After a game of Scrabble, the board looks like a mosaic: tiles are scattered but form a connected pattern — islands of words in a sea of empty cells. Such a pattern can be described mathematically, but usually that requires complex rules. The authors of the study took a different approach: they used real games in different languages and found the simplest description that captures only the average properties — how many cells are occupied on average and how often neighboring cells are occupied together. This is like describing a crowd in the subway not by faces but by density and whether people are holding hands.
This simple model reproduces real boards remarkably well. It predicts the lengths of words that will appear and the geometry of the pattern. Moreover, the model's parameters turned out to be interpretable: they reflect game strategies. For example, one parameter shows how much players prefer to place long words along lines rather than short ones sideways. This is reminiscent of a gardener shaping a hedge: you can trim randomly, or you can set a direction of growth.
Using this model, the scientists compared games in different languages without even looking at the letters. They computed the entropy of the patterns — a measure of their diversity. Interestingly, the entropy depended more on tactics (such as the average word length on the board) than on dictionary size. Finally, the model was able to identify the language of the game from the pattern alone, without analyzing words. It's like guessing the language of a crossword puzzle just by the shape of the empty and filled cells.
In English Scrabble, there are about 280,000 valid words, but a typical game uses only a small fraction of them — the board pattern says more about the style of play than about the richness of the vocabulary.