The story
From maxi(mum), maxi(mize) + max(imum).
Etymology from Wiktionary, CC BY-SA 4.0.
maximax
Today it means: A strategy or algorithm that seeks to maximize the maximum possible result (that is, that prefers the alternative with the chance of the best possible outcome, even if its expected outcome and its worst possible outcome are worse than other alternatives); often used attributively, as "maximax strategy", "maximax approach", and so on. Full definition →