© 2017 Wiley Periodicals, Inc. Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within (Figure presented.) of optimal. Our construction provides a direct and natural way for proving the (Figure presented.) -optimality gap. An earlier proof of the same result made crucial use of a key inequality of Bruss and Delbaen  and of de-Poissonization.