Themes
Who moves last
The player unable to move loses. That single convention generates the whole theory, and reversing it — misère play — destroys almost all of it.
One clause decides it
Change a word of the rule and the values change completely. A cliff or a wall, a jump allowed or forbidden, a pass that may or may not end the game — the same board, and nothing in common.
The sum is the object
Real positions break into independent parts that are played at once, and adding them up is what the theory was built to do. The hard step is the splitting, not the addition.
The parts do not decide the whole
Outcomes do not add. Neither do temperatures, atomic weights, misère outcomes or the value of an auction. Which quantities survive being added is the question every method here turns on.
Not every game is a number
Some positions are worth a half or a quarter. Others are worth something no number can express, and the ones that are not numbers are where the subject becomes interesting.
How much is at stake
A position is worth something on average and worth something more to move in first, and the second number is the one a player feels. Temperature is that number, and most of what it measures is not where it is expected.
Small things decide
Infinitesimals are smaller than every positive number and are not zero. In a close game they are the whole margin, which is why the theory bothers with them.
Equal, better, or neither
Two positions can be equal, one can be better, or the pair can be genuinely incomparable — a fourth relation with its own symbol. Deciding which is a search rather than a look, and equality quantifies over every game there is.
The notation is not the position
A brace form, a binary numeral, an octal code and a thermograph are four ways of writing a position down, and each throws something away. Occasionally one of them turns out to be the argument.
A theorem that names no move
Knowing who wins and knowing what to play are different achievements, and the subject is full of results that supply the first and refuse the second. A bound is sometimes all there is.
It depends on the company
Sente, independence, equality, the size of a move and even the winner turn out to be facts about the rest of the board rather than about the position in front of the reader.
It has to end
Every value here is defined by a recursion that needs play to stop. Sometimes that is obvious, sometimes it is a theorem, and sometimes the game ends with nothing bounding when.
The theory runs out
Misère play, scoring, three players and computational hardness each break something essential. Knowing which of them is biting is most of knowing where a game stands.
Play it and lose
The strongest argument this subject can make is to state the winner before the reader starts, and then be right. These are the essays carrying a figure that plays back.
Assertions that reject
Every claim here is given a test it could fail, and the tests that matter are the ones that have failed. These are the essays where a check refused something — a guess, a rival explanation, or the essay's own first draft.
What a search costs
A value is worth what it costs to find. These essays price the search rather than quoting the answer: positions visited, states stored, and the size of the board where the counting stops.