AMERICAN STATISTICAL ASSOCIATION JOURNAL, JUNE 1966
320
Hence
K
(?max = £ Ck(pk l0g2 (lOpk) + (1 — Pk) l0g2 (10(1 - pk)/9)). (11)
Jfc=l
7. THE WINNING STRATEGY
All the formulas needed to construct the strategy are now available. Given that n cards remain, t of which are nines, and a corresponding probability pn,t of winning, certain values of pntt satisfy pn,*>l/10. This is a conditional probability, given an event that occurs with probability cn,t. For those pairs (ft, t) such that pn,t> 1/10, the optimal fraction is