Cincinnati Reds First-Place Eliminiation Scenario
Cincinnati must win 24 more games (38 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Cincinnati finishes in first place with 38 wins:

Team             W	L	PCT	GB
Cincinnati       38	124	0.235	0.00
Milwaukee        38	124	0.235	0.00
Pittsburgh       38	124	0.235	0.00
St. Louis        38	124	0.235	0.00
Chicago          37	125	0.228	1.00

Tie breakers
Cincinnati wins the series with Milwaukee 11 games to 2
Cincinnati wins the series with Pittsburgh 7 games to 6
Cincinnati wins the series with St. Louis 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Milwaukee        15	8	139	0.652	0.0
Chicago          15	9	138	0.625	0.5
Cincinnati       14	10	138	0.583	1.5
Pittsburgh       13	12	137	0.520	3.0
St. Louis        11	14	137	0.440	5.0

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 13 additional game(s) against Cincinnati and loses 0.
Chicago wins the series 13 games to 0.
Chicago wins 0 additional game(s) against teams outside the division and loses 86.

Chicago currently has 0 win(s) against Milwaukee and 0 loss(es).
Chicago wins 0 additional game(s) against Milwaukee and loses 13.
Chicago loses the series 0 games to 13.
Chicago wins 0 additional game(s) against teams outside the division and loses 86.

Chicago currently has 0 win(s) against Pittsburgh and 0 loss(es).
Chicago wins 9 additional game(s) against Pittsburgh and loses 4.
Chicago wins the series 9 games to 4.
Chicago wins 0 additional game(s) against teams outside the division and loses 86.

Chicago currently has 0 win(s) against St. Louis and 0 loss(es).
Chicago wins 0 additional game(s) against St. Louis and loses 13.
Chicago loses the series 0 games to 13.
Chicago wins 0 additional game(s) against teams outside the division and loses 86.

Cincinnati currently has 1 win(s) against Milwaukee and 2 loss(es).
Cincinnati wins 10 additional game(s) against Milwaukee and loses 0.
Cincinnati wins the series 11 games to 2.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 89.

Cincinnati currently has 0 win(s) against Pittsburgh and 0 loss(es).
Cincinnati wins 7 additional game(s) against Pittsburgh and loses 6.
Cincinnati wins the series 7 games to 6.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 89.

Cincinnati currently has 0 win(s) against St. Louis and 0 loss(es).
Cincinnati wins 7 additional game(s) against St. Louis and loses 6.
Cincinnati wins the series 7 games to 6.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 89.

Milwaukee currently has 1 win(s) against Pittsburgh and 2 loss(es).
Milwaukee wins 0 additional game(s) against Pittsburgh and loses 10.
Milwaukee loses the series 1 games to 12.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 96.

Milwaukee currently has 3 win(s) against St. Louis and 0 loss(es).
Milwaukee wins 10 additional game(s) against St. Louis and loses 0.
Milwaukee wins the series 13 games to 0.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 96.

Pittsburgh currently has 0 win(s) against St. Louis and 0 loss(es).
Pittsburgh wins 5 additional game(s) against St. Louis and loses 8.
Pittsburgh loses the series 5 games to 8.
Pittsburgh wins 0 additional game(s) against teams outside the division and loses 88.

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