1
$\begingroup$

What is the name of the following combinatorial game:

Two players, moving in turn.

Positions: $0,1,2,\ldots$.

Moves: $n\longmapsto n-1$ or $n\longmapsto \lfloor n/2\rfloor$ if $n>0$.

No move for $0$ which loses.

The determination of the winning strategy is easy: $n=2^k(2m+1)>0$ wins if and only if $k$ is even.

Determinating the winning strategy for the misere convention ($0$ wins) is also easy:

$2^k$ wins for $k$ odd and loses for $k$ even,

$2^k(2m+1)$ with $m\geq 1$ wins for $k$ even and loses for $k$ odd.

This game has certainly been described somewhere. Does it has a name? Does somebody have a reference?

$\endgroup$

1 Answer 1

3
$\begingroup$

This is "Mark", supposedly due to Mark Krusemeyer; see the first sentence of the introduction to https://arxiv.org/abs/1509.04199 and section 2 of https://doi.org/10.37236/2015.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.