Definition of bank on phrasal verb from the Oxford Advanced American Dictionary

 

bank on

 phrasal verb
phrasal verb
 
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Phrasal Verbs

bank on somebody/something

 
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to rely on someone or something I'm banking on your help. “I'm sure he'll help.” “Don't bank on it (= it is not likely to happen).” bank on somebody to do something I'm banking on you to help me. bank on doing something I was banking on getting something to eat on the train.
See the Oxford Advanced Learner's Dictionary entry: bank on