I would like to propose a game where a modest amount of simple information makes a binary tree appropriate. Branches can be labeled so that the ordering of the data is not critical.
Guessing an animal is a game which many children approach on a random basis. Especially when the starting letter is given, the child begins a scan through his "animal vocabulary" looking for a possible match with any entry beginning with that letter.
Guess That Animal!, subtitled Simulating Learning in Computers, was written by Daniel Hastie and published as type-in source code in Compute! Issue 27, August 1982. It presents a simple "learning" program that will guess the animal the player is thinking about.
Nine months later a version titled Sinclair/Timex Guess That Animal, written by Ralph Kennedy, was presented for the Sinclair ZX-81 - it was published in Compute! Issue 36, May 1983.