Cincinnati Reds First-Place Eliminiation Scenario
Cincinnati must win 20 more games (45 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Cincinnati finishes in first place with 45 wins:

Team             W	L	PCT	GB
Cincinnati       45	117	0.278	0.00
Pittsburgh       45	117	0.278	0.00
St. Louis        45	117	0.278	0.00
Chicago          45	117	0.278	0.00
Milwaukee        44	118	0.272	1.00

Tie breakers
Cincinnati wins the series with Chicago 7 games to 6
Cincinnati wins the series with Pittsburgh 7 games to 6
Cincinnati wins the series with St. Louis 9 games to 4

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          30	20	112	0.600	0.0
St. Louis        27	23	112	0.540	3.0
Cincinnati       25	26	111	0.490	5.5
Milwaukee        25	26	111	0.490	5.5
Pittsburgh       17	34	111	0.333	13.5

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 0 additional game(s) against teams outside the division and loses 66.

Chicago currently has 2 win(s) against Milwaukee and 1 loss(es).
Chicago wins 5 additional game(s) against Milwaukee and loses 5.
Chicago wins the series 7 games to 6.
Chicago wins 0 additional game(s) against teams outside the division and loses 66.

Chicago currently has 2 win(s) against Pittsburgh and 1 loss(es).
Chicago wins 0 additional game(s) against Pittsburgh and loses 10.
Chicago loses the series 2 games to 11.
Chicago wins 0 additional game(s) against teams outside the division and loses 66.

Chicago currently has 0 win(s) against St. Louis and 0 loss(es).
Chicago wins 4 additional game(s) against St. Louis and loses 9.
Chicago loses the series 4 games to 9.
Chicago wins 0 additional game(s) against teams outside the division and loses 66.

Cincinnati currently has 1 win(s) against Milwaukee and 3 loss(es).
Cincinnati wins 3 additional game(s) against Milwaukee and loses 6.
Cincinnati loses the series 4 games to 9.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 73.

Cincinnati currently has 4 win(s) against Pittsburgh and 2 loss(es).
Cincinnati wins 3 additional game(s) against Pittsburgh and loses 4.
Cincinnati wins the series 7 games to 6.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 73.

Cincinnati currently has 2 win(s) against St. Louis and 2 loss(es).
Cincinnati wins 7 additional game(s) against St. Louis and loses 2.
Cincinnati wins the series 9 games to 4.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 73.

Milwaukee currently has 1 win(s) against Pittsburgh and 0 loss(es).
Milwaukee wins 5 additional game(s) against Pittsburgh and loses 7.
Milwaukee loses the series 6 games to 7.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 70.

Milwaukee currently has 1 win(s) against St. Louis and 2 loss(es).
Milwaukee wins 3 additional game(s) against St. Louis and loses 7.
Milwaukee loses the series 4 games to 9.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 70.

Pittsburgh currently has 2 win(s) against St. Louis and 4 loss(es).
Pittsburgh wins 7 additional game(s) against St. Louis and loses 0.
Pittsburgh wins the series 9 games to 4.
Pittsburgh wins 0 additional game(s) against teams outside the division and loses 75.

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