Chicago White Sox First-Place Eliminiation Scenario
Chicago must win 28 more games (56 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Chicago finishes in first place with 56 wins:

Team             W	L	PCT	GB
Chicago          56	106	0.346	0.00
Kansas City      56	106	0.346	0.00
Detroit          55	107	0.340	1.00
Cleveland        54	108	0.333	2.00
Minnesota        54	108	0.333	2.00

Tie breakers
Chicago wins the series with Kansas City 8 games to 5

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Detroit          54	33	75	0.621	0.0
Minnesota        41	45	76	0.477	12.5
Cleveland        40	44	78	0.476	12.5
Kansas City      40	47	75	0.460	14.0
Chicago          28	58	76	0.326	25.5

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

Chicago currently has 0 win(s) against Cleveland and 3 loss(es).
Chicago wins 8 additional game(s) against Cleveland and loses 2.
Chicago wins the series 8 games to 5.
Chicago wins 1 additional game(s) against teams outside the division and loses 46.

Chicago currently has 2 win(s) against Detroit and 5 loss(es).
Chicago wins 6 additional game(s) against Detroit and loses 0.
Chicago wins the series 8 games to 5.
Chicago wins 1 additional game(s) against teams outside the division and loses 46.

Chicago currently has 2 win(s) against Kansas City and 5 loss(es).
Chicago wins 6 additional game(s) against Kansas City and loses 0.
Chicago wins the series 8 games to 5.
Chicago wins 1 additional game(s) against teams outside the division and loses 46.

Chicago currently has 2 win(s) against Minnesota and 4 loss(es).
Chicago wins 7 additional game(s) against Minnesota and loses 0.
Chicago wins the series 9 games to 4.
Chicago wins 1 additional game(s) against teams outside the division and loses 46.

Cleveland currently has 3 win(s) against Detroit and 1 loss(es).
Cleveland wins 8 additional game(s) against Detroit and loses 1.
Cleveland wins the series 11 games to 2.
Cleveland wins 0 additional game(s) against teams outside the division and loses 45.

Cleveland currently has 4 win(s) against Kansas City and 2 loss(es).
Cleveland wins 0 additional game(s) against Kansas City and loses 7.
Cleveland loses the series 4 games to 9.
Cleveland wins 0 additional game(s) against teams outside the division and loses 45.

Cleveland currently has 4 win(s) against Minnesota and 2 loss(es).
Cleveland wins 4 additional game(s) against Minnesota and loses 3.
Cleveland wins the series 8 games to 5.
Cleveland wins 0 additional game(s) against teams outside the division and loses 45.

Detroit currently has 5 win(s) against Kansas City and 2 loss(es).
Detroit wins 0 additional game(s) against Kansas City and loses 6.
Detroit loses the series 5 games to 8.
Detroit wins 0 additional game(s) against teams outside the division and loses 47.

Detroit currently has 4 win(s) against Minnesota and 2 loss(es).
Detroit wins 0 additional game(s) against Minnesota and loses 7.
Detroit loses the series 4 games to 9.
Detroit wins 0 additional game(s) against teams outside the division and loses 47.

Kansas City currently has 4 win(s) against Minnesota and 3 loss(es).
Kansas City wins 3 additional game(s) against Minnesota and loses 3.
Kansas City wins the series 7 games to 6.
Kansas City wins 0 additional game(s) against teams outside the division and loses 50.

# Chicago White Sox' magic number
# Chicago's magic number
# White Sox' magic number
# MLB Playoff Race