Adversarial Indistinguishability
An adversary can easily win this game with $\epsilon = 0.5$ when the scheme under examination is any block cipher in ECB mode.

Simply set $m_0$ and $m_1$ to the same block value, $q$. This guarantees that you'll get the encryption of $q$ back, which we'll call $r$.

Then you can distinguish between $q$ and some other block value with probability $1$ on subsequent trial by checking whether $r$ is returned or not.