We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the unconstrained 100 prisoner problem. After introducing the 3 main classes of strategies, we define a variety of `hybrid' strategies and quantify their winning-efficiency. Whenever analytic results are not available, we make use of Monte Carlo simulations to estimate with high accuracy the winning-probabilities. Based on the results obtained, we conjecture that all strategies, except for the strategy maximizing the winning probability of the classical (constrained) problem, converge to the random strategy under weak conditions on the number of players or empty boxes. We conclude by commenting on the possible applications of our results in understanding processes of information retrieval, such as ``memory'' in living organisms.
翻译:我们考虑将典型的100名囚犯问题及其变体(其中涉及空箱)加以概括化,即一个团队的赢赢概率取决于尝试次数和赢家人数。我们称之为无限制的100名囚犯问题。我们提出三大类战略之后,我们定义了各种“杂交”战略,并量化了它们的赢利效率。当没有分析结果时,我们利用蒙特卡洛模拟来非常准确地估计赢利概率。根据所获得的结果,我们推测除了使传统(受限制的)问题赢得概率最大化的战略外,所有战略在玩家或空箱数目的脆弱条件下都与随机战略汇合。我们最后评论了我们在了解信息检索过程(例如“模拟”在活生物体中的“模拟”中)的结果的可能应用。