Byzantine Agreement: Why does OM need f+1 rounds in a synchronous setting? To get Byzantine Fault Tolerance in a synchronous model you can use an Oral Message Algorithm. For n &gt; 3f+1 it gets an Byzantine agreement in f+1 rounds. Why f+1?
I will use $m$, not $f$  according the original paper.  It gets an Byzantine agreement in $m+1$ rounds.      

The paper the byzantine generals problem       says:            


  THEOREM 1. For any m, Algorithm OM (m ) satisfies conditions IC1 and IC2
  if there are more than 3m generals and at most m traitors.      


Since it is a recursive algorithm, 
from  $OM(0)$ to $OM(m)$, so it is $m+1$ rounds.