Past tense of 'reckon': to calculate or count something, or to suppose or believe something (often used in dialect or older English).
From Old English 'gecyrcan' and Middle English 'recken,' ultimately from Frisian and related to German 'recken' (to stretch or direct). The 'calculate' meaning is oldest, while 'suppose/believe' developed in informal speech and dialectal English.
In American Southern dialect and Appalachian English, 'I reckon' is still the primary way speakers express conjecture or belief — linguists see this as a direct survival of 17th-century English that was brought by settlers and preserved in relative isolation, making Appalachia a kind of living museum of older English speech patterns.
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