This chapter focuses on a simple but widespread Native American game of chance and then at a Maori game of strategy. It discusses a ubiquitous logical puzzle found in Western mathematics recreation books, in Western folk culture, and in several variants in African culture. The name of the game varies but usually reflects the type of objects used: peach stones among the Cayuga; and butter beans among the Cherokee. The close correspondence of the point values used by the Cayuga and those based on our ideas of probability strongly implies a probabilistic basis for the Cayuga's choices. The chapter summarizes all the possible composite results of one, two, or three consecutive tosses and includes the probability of each result. Games of strategy, even more than games of chance, capture people interest as somehow mathematical. In any game of strategy, just as in the creation of a mathematical proof or solution of a mathematical problem, there is a specific end goal.