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In the Oriented-cycle game, introduced by Bollob\'as and Szab\'o, twoplayers, called OMaker and OBreaker, alternately direct edges of $K_n$. OMakerdirects exactly one edge, whereas OBreaker is allowed to direct between one and$b$ edges. OMaker wins if the final tournament contains a directed cycle,otherwise OBreaker wins. Bollob\'as and Szab\'o conjectured that for a bias aslarge as $n-3$ OMaker has a winning strategy if OBreaker must take exactly $b$edges in each round. It was shown recently by Ben-Eliezer, Krivelevich andSudakov, that OMaker has a winning strategy for this game whenever $b\leq\frac{n}{2}-2$. In this paper, we show that OBreaker has a winning strategywhenever $b\geq \frac{5n}{6}+2$. Moreover, in case OBreaker is required todirect exactly $b$ edges in each move, we show that OBreaker wins for $b\geq\frac{19n}{20}$, provided that $n$ is large enough. This refutes the conjectureby Bollob\'as and Szab\'o.

A non-trivial upper bound on the threshold bias of the Oriented-cycle game