Aniki-Bóbó is akin to a children's counting rhyme that has existed in various forms since well before when?
Eeny, meeny, miny, moe "Eeny, meeny, miny, moe"—which can be spelled a number of ways—is a children's counting rhyme, used to select a person in games such as tag. It is one of a large group of similar rhymes in which the child who is pointed to by the chanter on the last syllable is either "chosen" or "counted out". The rhyme has existed in various forms since well before 1820, and is common in many languages with similar-sounding nonsense syllables.
London Bridge Is Falling Down "London Bridge Is Falling Down" (also known as "My Fair Lady" or "London Bridge") is a traditional English nursery rhyme and singing game, which is found in different versions all over the world. It deals with the depredations of London Bridge and attempts, realistic or fanciful, to repair it. It may date back to bridge rhymes and games of the Late Middle Ages, but the earliest records of the rhyme in English are from the seventeenth century. The lyrics were first printed in close to their modern form in the mid-eighteenth century and became popular, particularly in Britain and the United States in the nineteenth century.