Properties of Subsets of Unobserved Items Constructed by Using Blackwell's Bet

Blackwells Bet (also known as the Cover Guessing Game) is an extremely clever use of a random variable to improve the probability of guessing which of two numbers is larger when you are only allowed to observe one of those numbers. This technique has hitherto been used to guess or predict outcomes with better-than-chance results. We show that this technique can also be used to construct subsets of unobserved items which have expected values below and above the expected value of the parent set. We discuss this in two situations: when the items in question can have arbitrary values, and when the items in question are Bernoulli trials. We also include simulations in an instance when the actual formulas require extensive.iteration of recursively-defined relations.