Allison, thanks for posting that example.

I've observed children doing circle slaps like this {though not to this specific rhyme}. When there were only two players left, they would stand facing each other and do partner handclaps. The handclap routine and the recitation might speed up or it might stay at the same speed with the slaps not being harder than they were when all the children were in the circle. But those two 'partners' will continue doing same back & forth two hand/one hand handclap routine until one of them messes up. The person who messes up first is out, and the other person is the "winner".

Btw, this wasn't a heavy duty competition. For instance, I never heard anyone say "You won." or "I'm the winner". But there's some sense of accomplishment and status for being "the winner".