Such are the numerous scenarios available in Group Lleyton Hewitt that Federer could win against the South African and still have his hopes of a 100th career title dashed, while he could lose and yet make the final four.
Kei Nishikori, who defeated Federer in Sunday’s opening group match, earlier faces Dominic Thiem, who despite having lost his opening two matches can also still qualify.
Victory for Federer and win for Thiem against Nishikori will ensure the 20-time Grand Slam champion finishes top of the group.
A straight-sets win coupled with a Nishikori victory in the same fashion would also see Federer finish above Anderson but should he win in straight sets and Nishikori win in straight sets then the semi-final spots would be defined by the highest percentage of games won.
After a disappointing start to his 16th appearance at the season finale, Federer hit some form against Thiem in a 6-2 6-3 victory ahead of his intriguing contest against Wimbledon finalist Anderson.
The 37-year-old, who has only ever failed to qualify from his group once, is bidding to win a record-extending seventh title and first since 2011 but comes up against a confident opponent.
Anderson memorably defeated Federer from two sets down at Wimbledon this summer on his way to reaching his second Grand Slam final.
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