Did you play this, as a child?
In this game, the players are arranged in groups of two. All but one of the couples form a big circle facing toward the center, each couple with one player behind the other. There should be good wide spaces between the couples.
One of the two free players is chosen to chase the other. They run around outside the circle. If the one chased is tagged, he becomes the one to do the chasing. At any time, the one who is being pursued may run into the circle and take his place in front of one of the standing couples. This makes that group "three deep" and the third or outside player of the group must immediately leave it to be chased until he either is tagged or causes someone else to be chased by stopping in his turn in front of one of the couples.
If the game is played long enough and with frequent changes, everyone will have a chance to run.
It is not permitted to run across the circle, and the runner may only go into it at the point where he stops in front of a couple. Nor is it permissible for a third man to go directly to the couple immediately to the left or the right of the one he has left. He must run a bit at least. This game makes for alertness and speed in running and is good fun.
Source: Mabie, Hamilton Wright, Edward Everett Hale, and William Byron Forbush. The Young Folks Treasury Vol. X: Ideal Home Life. New York: The University Society, 1919. Print. This excerpt is from p. 159.