StLouis has been eliminated from first place.

To show that StLouis is eliminated from first place, we start with the current standings:
            Team	W	L	GL	PCT	GB
       Milwaukee	103	59	0	0.636	0.0
     ChicagoCubs	89	73	0	0.549	14.0
      Pittsburgh	82	80	0	0.506	21.0
         StLouis	77	85	0	0.475	26.0
      Cincinnati	75	87	0	0.463	28.0
           Total	426	384	0

StLouis can finish the season with at most 77 + 0 = 77 wins and will finish the season behind the following teams:
Milwaukee has already won 103 games.
ChicagoCubs has already won 89 games.
Pittsburgh has already won 82 games.
# StLouis Cardinals' magic number
# StLouis's magic number
# Cardinals' magic number
# MLB Playoff Race