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10 votes
2 answers
328 views

For which number of pairs is it an advantage to start in memory

Players A and B play memory starting with $n$ pairs of cards. We assume that they can remember all cards which have been turned. At his turn a player will first recall if two cards already turned ...
Markus Sprecher's user avatar
4 votes
2 answers
426 views

Study of Hex on the Torus

Hex is usually played on a parallelogram shaped board. What if you play it on a Torus? One thing I notice is that the idea of connecting opposite sides doesn't make much sense anymore, since a torus ...
Christopher King's user avatar
7 votes
2 answers
671 views

Determinacy of (infinite, possibly loopy) combinatorial games

I am looking for references and hopefully enlightening proofs of the following statement(s) concerning the determinacy of not-necessarily-well-founded (i.e., possibly infinite, possibly loopy) ...
Gro-Tsen's user avatar
  • 32.5k
3 votes
1 answer
337 views

Minimal Birthdays

In combinatorial game theory: The birthday of a game is defined recursively as 1 plus the maximal birthday of its options, with the zero game having birthday 0. Suppose we define the quasi-birthday ...
Halbort's user avatar
  • 1,129
5 votes
0 answers
306 views

Generalization of Sprague-Grundy Theorem

In my research on Combinatorial Game Theory, I used a certain theorem that is essentially a generalization of the Sprague-Grundy theorem. Because the result hinges too much on the work of others to be ...
Halbort's user avatar
  • 1,129