If
, then you'd have
on the right hand side. Any value of
that makes the exponential denominator smaller than the numerator of 2 would make the whole expression bigger than 2, which is meaningless for a probabilistic bound. The case in point, any epsilon smaller than 0.83 makes this upper hoeffding bound useless. Of course, 0.83 is an useless value for epsilon because you want to be able to make epsilon as close to 0 as you want.