Commit 91281615 authored by Fabian Nuraddin Alexander Gabel's avatar Fabian Nuraddin Alexander Gabel 💬
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with high probability. This strong connection between deterministic games and random graphs/strategies, usually referred to as *probabilistic intuition*, has been verified for a plethora of games since then.
<img src="img/tournament.jpg" width="300">
Related to his result, Beck also considered the *tournament game* in which the winning sets are so-called tournaments (i.e. complete graphs with orientations on their edges) and in which Maker must give orientations to the edges that she claims. His aim was to find the largest integer $k=k(n)$ such that Maker can occupy a copy of any pre-defined tournament $\mathcal{T}_k$ on $k$ vertices, and, due to an application of the probabilistic intuition, he conjectured this value to be $k=(1-o(1))\log_2 n$. In [CGL2016] we however disproved the conjecture, and showed instead that $k=(2-o(1))\log_2 n$, which in turn shows that the additional constraint of adding orientations does not make the game much harder for Maker.
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