Played in university classes for preservice teachers as well as in middle and high schools, the River Crossing Game depends on the sum of tosses of two fair dice. This paper describes the game as well as some lines of thinking about winning strategies, which are not obvious even with an understanding of the overall distribution for the sum of two dice. Also, the paper highlights properties of the game that are counter-intuitive and sure to challenge the thinking of teachers and students alike. (Contains 5 figures and 10 tables.)