"Eenie, meanie, miney, mo Catch a tiger by his toe If he hollers make him pay fifty dollars ev'ry day"
It wasn't so much to "count", as we counted with the named of numbers. It was applied as a pseudorandom selector, with the assumption that the person counting hadn't thought through the math to the point of knowing which child would be "it" for the next game of tag. Whoever starting counting around the circle first got to point to the "eenie" person, then around the circle. Sometimes this would be followed by another rhyme and there were a few options for that.