I've seen these terms used by adults to categorize children's playground rhymes where the last remaining child is selected as the seacher for hide & go seek, or {saying the rhyme two times in succession} the last two children become the team captains:

choosing "it"

counting out rhymes

elimination rhymes

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Note that contrary to some books I have read, it seems to me that more often than not children want to be choosen as "it".

BTW: when the two team captains are chosen, one at a time they chose members of their team by calling out the name of the remaining children. I believe that it still hurts to be the last child or one of the last child selected. When the children I meet with choose team captains, they use a choosing it rhyme like:

Eenie meenie
minie mo
catch a tiger by the toe
if he hollers let him go
ee-nie meen-ie min-ie mo.

The children huddle close together in a semi-circle type formation. The child who selects the captains {because he or she raised his hand first and me or another adult picked him or her] stands in front of the other children. Each child in the semi-circle extends his or her right foot forward. On each word {or in the case of the last line, on each syllable} the "leader" points to each successive child's foot. The leader can not skip a child or add additional words or syllables. The child who the leader is pointing to on the word "mo" {pronounced "moh"} is out and the rhyme is repeated until there is only one child left. That child is "it" or [in the case of competitive games with two teams-one of the team captains]. The same "leader" then starts the rhyme again with the remainding children to pick the second team captain.

However, when that game [such as relay races]is played, and the group has time to play that game again, the way we do it in my groups is that the two new captains are the two children who were picked last.

I think doing this helps build those last picked children's
self-esteem.