Chicago Cubs First-Place Eliminiation Scenario
Chicago must win 21 more games (37 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Chicago finishes in first place with 37 wins:

Team             W	L	PCT	GB
Chicago          37	125	0.228	0.00
Cincinnati       37	125	0.228	0.00
Pittsburgh       36	126	0.222	1.00
Milwaukee        36	126	0.222	1.00
St. Louis        35	127	0.216	2.00

Tie breakers
Chicago wins the series with Cincinnati 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          16	10	136	0.615	0.0
Milwaukee        13	12	137	0.520	2.5
Cincinnati       12	13	137	0.480	3.5
Pittsburgh       10	15	137	0.400	5.5
St. Louis        10	15	137	0.400	5.5

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 7 additional game(s) against Cincinnati and loses 6.
Chicago wins the series 7 games to 6.
Chicago wins 0 additional game(s) against teams outside the division and loses 84.

Chicago currently has 0 win(s) against Milwaukee and 0 loss(es).
Chicago wins 7 additional game(s) against Milwaukee and loses 6.
Chicago wins the series 7 games to 6.
Chicago wins 0 additional game(s) against teams outside the division and loses 84.

Chicago currently has 0 win(s) against Pittsburgh and 0 loss(es).
Chicago wins 7 additional game(s) against Pittsburgh and loses 6.
Chicago wins the series 7 games to 6.
Chicago wins 0 additional game(s) against teams outside the division and loses 84.

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 84.

Cincinnati currently has 1 win(s) against Milwaukee and 3 loss(es).
Cincinnati wins 6 additional game(s) against Milwaukee and loses 3.
Cincinnati wins the series 7 games to 6.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 92.

Cincinnati currently has 3 win(s) against Pittsburgh and 0 loss(es).
Cincinnati wins 6 additional game(s) against Pittsburgh and loses 4.
Cincinnati wins the series 9 games to 4.
Cincinnati wins 0 additional game(s) against teams outside the division and loses 92.

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 92.

Milwaukee currently has 0 win(s) against Pittsburgh and 0 loss(es).
Milwaukee wins 1 additional game(s) against Pittsburgh and loses 12.
Milwaukee loses the series 1 games to 12.
Milwaukee wins 0 additional game(s) against teams outside the division and loses 89.

Milwaukee currently has 0 win(s) against St. Louis and 0 loss(es).
Milwaukee wins 13 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 89.

Pittsburgh currently has 2 win(s) against St. Louis and 1 loss(es).
Pittsburgh wins 4 additional game(s) against St. Louis and loses 6.
Pittsburgh loses the series 6 games to 7.
Pittsburgh wins 0 additional game(s) against teams outside the division and loses 91.

# Chicago Cubs' magic number
# Chicago's magic number
# Cubs' magic number
# MLB Playoff Race