An extension of the Last-Success-Problem

Combined Games with Randomly Delayed Beginnings

“…Among newer examples, and methods of solutions, we cite the work of Goldenshluger et al [12] which includes several such problems in a surprisingly unified form. We also like to mention a paper with a single specific objective function, namely the paper by Grau Ribas [13]. It shows us that, for certain generalisations of a last success objective, the classical dynamic programming approach may have clear advantages.…”

“…No optimality of the suggested solution can be claimed as for the solution of the Odds-Theorem. This is the price one has to pay for plugging in at each step what one knows so far about p, but not really knowing p. However, it is true that the latter performs in general well if the horizon is large enough for the estimates to have time to converge into a sufficiently close neighbourhood of p. This holds also if we have no prior distribution for p. In this case we propose in (12) to use the estimator pk = k −1 #{heads up to toss k} (15) and the corresponding definitions (13), since ( 15) is a both simple and unbiased estimator of p.…”