Reckon on
Definition 1 of 2
Pro Tip 1/3Expectation Context
Used when you have a strong belief that something will happen or be the case. 
They reckon on the new policies improving the economy.
Pro Tip 2/3Personal Assurance
Used to express reliance on someone's promise or commitment. 
You can reckon on me to finish the project on time.
Pro Tip 3/3Emotional Dependence
Can convey emotional reliance or need for support. 
After the loss, she really reckoned on her friends to be there for her.