Count On Meaning

(idiomatic, transitive) to rely upon, trust, or expect

Example:   Don't count on being able to get back into the building after 5pm.
  Can we count on you to help out?
Macaulay
  He was brewer to the palace; and it was apprehended that the government counted on his voice.
1999, Survivor, Chuck Palahniuk
  The first time you meet that someone special, you can count on them one day being dead and in the ground.
2001, Builder's Guide to Accounting‎
  Or perhaps something unusual occurred in the current period that you can't count on to repeat itself.
2009, USA Today - Going green: Young talent cuts costs, builds continuity
  "Hopefully you can count on them for a long period of time. Quite frankly, not often do you give those players up."