The expression “to reckon without one’s host” means to neglect important facts in reaching a conclusion.
This seems to have been a failing known also to our remote ancestors; at least, so long ago that the phrase had become proverbial when, in 1489, William Caxton printed (on his new wooden printing press) his own translation of the French “Blanchardyn and Eglantine”.
In that early example of English printing may be found the passage, “It ys sayd in comyn that ‘who soeuer rekeneth wythoute his hoste, he rekeneth twys for ones.'”
But, as shown in this quotation and in others of the next hundred years, “Thei reckened before their host, and so paied more then their shotte came to”; and “He that countis without his oist, Oft tymes he countis twyse”, the tendency of our ancestors, unlike that of the present era, was to include more factors into the reckoning than should have been considered, even “twyse” as many.