Cincinnati Reds First-Place Eliminiation Scenario
Cincinnati must win 25 more games (41 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Cincinnati finishes in first place with 41 wins:

Team             W	L	PCT	GB
Cincinnati       41	121	0.253	0.00
Milwaukee        41	121	0.253	0.00
Pittsburgh       41	121	0.253	0.00
Chicago          41	121	0.253	0.00
St. Louis        40	122	0.247	1.00

Tie breakers
Cincinnati wins the series with Chicago 7 games to 6
Cincinnati wins the series with Milwaukee 7 games to 6
Cincinnati wins the series with Pittsburgh 10 games to 3

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        19	11	132	0.633	0.0
Chicago          19	12	131	0.613	0.5
Cincinnati       16	15	131	0.516	3.5
St. Louis        14	17	131	0.452	5.5
Pittsburgh       14	18	130	0.438	6.0

Next, we show how the remaining series of games plays out in the scenario:

Chicago currently has 0 win(s) against Cincinnati and 0 loss(es).
Chicago wins 6 additional game(s) against Cincinnati and loses 7.
Chicago loses the series 6 games to 7.
Chicago wins 2 additional game(s) against teams outside the division and loses 77.

Chicago currently has 0 win(s) against Milwaukee and 0 loss(es).
Chicago wins 6 additional game(s) against Milwaukee and loses 7.
Chicago loses the series 6 games to 7.
Chicago wins 2 additional game(s) against teams outside the division and loses 77.

Chicago currently has 0 win(s) against Pittsburgh and 0 loss(es).
Chicago wins 1 additional game(s) against Pittsburgh and loses 12.
Chicago loses the series 1 games to 12.
Chicago wins 2 additional game(s) against teams outside the division and loses 77.

Chicago currently has 0 win(s) against St. Louis and 0 loss(es).
Chicago wins 7 additional game(s) against St. Louis and loses 6.
Chicago wins the series 7 games to 6.
Chicago wins 2 additional game(s) against teams outside the division and loses 77.

Cincinnati currently has 1 win(s) against Milwaukee and 2 loss(es).
Cincinnati wins 6 additional game(s) against Milwaukee and loses 4.
Cincinnati wins the series 7 games to 6.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 82.

Cincinnati currently has 0 win(s) against Pittsburgh and 0 loss(es).
Cincinnati wins 10 additional game(s) against Pittsburgh and loses 3.
Cincinnati wins the series 10 games to 3.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 82.

Cincinnati currently has 0 win(s) against St. Louis and 0 loss(es).
Cincinnati wins 2 additional game(s) against St. Louis and loses 11.
Cincinnati loses the series 2 games to 11.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 82.

Milwaukee currently has 2 win(s) against Pittsburgh and 2 loss(es).
Milwaukee wins 9 additional game(s) against Pittsburgh and loses 0.
Milwaukee wins the series 11 games to 2.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 90.

Milwaukee currently has 3 win(s) against St. Louis and 0 loss(es).
Milwaukee wins 2 additional game(s) against St. Louis and loses 8.
Milwaukee loses the series 5 games to 8.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 90.

Pittsburgh currently has 0 win(s) against St. Louis and 0 loss(es).
Pittsburgh wins 12 additional game(s) against St. Louis and loses 1.
Pittsburgh wins the series 12 games to 1.
Pittsburgh wins 0 additional game(s) against teams outside the division and loses 82.

# Cincinnati Reds' magic number
# Cincinnati's magic number
# Reds' magic number
# MLB Playoff Race