.<\/p>\n<p>The position in the diagram is a fundamental <em>zugzwang<\/em> position, where Black can&#8217;t retreat any more. If 116. &#8230; Kd8 then 117. Qe6! wins (putting the queen on the square a knight&#8217;s move away from the bishop and king). After 117. &#8230; Bb8 White has 118. Qg8+! and Black has to block the bishop in order to defend it: 118. &#8230; Kc7 119. Qxg3+ and the win is easy.<\/p>\n<p>Alternatively, if 116. &#8230; Kb8, which the computer played, now 117. Qa6! forces the bishop to depart the b8-h2 diagonal. If 117. &#8230; Bd8 118. Kg2 Bc7 119. Kf3 and the g-pawn must die.<\/p>\n<p>For the sake of completeness, let me mention that this position was no accident. Going over the Nalimov tablebase, it became clear to me that White <em>always<\/em> wins with a Q vs. B+2P if the pawns are blockaded on the color of the bishop. It doesn&#8217;t matter how far advanced they are or what files they are on. This example is completely typical. In fact, it isn&#8217;t even necessary in most cases for White to win the trailing pawn (the g-pawn in this case). Usually, with enough care, White can use both his queen and king on the attack and either checkmate Black or force him to sac a pawn to avoid checkmate. The reason is that if Black ever tries to play &#8230; g2, White will be able to win one or the other of the pawns with a series of checks. White does need to keep an eye on f1, but it really isn&#8217;t that important to keep an eye on g2.<\/p>\n<p>It&#8217;s sort of funny that when I first saw the position after move 108, I saw all these insuperable obstacles. How can White ever chase the bishop away from the b8-h2 diagonal? How can White ever activate his king? It all seemed impossible. Yet in fact, it&#8217;s all possible! Now I&#8217;ve almost come around to the other point of view &#8212; I wonder why these things ever seemed like such huge obstacles to me in the first place.<\/p>\n<p>Now let&#8217;s skip ahead to the end of the game.<\/p>\n<p><a href=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3174 aligncenter\" alt=\"qb5\" src=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb5.jpg\" width=\"434\" height=\"434\" srcset=\"https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb5.jpg 482w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb5-150x150.jpg 150w, https:\/\/danamackenzie.com\/blog\/wp-content\/uploads\/2014\/09\/qb5-300x300.jpg 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/a>FEN: 6k1\/4Q3\/8\/5K2\/3b4\/8\/5p2\/8 w &#8211; &#8211; 0 131<\/p>\n<p><em>Position after 130. &#8230; Kg8. White to play and win.<\/em><\/p>\n<p>Even after I won the g-pawn [with oodles of help from the computer], the win still wasn&#8217;t completely trivial. What is the quickest way to finish Black off here?<\/p>\n<p>The answer, of course, is <strong>131. Kg6!<\/strong> After all this time (54 moves after Black played &#8230; f2, and 43 moves after diagram 1, where he had his first real opportunity to promote the f-pawn), I finally tell him, &#8220;Go ahead and queen your pawn.&#8221; After<strong> 131. &#8230; f1Q 132. Qd8+ Qf8 133. Qd5+ Kh8<\/strong> I don&#8217;t even have to take his bishop &#8212; I can mate in two moves with <strong>134. Qh5+<\/strong>. A neat trick to know about! The computer resigned after 131. Kg6.<\/p>\n<p>P.S. I&#8217;ve now written about a 211-move draw against Shredder and a 131-move &#8220;victory&#8221; (with a massive assist from the computer itself). I&#8217;m starting to think that if a game against the computer doesn&#8217;t last 100 moves, I haven&#8217;t gotten my money&#8217;s worth!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I know that games played against my computer aren&#8217;t the most interesting topic in the world, but recently I had an endgame against Shredder that blew my mind. I learned something new and I think you will, too. Let&#8217;s start on move 88, when the computer played a move that totally shocked me. (Parenthetical remark [&hellip;]<\/p>\n","protected":false},"author":80,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[10,16],"tags":[2989,2988,1706,2991,930,1245,768,2990,1171],"class_list":["post-3168","post","type-post","status-publish","format-standard","hentry","category-endings","category-positions","tag-formulaic","tag-hoodwinked","tag-nalimov","tag-overcoming-obstacles","tag-reuben-fine","tag-shredder","tag-stalemate","tag-superficial","tag-zugzwang"],"_links":{"self":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/3168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/80"}],"replies":[{"embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3168"}],"version-history":[{"count":8,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/3168\/revisions"}],"predecessor-version":[{"id":3183,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/3168\/revisions\/3183"}],"wp:attachment":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3168"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}