Infinitely More

Infinitely More

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March 2025

Buckets of Fish!
Can you take the last fish from the buckets? Or the last coin in the game of Whim?
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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.
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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…
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Joel David Hamkins
3
The hypergame paradox
A confounding paradox arising in the theory of finite games.
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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…
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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…
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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…
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Joel David Hamkins

January 2025

Chomp
We shall together play a game by chomping on a bar of chocolate, with a game-theoretic surprise, by which one player steals the strategy of another.
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Joel David Hamkins
Twenty one
Let's count together to twenty one, starting from one, with each person adding one, two, or three numbers. Whoever says “twenty-one” wins. Would you…
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Joel David Hamkins
2
Finding Fifteen
Shall we play the game of Finding Fifteen? It is a fun elementary game, which also reveals a subtle game-theoretic concept when looked upon from a…
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Joel David Hamkins
Interpretability of theories
We interpret one theory in another when we can translate all the concepts and structures of the first theory into the language and structural resources…
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Joel David Hamkins
4
© 2025 Joel David Hamkins
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