count the number of occurrences of "(" in a string

( is a special character. You need to escape it:

str_count(s,"\\(")
# [1] 3

Alternatively, given that you're using stringr, you can use the coll function:

str_count(s,coll("("))
# [1] 3

You could also use gregexpr along with length in base R:

sum(gregexpr("(", s, fixed=TRUE)[[1]] > 0)
[1] 3

gregexpr takes in a character vector and returns a list with the starting positions of each match. I added fixed=TRUE in order to match literals.length will not work because gregexpr returns -1 when a subexpression is not found.

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If you have a character vector of length greater than one, you would need to feed the result to sapply:

# new example
s<- c("(hi),(bye),(hi)", "this (that) other", "what")
sapply((gregexpr("(", s, fixed=TRUE)), function(i) sum(i > 0))
[1] 3 1 0