When you do a Stage1, you don't do a LL test, but P-1 factoring.

As a result, you can only find factors with this test (and thus prove the number non-prime). A LL test is done after Stage2 of P-1 factoring (which can even done with ~20 MB RAM - with lower bounds and hence less chance of success, though).

Concerning the chances, they are said to be near 1/250,000 - depending on factoring attempts already done for that number. So, every completed LL test gives you $0.20 in average (mean value).