So I was robbed today! Theft from my hotel room

I have spent hundreds of nights in hotels and apartments all over the world in the last 10 years. One thing that was always a myth to me was being robbed.

Last night I stayed in a Hyatt hotel in California. I'm intentionally not disclosing the location as I want to first see how the hotel is handling the situation.

Now I wasn't mugged by my wallet and computer bag were stolen from my hotel room. Fortunately neither my laptop nor phone were taken. Unfortunately the wallet had >$1,000 in cash in it. I know I should not do it but it was a special situation.

I only realized that both were missing upon check out today. I immediately spoke to the front desk and while searching for the How-To's online, suggested that the police be called immediately. To my surprise a very friendly officer showed up in seconds. He patiently walked with me through every step and I'm 100% certain it was taken from the room.

The GM was not reachable so 'Director of Housekeeping' (to be honest wasn't sure that this job title existed) took friendly care of me and the interaction with the police. The hotel pulled the key log and concluded that only housekeeping entered the room (on my request 3 times last night). I have a definitive suspect and how the person might have loped off my bag with the wallet but I'm not sure how I ever gonna prove it. The police gently explained to me that my chances of item recovery were not exactly huge but he mentioned that theft in this part of town is really, really rare.

I spent my time today calling the credit card companies for a card re-issuance.

Now the 'Director of Housekeeping' promised that I will receive a call tomorrow for the GM to assess the situation. She mentioned the hotel has an insurance policy against theft and cautiously implied that, if covered, I would be made whole.

From what I read each property handles the situation differently. So what are my options and my chances to get my bag and cash value back at all? Did it ever happen to you? What should I aim for?