WordNet (r) 3.0 (2006):

count on
    v 1: judge to be probable [syn: calculate, estimate,
         reckon, count on, figure, forecast]

Moby Thesaurus II by Grady Ward, 1.0:

41 Moby Thesaurus words for "count on":
   aspire to, bank on, bargain for, bet on, calculate on, confide,
   depend on, desire, expect, feel confident, figure on, forestall,
   gamble on, harbor the hope, hope, hope against hope, hope and pray,
   hope for, hope in, hope to God, lean on, lean upon, live in hopes,
   look for, look forward to, look out for, look to, nurture the hope,
   place reliance on, plan on, presume, reckon on, rely on, rely upon,
   repose on, rest assured, rest on, swear by, trust, trust to,
   watch out for