A Chinese game: got a similar one in North America?

or perhaps one with similar equipment?

The game is called da-gargar in Beijing dialect. Now virtually extinct, it used to be highly popular among children in Beijing and some other areas of north China.

Distinguished by simple but unusual equipment, the game essentially involves a scoring defender and a challenger. It starts when the defender, who stands in a outlined circle, makes a skill-demanding hit on a short stick with a wooden bat--which are all the gear needed for the game. The stick, called gargar, measures several inches long with tapering ends, so when laid flat on the ground and skillfully chopped on one end with the bat, it can be launched off ground in a spinning movement. While it is in midair, the defender swings the bat at it for a second hit, trying to propel it as far as possible.

The distance is vital to the defender: from the spot where the projected gargar comes to a stop, the challenger picks it up and tries to throw it back into the defender's circle, which, if successfully accomplished, will result in the challenger's victory for the round and the swapping of the players' positions. But the defender, now becoming the goalkeeper, can try to divert the coming gargar by hitting it with the bat, again the farther the better.

With the hit gargar coming to a stop on the ground, the defender now can demand scores based on his estimation of the distance from the gargar to the circle, in paces or in bats. The challenger can grant the demanded scores, or doubt it--if he/she thinks the defender is asking for more than the actual distance allows. In the latter case, a joint field measurement is conducted with the defender's feet or the bat. If the overestimation is proven, the defender's greed will cost his defending position, so his chance to score more in the next round is surrendered to the triumphant (former) challenger.