We consider a Maker-Breaker type game on the square grid, in which each player takes $t$ points on their $t^\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show that, despite Maker's apparent advantage, Breaker can prevent Maker from winning until about his $n^\textrm{th}$ turn. We actually prove a stronger result: Breaker only needs to claim $\omega(\log t)$ points on his $t^\textrm{th}$ turn to prevent Maker from winning until this time. We also consider the situation when the number of points claimed by Maker grows at other speeds, in particular, when Maker claims $t^\alpha$ points on his $t^\textrm{th}$ turn.
@article{10_37236_4961,
author = {Joshua Erde and Mark Walters},
title = {An \(n\)-in-a-row type game},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {3},
doi = {10.37236/4961},
zbl = {1344.05095},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4961/}
}
TY - JOUR
AU - Joshua Erde
AU - Mark Walters
TI - An \(n\)-in-a-row type game
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/4961/
DO - 10.37236/4961
ID - 10_37236_4961
ER -
%0 Journal Article
%A Joshua Erde
%A Mark Walters
%T An \(n\)-in-a-row type game
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/4961/
%R 10.37236/4961
%F 10_37236_4961
Joshua Erde; Mark Walters. An \(n\)-in-a-row type game. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/4961
