Combinatorial Game Theory
who wins, and by how much
Ladder

Sprague grundy — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. a heap of 10, taking 1, 3, 4options lead to heaps of 9, 7, 6whose values are 0, 0, 2mex of those is 1plays exactly likea Nim heap of 1= ∗the value is the heap size — nothing else about the position survives

    Every impartial game is a Nim heap

    Sprague and Grundy proved, independently and four years apart, that any position in any impartial game is equivalent to a single heap of counters. Not similar to one — equal to one, interchangeable with it inside any larger game.

    rung 1 · impartial

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