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Gary Rowett‘s side had a slim chance of reaching the playoffs with four games to go thanks to successive victories over Middlesbrough, Rotherham United and Stoke City.
However, the South London side have since taken one point from the last 12 on offer and are now effectively battling for a top-half finish.
Rowett will be disappointed with his side’s recent form, having lost by three goals at home to Swansea City and Bournemouth, as well as going down 1-0 at Watford last time out.
The Lions’ only point since April 5 came in a goalless draw with Brentford, though not since under Neil Harris in March 2019 have they lost three league games in a row.
While Millwall can finish as high as eighth if results go their way, the best Bristol City can hope for is a 13th-place finish, though even that looks highly unlikely.
The Robins have endured a poor campaign, with experienced boss Nigel Pearson not quite being able to turn things around at Ashton Gate.