Drawing strategies in Strong Ramsey games for 3-uniform hypergraphs

The Strong Ramsey game $\mathcal{R}(B,G)$ is a two player game with players $P_1$ and $P_2$, where $B$ and $G$ are $k$-uniform hypergraphs for some $k\ge 2$. $G$ is always finite, while $B$ may be infinite. $P_1$ and $P_2$ alternately color uncolored edges $e\in B$ in their respective color and $P_1$ begins. Whoever completes a monochromatic copy of $G$ in their own color first, wins the game. If no one claims a monochromatic copy of $G$ in a finite number of moves, the game is declared a draw. In this paper, we give an infinite set of 3-uniform hypergraphs $\{G_t{\}}_{t\ge 3}$, such that $P_2$ has a drawing strategy in the Strong Ramsey game $\mathcal{R}(K_{{\mathrm{\aleph }}_0}^{(3)},G_t)$. This improves a result by David, Hartarsky and Tiba.