Combinatorial Game Theory
who wins, and by how much
Ladder

Outcomes — 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. 0outcome P= 0whoever must move, loses10outcome L> 0Left wins, whoever starts-10outcome R< 0Right wins, whoever starts∗00outcome N‖ 0whoever moves first, winsblue edges are Left's moves, red are Right'sthree of the four are comparisons with zero; the fourth is not

    Who moves last

    The player who cannot move loses. That single convention generates the whole theory — and it produces four outcomes rather than three, because a position can be confused with zero rather than greater, smaller or equal to it.

    rung 1 · values

All ladders