  It is an established fact that entanglement is a resource. Sharing an
entangled state leads to non-local correlations and to violations of Bell
inequalities. Such non-local correlations illustrate the advantage of quantum
resources over classical resources. Here, we study quantitatively Bell
inequalities with $2\times n$ inputs. As found in [N. Gisin et al., Int. J. Q.
Inf. 5, 525 (2007)] quantum mechanical correlations cannot reach the algebraic
bound for such inequalities. In this paper, we uncover the heart of this effect
which we call the {\it fraction of determinism}. We show that any quantum
statistics with two parties and $2 \times n$ inputs exhibits nonzero fraction
of determinism, and we supply a quantitative bound for it. We then apply it to
provide an explicit {\it universal upper bound} for Bell inequalities with
$2\times n$ inputs. As our main mathematical tool we introduce and prove a {\it
reverse triangle inequality}, stating in a quantitative way that if some states
are far away from a given state, then their mixture is also. The inequality is
crucial in deriving the lower bound for the fraction of determinism, but is
also of interest on its own.
