Meaning: do with certainty (definition).

Example: Her recipe for cherry pie is a winner, you may bank on it.


Origins: Late 1800s; alludes to banks as a place of safe storage for money. (Source.)
Rewrites:

deposit on it invest with it secure a loan with it bet your house on it build a career on it give a blind date a second call over it
Discussion: This rewrite is about being so confident in something that you can move ahead as you would in other interactions of life with confidence.