For Maximum 3-Satisfiability Problem (MAX-3SAT), we discuss about the expected number of unsatisfiable clauses on optimal 
assignment.

We proved two lower bounds theoretically.
One is $\Omega(m / \ln m)$ for $m \ge 5.19 n$ and the other is $m/8 - O(\sqrt{mn})$ for $m \ge 9.7n$ where $n$ is the 
number of variables and $m$ is the number of clauses.

We also compare these theoretical lower bounds with experimental results.