Why do banks keep vault cash instead of depositing all reserves at the central bank? In what way to commercial banks benefit from keeping some of their excess reserves in the vault as opposed to depositing all of their excess reserves with the central bank (assuming the central bank pays IOER)?

What sort of proportion of a banks reserves are kept in vault VS at the central bank?

Thanks!
"Vault cash" is the money that a bank will keep on premises (which is usually kept in their vault) to deal with their day-to-day cash needs. 

The bank must have a certain amount of cash on hand in order to deal with these types of every day transactions.  "vault cash" is considered to be part of a bank's reserves, and banks will usually be required to have a certain amount of "vault cash" on hand.

Bank reserves are essentially an antidote to panic. The Federal Reserve obliges banks to hold a certain amount of cash in reserve so that they never run short and have to refuse a customer's withdrawal, possibly triggering a bank run.

The required bank reserve follows a formula set by the Federal Reserve Board's regulations that are based on the amount deposited in net transaction accounts. These include demand deposits, automatic transfer accounts, and share draft accounts.