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Tracking Issue: Combinatorial Game Theory #18161

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LeoDog896 opened this issue Oct 24, 2024 · 0 comments
Open
16 tasks

Tracking Issue: Combinatorial Game Theory #18161

LeoDog896 opened this issue Oct 24, 2024 · 0 comments
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t-set-theory Set theory

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@LeoDog896
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LeoDog896 commented Oct 24, 2024 •
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This keeps track of some missing concepts in combinatorial game theory, including mentions in PGame's future work section

  • The theory of dominated, reversible positions, and unique normal form for short games.
  • Analysis of basic domineering positions
  • Board-splitting utilities (for Chomp, Domineering, Nim, Sprouts)
  • Temperature
  • Loopy games
    • Stopper games
  • Impartialness via the equivalence of L/R moves
  • Strategy Stealing Argument (Chomp/Hex as examples)
  • Pairing Strategy for State games (unsure what the typical example is here for normal-play games, but perhaps Tic-Tac-Toe for a positional game?)
  • Non normal-play short games
    • Proof of the fundamental theorem of the trichotomy of the perfect states of combinatorial game theory

Game archive:

  • (discuss) Move domineering to the Archive?
  • Proof of Sim's inability to tie via Ramsey Theory
    • (hard) Proof of Sim winning 2nd player? (This seems to be done by computer search only)
  • Sprouts
    • Proof of winning state for Brussel Sprouts despite suboptimal play
@LeoDog896 LeoDog896 added the t-set-theory Set theory label Oct 24, 2024
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