2^{-\binom{h}{2}}$ for $x \in [0,1] \setminus \{\frac {1}{2}\}$.

Note that if $H$ is not locally forcing then there is a tournament $T$ which is not quasirandom but has the same local counts of $H$ as the random tournament $\mathcal{T}(n,1/2).$ We will see that not being [$\mathcal{T}_{cliq}$-forcing]{} implies that there exists an $\alpha \neq 1/2$ such that $\mathcal{T}(n,\alpha)$ has the same local counts of $H$ as the random tournament $\mathcal{T}(n,1/2)$. Indeed, in the next theorem we prove that any locally forcing tournament must be [$\mathcal{T}_{cliq}$-forcing]{}, which will allow us to pass any restrictions imposed on the tournament by being [$\mathcal{T}_{cliq}$-forcing]{} to locally forcing tournaments and in particular prove Theorem \[thm: locally-forcing\].

\[thm: locally-forcing-is-simple\] Every locally forcing tournament is [$\mathcal{T}_{cliq}$-forcing]{}.

Suppose that $H$ is not [$\mathcal{T}_{cliq}$-forcing]{}. Then by definition ${p_H}(\alpha ) = 2^{-\binom {h}{2}}$ for some $\alpha \in [0,1] \setminus \{1/2\}$. As $p_H(x)$ is symmetric about $1/2$ by Lemma \[lemma: properties of counting poly\] *(iii)* we can assume $\alpha > 1/2$. Now select $T \sim {\cal T}(n,\alpha )$. For a set $U \subset V(T)$ let $X_U$ denote the random variable $X_U(T) = N^*_{T}(H;U)$. Noting that for $T \sim {\cal T}(n,\alpha )$ we have $T[U] \sim {\cal T}(|U|,\alpha )$, by Lemma \[lemma: properties 