An outline of a short talk that I have in Vienna on 20. July 2022.

  • Combinatorial games – we have full information, deterministic
  • How to play chess, game tree, heuristic to count winning chance, minmax
  • Basics of game theory
    • domineering – L has vertical moves, R has horizontal moves
    • winning states L, R, N, and P; first vs second player
    • examples of plays
      • L-shape je N
      • I-shape je L
      • I-hor. I je R
      • square je N
      • 2x square P
      • square and L-shape N
      • bigger L P
  • impartial vs partizan games
  • impartial: standardni triky
    • Chocolate – parity
    • Placing dominos without restrictions – symetrie
    • Chomp – strategy stealing
    • Changing snake – matching strategy
  • building a theory
    • lost game = 0
    • one move for L is 1, for R is 1
    • {|} = 0, creating numbers
    • birthday – step when created
    • sum of games
      • 0 does not change it
      • other than that, we can only say L+L=L, R+R=R, L+N=LuN, R+N=RuN
    • numbers
      • we have -1,0,1
      • N={N-1|} a -N={|1-N}
  • impartial
    • nimbers and mex
    • nim
    • winning strategy for nim
    • nim in misere variant