What are the Nitto ATP Finals qualification scenarios?

The Nitto ATP Finals is down to the final round of group-play matches. Who will advance to the semi-finals of the season finale?

Jannik Sinner topped the Ilie Nastase Group and Taylor Fritz finished second. Both men will compete in the last four at the year-end championships. Alexander Zverev finished with a perfect 3-0 record in the John Newcombe Group. The final spot in the singles semi-finals will be decided Friday evening.

Harri Heliovaara and Henry Patten won the Mike Bryan Group with a 3-0 record, followed by Max Purcell and Jordan Thompson (2-1).

Kevin Krawietz and Tim Puetz have won the Bob Bryan Group. However, the second spot in the group is still up for grabs. 

See below for the full list of Nitto ATP Finals qualification scenarios. 

Singles John Newcombe Group qualification scenarios after the completion of Zverev's straight-sets win against Carlos Alcaraz:

1) If C. RUUD defeats A. RUBLEV, then A. ZVEREV wins the group and C. RUUD qualifies 2nd.

2) If A. RUBLEV defeats C. RUUD in 2 sets, then A. ZVEREV wins the group and order of remaining players is determined by % of games won.

3) If A. RUBLEV defeats C. RUUD in 3 sets, then A. ZVEREV wins the group and C. RUUD qualifies 2nd.

Doubles Bob Bryan Group qualification scenarios after the completion of the 2nd round of the event's group stage:

1) Regardless of score, if M. AREVALO / M. PAVIC defeat S. BOLELLI / A. VAVASSORI and R. BOPANNA / M. EBDEN defeat K. KRAWIETZ / T. PUETZ, then K. KRAWIETZ / T. PUETZ win the group and M. AREVALO / M. PAVIC qualify 2nd.

2) Regardless of score, if M. AREVALO / M. PAVIC defeat S. BOLELLI / A. VAVASSORI and K. KRAWIETZ / T. PUETZ defeat R. BOPANNA / M. EBDEN, then K. KRAWIETZ / T. PUETZ win the group and M. AREVALO / M. PAVIC qualify 2nd.

3) Regardless of score, if S. BOLELLI / A. VAVASSORI defeat M. AREVALO / M. PAVIC and R. BOPANNA / M. EBDEN defeat K. KRAWIETZ / T. PUETZ, then K. KRAWIETZ / T. PUETZ win the group and S. BOLELLI / A. VAVASSORI qualify 2nd.

4) Regardless of score, if S. BOLELLI / A. VAVASSORI defeat M. AREVALO / M. PAVIC and K. KRAWIETZ / T. PUETZ defeat R. BOPANNA / M. EBDEN, then K. KRAWIETZ / T. PUETZ win the group and S. BOLELLI / A. VAVASSORI qualify 2nd.