I might need two umbrellas if I were a Siamese twin or pay twice to own my home sooner. And I just happen to run multiple firewalls in the intranet.

To answer the question "Am I invisible?" NO, not ever!

Consider an ISP which responds to probes to unallocated IP's with ICMP's. In such a case, where your box drops probes silent and stealthy-like, it is actually screaming "Here I AM."

Do try to turn off all unnecessary services regardless of how many walls you want to employ. A misdirected tcp packet to a closed port ain't gonna give'm nothing but an tcp reset anyhow. I used to head on over to G R C dot C0M and run the "Probe My Ports" thingy way back when. Nowadays I like to be seen by all them Internet peepin' zombies. Seein' their I-balls swell and that lo-brawl shell is good clean fun.

Oh and don't forget to pay attention to what your wall allows out. It can be just as important as what you do or don't let in. I think G R C dot C0M had some kinda "Leak Test" too.