The problem of compact tables is to maximise the overlap when building a word that is to include permutations of every given words (all the words being the same length). This problem is shown to be NP-complete in the general case, and some specific restrictions are studied.
To show this on a small example (beyond what is in the article), imagine that in a game (like checkers) if blue takes red, on a result of 1, both are eliminated, on 2 or 3, red remains and blue remains in the other cases. If red takes blue, results 1 to 4 make red win and on 5 to 6, blue wins. The compact table in this case would be to keep the table as is in the blue versus red, add +2 if red versus blue, with results 7 and 8 letting red win.