Chess, as a game of zero sum and total information is, theoretically, a game that can be solved. The problem is the immensity of the search tree: the total number of positions surpass the number of atoms in our galaxy. -- Diego Rasskin-Gutman, from Chess Metaphors: Articial Intelligence and the Human Mind

More Possibility than Atoms in the Universe

Heat-Map for All Pieces



KEY: The more red a square is, the more frequently a piece OCCUPIES it.

The larger the circle in a square, the more frequently a piece is CAPTURED in it.





Heat-Map for Pawns

Heat-Map for Knights

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The Squares Two Central Knights Cover

Heat-Map of All Moves Putting a King in Check





This is largely because the hard work has already been done by a strong centre, opening the avenues for direct attacks on the opponent's king, the capture of which is the goal of the match. Guardiola and his Barça players understand the importance of playing on their front foot, of making the opponent a reactive entity, and their methodological breaking down of opponents via their play in the centre of midfield is perhaps the best example the game of football has of how classical chess can be applied between the touch-lines.

Real Madrid has the best collection of physically-gifted and versatile attacking players in the game today, complemented by more-than-offensively-capable fullbacks and a host of creative options in midfield. Yet José Mourinho, for all of his extensive tactical brilliance, refused to play a brave game against Barcelona, and when needing a goal, switched to a stillborn back-up plan. Barça has their Monolith in Pep Guardiola, but does Madrid have their Monolith in Mourinho?



Or does the self-anointed Special One need to seek out his own evolution first?

A Bishop's Advantage Over a Knight: Space Covered

Heat-Map for Bishops

The versatility of a bishop also allows it to take up positions inside in either a supporting or capturing capacity, making it a more than capable solution to controlling the game and gaining tempo without encroaching upon d4 and d5 and e4 and e5. This is not an unflattering or untoward surrogate for Ángel di María, or Xabi Alonso's vaunted long-balls out to the wings.





Heat-Map for Rooks





Also able to play from afar is the rook, a piece which, like the bishop, is only limited in movement by where the open space ahead runs out, but has the advantage of moving not diagonally but horizontally and vertically. A rook is a looming specter over any file it resides on, able to advance from the first row to the last or, after castling with the king or with sufficient promotion of the interior pieces, bear down on the centre. Madrid's full-backs, Marcelo, Fabio Coentrão and, at times, Álvaro Arbeloa, surge forward down the touch-line like a rook does down an open file





Heat-Map for Queens





Queens are the most valuable of attacking pieces on a chess board, evidenced by each side not just having only one, but by the relative reluctance to send the piece into the battleground of the centre. Their value comes from combining the movement of a bishop and a rook, leaving a queen free to move as it pleases, and it is this flexibility and ability to adapt to multiple positions which makes it a favourite to initiate or finish off a checkmating-sequence. Where Özil either supplies playmaking in midfield how a rook might -- where the squares advanced are either passes forward or hurrying the ball along -- or plays a role similar to di María's bishop, Cristiano Ronaldo is a true queen, able to play any way or direction at any pace all at once. [Editor's note: That has to be the first time Ronaldo's been called a queen and it hasn't been a homophobic slur, right?]





Hypermodernism, while it allows the centre of the board to be occupied by the opposition's pieces, doesn't truly cede the tempo or control that would normally come with such an allowance. In following with this thought, Mourinho has it wrong against Barça: instead of handing tempo to Guardiola's men on a silver platter by trying to stop Barça's midfielders with a deputized centre-back, Mourinho should look to completely bypass the centre of midfield in an attempt to control the game.





The idea of Barça's defending is to have at least one free man at the back. When in their 3-4-3 -- or various three-man back-line exotics -- against a team with three forwards or three players who end up in forward roles, Sergio Busquets drops deep to form a four-man back-line. When in their 4-3-3, rightback-cum-midfielder-cum-winger Dani Alves simply assumes more defensive responsibilities. What is called for against Barça, to take the game to them, at mininum, is four players who, if not altogether are outright forwards, can play the part of a four-man front-line. Madrid has this in Ronaldo, Gonzalo Higuaín, Karim Benzema and di María. Or, in the event di María is still unfit, Özil.





The next requirement would be a pair in midfield who, beyond defending, can distribute the ball out to the wings, with one of them able to get forward as a sort of advanced pivot to switch flanks in the attacking half and provide a creative influence. Madrid also has this in Xabi Alonso and last season's Bundesliga Player of the Year, Nuri Şahin, who, for reasons unknown, finds himself riding the pine for Mourinho. In defense, tandem full-backs are needed that can make runs forward just as ably as they can defend. Up to the task are Marcelo and Coentrão.





The Hypermodern Madrid

The Drop Into Defense with the Ball Down the Right





With Barça attacking down Madrid's right, Mourinho's tactics would need not be entirely new from the first leg. Notably, Cristiano Ronaldo would still drop deep down the opposite flank, allowing the left-most defenders to move centrally. This would give the most mobile of Madrid's centre-backs, Sergio Ramos, the freedom to act as a sweeper. Opposite Ronaldo, di María would also assume defensive responsibilities, picking up the widest of Barça's players, or going where help is needed, either deeper down the flank or more to the centre. This gives Madrid a four-man back-line, a three-man marking-and-sweeping unit in the centre and a rover down the right to assist where needed. This leaves the direct, cross-the-field switch pass open, but of all the things to leave open against Barça, Madrid could do much, much worse.





Counter-Play





After winning possession, the counter needs to be crisp and fast, taking advantage of the advanced Barça fullbacks or, if Barça plays three at the back, to look for immediate 3-on-3 or better opportunities. Marcelo and Coentrão pushing forward will also free Ronaldo and the rest of the forward line to look to get on the end of crosses, directly challenging Barça's aerial weakness at the back. Of the two pivots, Alonso and Şahin, one will work towards where the ball is won to assist in the advancing down the flank and the other will push forward, demanding the attention of Barça's defense.

A preview of the second leg of Barcelona and Real Madrid'squarter-final clash.If the number of legal chess positions, 10^40, is astronomical to the point of being galaxial, then the number of discrete games, 10^120, is truly all-encompassing, a number greater than that of any estimate of atoms in the universe. In that difficult to even fathom number lies every game ever played on this planet, every game still to be played and an even larger set of games that will never find their way onto a chess board. But even with the vastness of the permutations, all possibilities are bound together by one single nexus: White always moves first.White enjoys quite the advantage doing so: per chessgames.com's summary of over 622,000 games spanning 538 years, White wins a hair over thirty-seven percent of all games played, with Black only winning at a rate just over twenty-seven percent. And since each side starts with their pieces in positions mirrored to those of their opponent, White's advantage comes from having, the ability to initiate. As a result, White's selectedthe series of moves for a side at the game's outset, dictates the course of the game. Such is the case that if Black does not act with consideration to White's opening, any capable opponent will see to either an early superiority or checkmate.After beginning with White, tempo becomes a commodity not bought or sold but gained or lost: gained by achieving the goal or goals of a move or sequence of moves in as short a manner of possible or preventing one's opponent from doing so, lost by needing even one move more than necessary to achieve the wanted end or ends or allowing the opponent the ability to take those extra moves. Example: to begin the game, White wants to move the pawn in front of its queen two spaces to square d4. However, if White only moves the pawn one space instead of the allowed two, making an extra move required, a tempo is lost for White and gained for Black. From here, Black would then be free through its own opening to establish the type of game the match would be: angame characterized by space in the middle of the board for pieces to freely move, or agame characterized by a congested middle making the navigation of pieces from side-to-side and end-to-end a potentially difficult endeavor.A good chess opening bothpieces -- freeing those on the back-line from their immediate constraint - and seeks to control the centre of the board. Seeks to control the centre, because that's where the crux of game resides, where the most positions are occupied, where the most captures are made:This tactical orchestration on a chess board is not entirely dissimilar to the strategy and ethos employed by a manager on a football pitch. Much like how the course of a chess match is determined by the openings used, a football game's style plays out according to the contrasting formations and tactics utilized by opposing managers, creating free-flowing affairs, counter-attacking stand-offs and everything in between.Under Pep Guardiola, Barcelona has furthered their embrace of controlling the centre, fielding more players in the centre of midfield than their opponents and more players capable of playing in the centre of midfield than their opponents . Barça's numbers superiority in the centre ensures theside a dominance of possession over their opponents, a dominance enacted by playing short, concise passes around and through the middle in lieu of hopeful long-balls down the wings to well-marked forwards.Analogous to the short passes favoured by Barça are pawns, the shortest movers of all non-King pieces. Even though they are the least valuable of all pieces on the board, and even though the attack threat of a pawn is virtually non-existent in the game's opening stage, the classical approach to chess calls for pawns and pawn structure to be the chief determinant of centre-dominance, usually exhibited as an ability to control squares d4 and d5 and e4 and e5. In fact, what often keys a novice chess player's progression in the game is an understanding of the great use pawns have in staking claims to the centre, recognizing that they can immediately be deployed to the battlefield or support pawns already there instead of wantonly sacrificed.Also analogous are the two knights each side has in its envoy. Where a pawn can only move two squares forward for its first move and one square forward each move thereafter -- or one diagonal square to attack another piece-- a knight always moves two squares vertically or horizontally before then moving one square horizontally or vertically, opposite of the initial two square movement, so long as the square the knight would land on is not occupied by a piece of its own colour. This ability to move to any of squares creates an almost aura-like area of influence for knights, a fluidity to support more than one piece at a time or, in more advanced positions, seize control of the match:Two adjacent knights can cover an entire quarter of the board, and a side realizing and combining this flexibility with pristine pawn positioning can gift themselves the ability to be proactive by having all the tempo. This is important, because more checks of the opponent's king are made in the centre than anywhere else:Where Barça again looked to overwhelm Real Madrid's midfield in the first leg of theirquarter-final, José Mourinho made a tough ask of his side, changing their favoured tactics to incorporate into his midfield a centre-back in Pepe, the kindest, bravest, warmest, most wonderful human being anyone has ever known in their whole lives . Beyond being a negative move by removing the German playmaker Mesut Özil, the fielding of three defensive midfielders -- of which only one, Xabi Alonso, could create -- meant Mourinho was ceding the game's tempo entirely, hoping to defend in midfield rather than win it, needing his defense to hold and for opportunities to break to present themselves instead of taking the offensive initiative.It "worked", so much as Barça Copa del Rey goalkeeper José Manuel Pinto's blundering of a save can be attributed to Madrid's play, and Mourinho saw hisahead early. But the game was controlled by Barça, with theenjoying scores of possession and creating the greater and more numerous of the chances, having the tempo seemingly secured via multiple padlocks and an eye-recognition security system. Barça went on to score two unanswered second half goals -- the second of which was the direct result of a tactical change Guardiola was free to make -- thereby putting their boots on neck of the quarter-final tie like Pepe did to Lionel Messi's left hand.With Barça dogmatic in their strict adherence to their classical brand of play, Mourinho needs only to look to the evolution of chess for guidance in combating Madrid's arch-rivals.He needs to play agame.It's a much simpler ask of Mourinho than the almost tail-betweeen-the-leg demands he made of his team that's five points clear of Barça atop. Utilizing counter-attacks like Madrid is already wont to do, hypermodernism forgoes the notion that the centre must be occupied first and foremost by pawns, seeking instead to controlthe game from the flanks, defend soundly and to eventually gain tempo.Where pawns and knights have set limitations on the number of squares they can move, a bishop's only limit is where space runs out ahead of it. This, combined with only moving diagonally, makes the bishop the ideal piece to seek centre-control from the flanks.Where a team like Manchester City will play a similar shape and still look to to flood the center with David Silva and Samir Nasri floating inside, Madrid would do well to eschew the the traditional, classical approach and advance the ball down the flanks as directly as possible, with Alonso and Şahin providing outlet balls to the flanks instead of linking up play with a deep-lying playmaker like Özil. Di María, while enjoying great success this season cutting inside, should wait until being overlapped by Coentrão before doing so, thereby keeping Barça's back-line stretched and making his floating inside even more dangerous. This also keeps the crossing option available down the right flank, another green-light for Ronaldo to get into the penalty area.This isn't to say Madrid should forget about defending, or that hypermodernism neglects defending, or that a loose 4-2-4/4-2-2-2 guarantees Madrid more tempo than Barça. Rather, given Madrid needing two away goals and the inability of their 4-2-3-1 to be productive against an in-shape Barça -- remember, Barça came back from the United States preseason tour ragged for theand was training to be fit for January, not September, and even if this isn't accepted, their tactics weren't even the same -- Madrid needs something outside of what they've shown of late against this Barça side, something versatile enough to both weather the storm of Barça's attacks and attack their back-line.The upcoming Clásico comes amid reports José Mourinho has already decided to step down as Real Madrid manager in June, adding another level of intrigue to the sixty-fourth Clásico played since November of 2010. It'd be a shame, however, if this distracted from the real issue of the recent Barcelona-Madrid contests: Mourinho's lack of answers for Guardiola'stactics. Madrid has more than enough talent to play with Barcelona. Their players are frustrated by the negative tactics Mourinho has forced upon them. Willearn his self-anointed nickname?: Steven Kay, for the chess heat-maps