"Tit, Tat, Toe" is a game that's currently called "Tic, Tac, Toe" in the United States. It's also called "Noughts and Crosses".

Tit, Tat, Toe - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

To Play Tic Tac Toe: First draw a 3 by 3 grid like the one above. Two players take turns - one is "X" the other is "O". Whoever gets three of their symbols in a row, either across, down or diagonally, wins! In the board above, "O" won by getting three "O"'s in a row diagonally.

Tit, Tat, Toe - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Comment After Song Image

Thanks and Acknowledgements

This rhyme can be found in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, and printed in the USA. The 2nd illustration is from The Big Book of Nursery Rhymes (circa 1920) edited by Walter Jerrold (1865 - 1929) and illustrated by Charles Robinson (with some graphical editing by Lisa Yannucci).