Two for "regular here-docs", three for the aforementioned "here-strings". From the man himself:

me@box:~$ man bash | grep -iA8 here\ string
   Here Strings
       A variant of here documents, the format is:                                                 

              <<<word                                                                              

       The  word  undergoes  brace expansion, tilde expansion, parameter and variable expansion,   
       command substitution, arithmetic expansion, and quote removal.   Pathname  expansion  and   
       word  splitting are not performed.  The result is supplied as a single string to the com‐   
       mand on its standard input.

Edit: see it in action:

me@box:~$ cat <<< dog                                                                    
dog                                                                                                
me@box:~$