Private data is cleared but Flash apps remember settings. How?

I always clear all my private data when I close Firefox yet I have noticed that some Flash games are able to remember my previous state when I play them again. Note: I do not log in or explicitly identify myself in any way. How is this possible? Does Flash have a private cache or custom cookies that it is able to store on my hard drive that Firefox does not clear?

The only other alternative that I can think of is that the server is identifying me via my IP address but that seems like a lot of work and a bit of invasion of privacy. Does anybody know the answer?

I am using Firefox 3.0b5 on 64-bit Ubuntu 8.04.
The application that handles Flash in my copy of Firefox is "Shockwave Flash" and right-clicking a Flash applet identifies the version as "Adobe Flash Player 9".

Thanks.