Games

Some notes on different card games, board games and other miscellaneous stuff.

• Backgammon^N
• Chess^N (common openings, traps and other stuff)
• redacted^? (interesting two player combat card game)
• Wordsworth, a pencil-and-paper game^B (compete to create the most words in a 5x5 grid)

Combinatorial Games

A combinatorial game is a two-player perfect information game with no chance, and are studied extensively in Winning Ways for your Mathematical Plays^N and On Numbers and Games, Conway^N.

• Nim^N
  • On Numbers and Games, Conway^N, Chapter 11
  • Winning Ways for your Mathematical Plays^N, Chapter 2
  • Variations:
    • Prim
      • On Numbers and Games, Conway^N, Chapter 11
      • Variant of Nim
      • Remove from a heap of size $n$ any number prime to $n$
      • $\mathcal G(n)$ is $k$ if the least prime divisor of $n$ i s the $k$th prime.
    • Rims
      • On Numbers and Games, Conway^N, Chapter 11
    • Dim
      • On Numbers and Games, Conway^N, Chapter 11
      • Variant of Nim
      • Remove from a heap of size $n$ any divisor of $n$ not equal to $n$
      • $\mathcal G(n) = k$ if $2^{k-1}$ exactly divised $n$.
    • Poker Nim
      • Winning Ways for your Mathematical Plays^N, Chapter 3
    • Colourful Nim^N
      • Winning colourful Nim with the eeny-meeny rule^B
• Ski Jumps^N
  • Winning Ways for your Mathematical Plays^N, Chapter 1
• Toads-and-Frogs
  • Winning Ways for your Mathematical Plays^N, Chapter 1
• Silver Dollar Game
  • On Numbers and Games, Conway^N, Chapter 11
  • Without the Dollar
  • With the Dollar
• Northcott’s Game
  • On Numbers and Games, Conway^N, Chapter 11
  • Winning Ways for your Mathematical Plays^N, Chapter 3
• Kayles
  • On Numbers and Games, Conway^N, Chapter 11
  • Rayles
• Diminishing Rectangles
  • On Numbers and Games, Conway^N, Chapter 11
• Traffic Jams
  • On Numbers and Games, Conway^N, Chapter 11
• Hackenbush
  • Green Hackenbush
  • Blue-Red Hackenbush
    • Winning Ways for your Mathematical Plays^N, Chapter 1
  • Blue-Red-Green Hackenbush
    • Also known as “Hackenbush Hopscotch”
    • Winning Ways for your Mathematical Plays^N, Chapter 1
  • Childish Blue-Red Hackenbush
    • No edges may fall
• Cutcakes
  • Winning Ways for your Mathematical Plays^N, Chapter 2
• Maundy Cake
  • Winning Ways for your Mathematical Plays^N, Chapter 2
• Col
  • Winning Ways for your Mathematical Plays^N, Chapter 2
• Seating Couples
  • Winning Ways for your Mathematical Plays^N, Chapter 2
• White Knight
  • Winning Ways for your Mathematical Plays^N, Chapter 3
• Wyt Queens
  • Winning Ways for your Mathematical Plays^N, Chapter 3
• Tic-Tac-Toe^N
• “A game on Noetherian rings”