Use 'reckon without' when an unforeseen event affects your plans, hinting at a lack of preparation. They planned the picnic but reckoned without the sudden rainstorm.
Pro Tip 2/3
Idiomatic Usage
This phrase is idiomatic; it expresses a thought in a fixed, non-literal way, unique to native speakers. He reckoned without the new regulations that affected his business.
Pro Tip 3/3
Planning Pitfalls
'Reckon without' is often used when commenting on an oversight that leads to complications in one's plans. She wanted an outdoor wedding but reckoned without the seasonal bugs.