Infinitely More

Infinitely More

Home
The Book of Infinity
A Panorama of Logic
Infinite Games
Proof and the Art
Philosophy of Mathematics
My books
Music videos
Archive
Leaderboard
About

March 2025

Buckets of Fish!
Can you take the last fish from the buckets? Or the last coin in the game of Whim?
 • 
Joel David Hamkins
2
The fundamental theorem of finite games
In every finite two-player game of perfect information, either one player has a winning strategy or both players have drawing strategies.
 • 
Joel David Hamkins
2
The penny partition paradox
The penny partition paradox, a perplexing parable of profit—the penny players parlay perfectly precise provable principles to a peculiarly puzzling…
 • 
Joel David Hamkins
3
The hypergame paradox
A confounding paradox arising in the theory of finite games.
 • 
Joel David Hamkins
2

February 2025

Tic tac toe and variants
We consider various game-theoretic aspects of several variations of the school-child game of tic-tac-toe, including 4 × 4 tic-tac-toe, recursive…
 • 
Joel David Hamkins
2
The Gold Coin game
Let us play the Gold Coin game―with proper play, you can become rich! We shall make some strategic insights, but eventually we shall realize the game is…
 • 
Joel David Hamkins
4
The game of Nim
We shall study the classic game of Nim, learning the secret mathematical strategy that will enable you to win against those who don’t yet know the…
 • 
Joel David Hamkins

January 2025

© 2025 Joel David Hamkins
Privacy ∙ Terms ∙ Collection notice
Start writingGet the app
Substack is the home for great culture