Does the choice of "on" or "with" make any difference in the following?
I didn't think that there would be a traffic jam, and didn't plan extra time in the journey. I didn't reckon on/with there being a traffic jam.
I'd appreciate your help.
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According to Merriam Webster dictionary, 'reckon on' means 'to expect (something) to happen : to plan on (something)'.
According to Macmillan dictionary, 'reckon with' means 'to consider something important when you are making plans and so be prepared for it'.
As per these definitions, in your sentence either 'on' or 'with' is possible with difference in meaning :
'I didn't reckon on there being a traffic jam.'
It means I didn't expect a traffic jam to happen there.
'I didn't reckon with there being a traffic jam.'
It means I didn't consider the traffic jam to be something important, and so I didn't make any plan for it or I was not prepared for it.