Looking at Gate 10's website, it notes that the online listing for GenCon is all closed and done, but implies that there is still parking available on a first come, first served basis.

Does someone getting into Indy in the early afternoon on Wednesday have a sporting chance at getting a spot, or is that just a pipe dream? If they will let you in, will they let you get a spot for the weekend, or are you on a day by day basis?

Wondering same.  Need to park my car for the entire weekend.

I'd just call them and ask:

317.737.2036

I called them today to add Tuesday parking (I did the same last year) and to see if I could purchase an additional three day pass for friends. They have space available but you will have to show up in person and it will be in the out lots

To follow up, as of now G10 does still have parking for the weekend.

Parking on weekends may be more difficult heardle online.

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