In my grade school we had a different version from any of these.

It went:

Down by the banks of the hanky pank'
where the bullfrogs jump from bank to bank
fee, fi, fo, fum
your momma smells like King Kong
daddy smells like Donkey Kong
east side, west side, ding, dang, dong
Mickey Mouse built a house
Donald Duck messed it up
who will pay the consequences
and responsibilities
Y-O-U spells you!

And whoever got their hand slapped on "you" was out.

Spent so many mornings playing this and "Shame, Shame, Shame" when I was a little kid.