In a position with legs spread wide on either side of something.
From a- (in a state of) combined with straddle (to stand with legs apart). This formation follows the same Middle English pattern of using a- as a prefix to create adverbial expressions of position or state.
Cowboys would naturally say they're 'astraddle' their horse instead of 'straddling' it—it's the kind of economical language you'd expect from people who spoke while riding.
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