Reference

Strategy

The strategy skills, track by track

• Act with more informationStrategy idea, intermediate

  Deciding after the other side has shown its hand is an advantage when their move tells you something you lack. When you already know the value, moving first can be the edge.

• Ask what the rule rewardsStrategy idea, intermediate

  A rule or target changes what everyone does. Before you set one, ask what is the cheapest way to score on it, because that is what you will get.

• Be unpredictableStrategy idea, intermediate

  If the other side can predict you, they can exploit you. Sometimes the best plan is to vary.

• Cooperate or defendStrategy idea, intermediate

  When you will meet again, cooperation and reputation pay. In a one-off, protect yourself in the terms, but remember that few deals are truly one-off.

• Count it throughStrategy idea, beginner

  Follow a sequence of moves to its end before you start it, counting what each side wins.

• Don't overpay to winStrategy idea, intermediate

  When many people bid on something uncertain, the winner is often the one who overestimated it.

• Estimate alone, then poolStrategy idea, intermediate

  In a group, have everyone make their estimate on their own before anyone hears another. Averaged, independent guesses cancel each other’s errors; guesses that follow the first voice do not.

• Fix your weakest linkStrategy idea, intermediate

  When there is nothing urgent, improve the part of your position that is doing least.

• Judge decisions, not resultsStrategy idea, beginner

  A good decision can turn out badly, and a bad one can get lucky. Judge by what you knew, and what you could reasonably have found out, when you decided.

• Keep a cool headStrategy idea, beginner

  Decide as well after a setback as before it.

• Know your walk-away pointStrategy idea, intermediate

  Before you bargain, know what you will do if there is no deal. That sets the least you should accept, and any deal lies between your walk-away point and theirs.

• Lead or answer wellStrategy idea, intermediate

  Either set the agenda with threats, or answer the other side precisely. Drifting between the two loses.

• Patterns save thinkingStrategy idea, beginner

  Learn common patterns so you recognise them at a glance instead of working them out each time.

• ProphylaxisStrategy idea, advanced

  Stop the other side's best plan before it starts, often with a quiet move.

• Regression to the meanStrategy idea, intermediate

  When a result is part skill and part luck, an extreme result is usually followed by a more ordinary one, whatever you do.

• Say it both waysStrategy idea, intermediate

  The same choice, put as what you keep or as what you lose, gets different answers. Restate it the other way before you decide.

• Shrink the problemStrategy idea, intermediate

  When there are too many options, cut them to a few good candidates, then compare those properly.

• Simplify when aheadStrategy idea, intermediate

  When you are ahead, reduce the risk: trade pieces and head for a position where your advantage is easy to use.

• Start from the base rateStrategy idea, intermediate

  Before judging one case, ask how often cases like it turn out each way. Start from that, then adjust for what this case shows.

• Sunk costStrategy idea, beginner

  What you have already spent is gone. Decide on what happens next, not on what you put in.

• Test to disproveStrategy idea, beginner

  To find out whether you are right, include tests that would prove you wrong, not only ones that would confirm you.

• The blunder checkStrategy idea, beginner

  Before you act, ask what your move allows the other side to do.

• Their next moveStrategy idea, beginner

  After every move by the other side, ask what it wants to do next.

• Trade-offsStrategy idea, intermediate

  Material, time and position can be exchanged for one another. Give one up only for more of another.

• The blunder checkStrategy lesson

  Before you act, ask what could go wrong, and look at what the other side can do first.

• Their next moveStrategy lesson

  Think through how the other side will respond, as they see it, not as you hope.

• Count it throughStrategy lesson

  Follow a chain of consequences to the end before you agree to the first step.

• Small steps that stickStrategy lesson

  Each step should leave fewer ways for things to go wrong, and the last step needs as much care as the first.

• Patterns save thinkingStrategy lesson

  Learn the common shapes by heart, so the obvious answers come at once and your thinking goes where it is needed.

• Basics before brillianceStrategy lesson

  Get the plain, sound steps right first. Clever ideas pay on top of them, not instead of them.

• Lead or answer wellStrategy lesson

  Move first when your move commits you or anchors the other side; answer when their move tells you something. When you answer, choose on purpose, to level things or to change their shape.

• When the script runs outStrategy lesson

  Prepared plans run out. When they do, act on the reasons behind them.

• Two birds, one stoneStrategy lesson

  Look for the one move that serves two aims, so the other side cannot answer both.

• Find what everything depends onStrategy lesson

  Find the one part that holds everything else up. Strike it if it is theirs; back it up if it is yours.

• Not so fastStrategy lesson

  Before you push on with your plan, ask what the other side wants, and stop it before it starts.

• Fix your weakest linkStrategy lesson

  When nothing is urgent and the parts depend on each other, improve the part doing least.

• Simplify when aheadStrategy lesson

  When you are ahead and a sure win is what you need, remove the moving parts that could still go wrong.

• Give a little, get moreStrategy lesson

  Give up one thing only for more of another, and count both in the same units.

• A plan, step by stepStrategy lesson

  Turn a goal into a route of small steps, each worth having on its own, and look again after each one.

• Resources change valueStrategy lesson

  What a thing is worth depends on the situation. When the situation changes, value what you hold again.

• Pass the problem backStrategy lesson

  Some positions are bad for whoever must move next. When you can, make the move that leaves the hard choice with the other side.

• Look at three before choosingStrategy lesson

  Before you choose, name at least three options, including one you had not first thought of, and compare them.

• Spend effort where it mattersStrategy lesson

  Time and attention are limited. Decide small choices you can undo quickly, and spend your effort on the few that are large and final.

• Finish the jobStrategy lesson

  A winning position is not a win until it is finished. The last steps need as much care as the first.

• Make it hardStrategy lesson

  When you are behind, do not give in early. Find the defence that leaves the other side the most to get right.

• Review calmly: decisions, not resultsStrategy lesson

  Judge a choice by what you knew, and could have found out, when you made it, not only by how it turned out.

Chess

All chess lessons, in order

• Back-rank mateTactic, beginner

  A rook or queen mates a king trapped on its back rank by its own pawns.

• Caro-Kann DefenceOpening, beginner

  Black prepares ...d5 while keeping the light-squared bishop free: solid and reliable.

• CastlingRule, beginner

  The king moves two squares towards a rook, and the rook jumps over to the other side, in one move.

• Check and checkmateRule, beginner

  A king under attack is in check; if it cannot escape, it is checkmate and the game is over.

• Chess notationRule, beginner

  The short way to write moves: a piece letter, then the square it goes to.

• DevelopmentConcept, beginner

  Bringing pieces from their starting squares into play, usually knights and bishops first.

• Discovered attackTactic, intermediate

  Moving one piece uncovers an attack by another piece behind it.

• Double checkTactic, intermediate

  Two pieces give check at once, so the king must move: nothing can block or capture both.

• Draws by ruleRule, beginner

  Besides stalemate, a game is drawn by repetition, the fifty-move rule, agreement, or a position where no one can ever mate.

• Dutch DefenceOpening, intermediate

  Black grabs e4 with the f-pawn, aiming for kingside play at some cost to king safety.

• En passantRule, beginner

  A pawn that moves two squares can be captured by an enemy pawn standing beside it, as if it had moved one square, but only on the very next move.

• English OpeningOpening, intermediate

  White controls d5 from the side and keeps the choice of structure open.

• FianchettoConcept, intermediate

  Developing a bishop on the long diagonal, from b2, g2, b7 or g7, after moving the knight's pawn.

• ForkTactic, beginner

  One piece attacks two or more at once, so only one can be saved.

• French DefenceOpening, beginner

  Black prepares ...d5 to challenge the centre, accepting a cramped but solid position.

• GambitConcept, intermediate

  An opening that gives up material, usually a pawn, for time, development or attack.

• Grünfeld DefenceOpening, advanced

  Black invites White to take the centre with pawns, then attacks it with pieces.

• Hanging pieceConcept, beginner

  A piece that can be taken for free: nothing defends it, or it is attacked more times than it is defended.

• Isolated pawnConcept, intermediate

  A pawn with no pawns of its own side on the files next to it, so no pawn can defend it.

• Italian GameOpening, beginner

  White develops quickly and aims the bishop at f7, Black's weakest point at the start.

• King safetyConcept, beginner

  Keep the king sheltered, usually by castling, until the endgame.

• King's GambitOpening, intermediate

  White offers a pawn on move two for quick development and an attack on the f-file.

• King's Indian DefenceOpening, advanced

  Black gives White the centre, castles quickly, then attacks it and the kingside.

• London SystemOpening, beginner

  White sets up the same solid structure against almost anything: d4, Bf4, e3, Nf3, c3.

• Lucena positionEndgame, advanced

  The key winning position in rook endings: rook, king and pawn on the seventh against a rook, with the defending king cut off.

• LuftConcept, beginner

  A pawn move that gives a castled king an escape square, guarding against back-rank mates.

• Nimzo-Indian DefenceOpening, advanced

  Black pins the knight on c3 and is ready to give the bishop for it to damage White's pawns.

• Open fileConcept, intermediate

  A file with no pawns on it, the natural road for rooks into the enemy position.

• Opening familiesConcept, beginner

  Openings are grouped by their first moves, because the first pawn moves decide the kind of game.

• OppositionEndgame, intermediate

  Kings facing each other with one square between; the side not to move holds the opposition.

• OutpostConcept, intermediate

  A square in enemy territory that no enemy pawn can attack, ideal for a knight.

• OverloadingTactic, intermediate

  One piece has to defend two things at once, and cannot.

• Passed pawnConcept, beginner

  A pawn with no enemy pawn in front of it, on its own file or on either file next to it, so only pieces can stop it.

• Pawn structureConcept, intermediate

  The arrangement of the pawns, which changes slowly and decides the plans for both sides.

• Philidor positionEndgame, advanced

  The key drawing method in rook endings: with your king on or in front of the queening square, keep the rook on the third rank until the pawn advances.

• Piece valuesConcept, beginner

  A rough guide to what pieces are worth: pawn 1, knight 3, bishop 3, rook 5, queen 9.

• PinTactic, beginner

  A piece cannot move without exposing a more valuable piece behind it.

• Pirc DefenceOpening, intermediate

  Black lets White build a big centre, then attacks it from the flanks.

• PromotionRule, beginner

  A pawn that reaches the last rank becomes a queen, rook, bishop or knight.

• Queen's GambitOpening, beginner

  White offers the c-pawn to pull Black's d-pawn away from the centre.

• Queen's Indian DefenceOpening, advanced

  Black fianchettoes the queen's bishop to control e4 from a distance.

• Removing the defenderTactic, intermediate

  Capture, chase or lure away the piece that guards something, then take what it guarded.

• Réti OpeningOpening, intermediate

  White develops first and attacks the centre from the side with c4.

• Ruy LopezOpening, intermediate

  White attacks the knight that defends e5, building slow, lasting pressure.

• Scandinavian DefenceOpening, beginner

  Black hits the e4 pawn at once; after the exchange the queen comes out early.

• Scotch GameOpening, intermediate

  White strikes at once with d4, trading its d-pawn for Black's e-pawn to open the centre and gain space.

• Sicilian DefenceOpening, intermediate

  Black fights for the centre from the side and unbalances the game to play for a win.

• SkewerTactic, beginner

  A valuable piece is attacked and must move, exposing a piece behind it.

• Slav DefenceOpening, intermediate

  Black supports d5 with the c-pawn and keeps the light-squared bishop free.

• Smothered mateTactic, intermediate

  A knight mates a king that is boxed in by its own pieces.

• Square of the pawnEndgame, beginner

  A quick test of whether a king can catch a passed pawn, without counting moves.

• StalemateRule, beginner

  The side to move has no legal move and is not in check. The game is a draw.

• TempoConcept, intermediate

  A unit of time: one move. Gaining a tempo means making progress while forcing the other side to respond.

• The centreConcept, beginner

  The four middle squares, d4, e4, d5 and e5, from which pieces reach the most of the board.

• TriangulationEndgame, advanced

  Losing a move with the king, by walking a triangle, to hand the other side the move.

• ZugzwangEndgame, intermediate

  Any move makes your position worse, but you must move.

• ZwischenzugTactic, intermediate

  Instead of the expected reply, an in-between move with a bigger threat comes first.

• Name the squaresLesson, stage 0

  Every square has a name, file letter first, then rank number. Learn them, then find squares without looking at the edges.

• Set up the boardLesson, stage 0

  Two memory tricks so the board is never the wrong way round, and your first move.

• Rook and bishopLesson, stage 0

  The two line pieces. The rook goes straight, the bishop goes diagonally, and neither can jump.

• The queen and the kingLesson, stage 0

  The queen is a rook and a bishop in one. The king moves one square, and never into danger.

• The knightLesson, stage 0

  The knight moves in an L and jumps over anything in its way.

• The pawnLesson, stage 0

  Pawns move straight forward but capture diagonally, and never go back.

• Piece values and good tradesLesson, stage 0

  Pawn 1, knight 3, bishop 3, rook 5, queen 9. A trade is good if you get more than you give.

• Check and getting out of itLesson, stage 0

  When your king is attacked you must get out of check at once. There are three ways.

• Checkmate, stalemate and other drawsLesson, stage 0

  How games are won, and the draws that catch beginners out.

• CastlingLesson, stage 0

  Tuck the king away and bring a rook to the centre in one move, when the rules allow it.

• Promotion and en passantLesson, stage 0

  The two special pawn moves, becoming a queen and the capture in passing.

• How moves are writtenLesson, stage 0

  Read and write chess moves, so you can follow any book, video or game record.

• Take what is hangingLesson, stage 1

  Spot pieces you can win for nothing, and the habit that stops you giving yours away.

• Checks, captures and threatsLesson, stage 1

  The blunder check, for both sides, before every move.

• Is this move safe?Lesson, stage 1

  Before you let go of a piece, check that they cannot win something or mate you straight after.

• Back-rank mateLesson, stage 2

  A king hemmed in by its own pawns, mated along the back rank, and how to stop it.

• Mate with king and queenLesson, stage 2

  Box the lone king in, drive it to the edge, then mate. Without stalemating it.

• Mate with king and rookLesson, stage 2

  Cut the king off with the rook, walk your king up, and mate on the edge.

• The three phases of a gameLesson, stage 3

  Opening, middlegame and endgame, what each is for, and how to tell which one you are in.

• A map of the openingsLesson, stage 3

  Openings fall into five families by their first moves, because the first moves decide what kind of game it will be.

• Play a real gameLesson, stage 3

  The rules and manners you need for a full game over the board or online.

• The forkLesson, stage 4

  Attack two pieces with one move, so only one of them can be saved.

• The pinLesson, stage 4

  Freeze a piece in front of a more valuable one, then attack it.

• The skewerLesson, stage 4

  Attack a valuable piece so that it must move and expose the piece behind it.

• The discovered attackLesson, stage 4

  Move one piece out of the way, and the piece behind it attacks.

• What the middlegame is aboutLesson, stage 5

  Once the pieces are out, the question becomes "what is my plan?", and the pawns help answer it.

• What changes in the endgameLesson, stage 6

  With few pieces left, the king becomes a fighter and passed pawns decide.

• Coordinates: find the squarePractice drill

  Thirty seconds: find as many squares as you can, with no letters or numbers on the board.

• Coordinates: name the squarePractice drill

  The reverse: a square lights up, and you type its name. Thirty seconds.

• Pieces: where can it go?Practice drill

  A piece on a random square. Tap every square it can move to, then the next one. Five positions.

• Safety: is this move safe?Practice drill

  Before every move, ask: can they win something, or mate me, straight after it? Judge ten moves.

• Safety: spot the loose piecePractice drill

  Loose pieces drop off: a piece nothing defends is the first target for a fork. Tap every one, on both sides. Five positions.

• Basic mates against the clockPractice drill

  Mate the lone king from a random start. Your score is the moves you have left over.

Poker

• BluffConcept, intermediate

  Betting with a weak hand to make a stronger hand give up.

• EquityOdds and maths, intermediate

  Your share of the pot on average: the chance your hand ends up best (a tie counts as half), given the cards still to come.

• Expected valueOdds and maths, intermediate

  What a decision is worth on average, weighing each outcome by how likely it is.

• Hand rankingsRule, beginner

  From best to worst: straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, one pair, high card.

• Implied oddsOdds and maths, advanced

  Pot odds plus what you expect to win in later rounds if you hit your hand.

• OutsOdds and maths, beginner

  The unseen cards that would improve your hand to the one you want.

• PositionConcept, beginner

  Where you sit relative to the dealer, which decides whether you act before or after the others in each round.

• Pot oddsOdds and maths, beginner

  The price of a call compared with what is in the pot, which tells you how often you need to win to make the call worth it.

• RangeConcept, intermediate

  All the hands another player could have, given what they have done so far.

• TiltConcept, beginner

  Playing worse because of frustration, often after a bad loss.

Game theory

• Backward inductionConcept, beginner

  Solve the last decision first, then the one before it, until you reach the move you have to make now.

• Mixed strategyConcept, intermediate

  Choosing between options with set probabilities, so the other side cannot predict and exploit you.

• Nash equilibriumConcept, intermediate

  A set of choices where no player can do better by changing only their own.

• Prisoner's DilemmaConcept, beginner

  Two players each do better by betraying, yet both do better together if both cooperate.

• Tit for tatConcept, beginner

  Cooperate first, then copy what the other player did last time.

• Winner's curseConcept, intermediate

  In an auction for something of uncertain value, the winner tends to be the one who overestimated it most.

• Zero-sum gameConcept, beginner

  A game where one player's gain is exactly the other's loss, like chess.