Another advantage of de-Bruijn notation is in providing a very simple binary encoding of lambda terms, as demonstrated in my IOCCC submission [1].
Unrelated, but what would be your advice/study plan for a human to reach near perfect game play in Connect 4, and how difficult would it be?
[1] https://www.waterstones.com/book/the-complete-book-of-connec...
A more limited form of perfect play is knowing how to win when playing first. I cannot do that either, but I suspect that I might be able to get close if I were to study hard on it for a year, trying to minimize the size of the opening book I need to keep in my head. The leaves of that book will then resemble the positions where Allis' rules apply so that you can work out further play on the fly.