estimate vs count on

estimate is a noun but count on is not a noun.

Word	Noun	Adjective	Verb	Adverb
estimate	Yes	No	Yes	No
count on	No	No	Yes	No

As verbs, estimate and count on are synonyms defined as:

Other synonyms of estimate include calculate, figure, forecast, reckon.

estimate (noun)	count on (noun)
a judgment of the qualities of something or somebody
an approximate calculation of quantity or degree or worth
the respect with which a person is held
a document appraising the value of something (as for insurance or taxation)
a statement indicating the likely cost of some job

estimate (verb)	count on (verb)
judge tentatively or form an estimate of (quantities or time)	judge to be probable
judge to be probable