A "hill of beans" is how much the problems of three little people are worth in this crazy, mixed-up world (or so Bogart computed at the end of Casablanca). In other words, a "hill of beans" amounts to very little or nothing.

The original use of the phrase apparently dates to a farming manual published in 1858. The manual's author, J.J. Thomas, instructed the reader on the cultivation of lima beans: "A strong wire is stretched from the tops of posts placed at a distance from each other; and to this wire two diverging cords from each hill of beans are attached."

Later, as wordsmith Michael Quinion noted, someone (probably a bean farmer) was sufficiently seized by the worthlessness of beans to apply the phrase "figuratively to the illogical idea that if one bean was worthless, a whole hill of them would be even more so."

Reference: More on "hill of beans" at Michael Quinion's World Wide Words.
Recipe: Lima Beans With Yogurt And Basil (Cookthink)
Recipe: White Bean And Escarole Soup (Cookthink)