At the end of my article "Hunting the Ten-Square" (May 2004 Word Ways) I said that about one million 11-letter words might suffice to have a 50-50 chance of finding a square. I have since conducted some more investigations using both formula and programs, and conclude that more than two million words are needed to obtain a reasonable selection of squares.
"The Eleven-Square - Take One,"
Word Ways: Vol. 37
, Article 20.
Available at: https://digitalcommons.butler.edu/wordways/vol37/iss3/20