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mid-13c., "game of chess (or checkers);" c.1300, "a chessboard, board with 64 squares for playing chess or similar games; a set of chessmen" a shortening of Old French eschequier "chessboard; a game of chess," from Medieval Latin scaccarium (see check (n.)).
Meaning "pattern of squares" is late 14c. Meaning "a man or marker in the game of checkers" is from 1864. British prefers chequer. From late 14c. as "a checked design." The word had earlier senses of "table covered with checked cloth for counting" (late 12c. in Anglo-Latin), a sense also in Old French (see checker (n.2)).
"table covered with a checked cloth," specialized sense of checker (n.1), late 14c. (in Anglo-Latin from c.1300); especially a table for counting money or keeping accounts (revenue reckoned with counters); later extended to "the fiscal department of the English Crown; the Exchequer (mid-14c.; in Anglo-Latin from late 12c.).