For all guest traveling from Chicago/Grundy/Will, taking the Amtrak is a great idea to help save the planet and allow you to have that hungover nap on the way back home!
From the Amtrak in STL, it would just be a short 20min Uber ride to the Ameristar.
Here is the link to the Amtrak line you would take to get to STL: https://www.amtrak.com/lincoln-service-missouri-river-runner-train
Typically,
The train runs TO STL FROM Dwight at 11:09AM or 6:42PM each day
The train runs FROM STL at 6:35AM and 2:55PM each day