College World Series - Hotel Question

I will be going to the Championship series with my father -- neither of us have ever been to the CWS before. Hotel prices already seem pretty steep (ie $500-1,000 per night roughly). Is there any rationale behind waiting until teams have been eliminated and inevitably more rooms become available? Will prices therefore drop closer to the championship series? Or are prices I see today pretty much what I will ultimately pay regardless? Peace of mind is great, but if there's a reason to hold off until closer to the championship series, I'll certainly do that. Sorry for the noob question, but I haven't seen this question asked before - just general inquiries/opening rounds/duration of CWS.

Thanks in advance for any tips!