In this note, we study a simulation optimization problem of selecting the alternative with the best performance from a finite set, or a so-called ranking and selection problem, in a special low-confidence scenario. The most popular sampling allocation procedures in ranking and selection do not perform well in this scenario, because they all ignore certain induced correlations that significantly affect the probability of correct selection in this scenario. We propose a gradient-based myopic allocation policy that takes the induced correlations into account, reflecting a tradeoff between the induced correlation and the two factors (mean-variance) found in the optimal computing budget allocation formula. Numerical experiments substantiate the efficiency of the new procedure in the low-confidence scenario.