The art of a right decesion

The solution of the problem of maximizing the probability of
stopping on a last success in a sequence of independent indicators
has many real-world applications, ranging from best choice
problems (secretary problems) over buying-selling strategies up to
applications in sequential search and clinical trials. If the odds are
known in advance, the odds-algorithm provides this solution in a
straightforward way, and this algorithm is, itself, optimal. If the
odds are unknown, and must be estimated from preceeding
observations, then the optimal rule is not obvious and can be made
explicit in special cases only. The objective of this work was to
examine the question wether there are good approximations for the
optimal rule. We have proposed an algorithm which is based on
the odds-algorithm and on a simple unbiased sequential estimator
of the successes probabilities pk = P(Ik = 1). Although we have no
precise estimates by how much it misses optimality, we have
established several importants facts.
F.Thomas Bruss, Guy Louchard The Odds-algorithm based on sequential updating and

Very good.Certainly worth more than a casual look .Thankyou.