Hefetz, Krivelevich and Tan's asymptotic Client-Waiter odd cycle game conjecture

Let $\mathcal{OC}_n$ denote the family of odd cycles on the board of the Client-Waiter game, and let $b_{cw}(\mathcal{OC}_n)$ be its threshold bias. Hefetz, Krivelevich and Tan's conjecture.

$$b_{cw}(\mathcal{OC}_n) = \big( 1/2 - o(1) \big) \,n.$$

The previously known bounds are $\big(1/(4\log 2)-o(1)\big)n\leq b_{cw}(\mathcal{OC}_n)\leq\lceil n/2\rceil-1$; the conjecture asserts that the upper bound is asymptotically tight.