The Maker-Breaker percolation game on a random board

Vojtěch Dvořák, Adva Mond, Victor Souza

The $(m,b)$ Maker-Breaker percolation game on $({\mathbb{Z}}^2{)}_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{…