This will be built in Central California, so no need to worry about snow. Rain and wind are the major weather effectors.
The Joists are 20' feet long and will be supported by 6"x6" posts/beams that are 18' from the house. The posts are 7' apart. The pitch will be around 1 to 5 (ie 1" drop for every 5" of run), or about 4' for the length of the patio. In other words the ledger will be bolted to the house about 4' higher that the posts/beams holding up the other end.
On the ledger board, how many lag bolts should I put in and how far should they go into the 2"x4" framing of the house. I want enough to properly support the structure, but I obviously don't want to weaken the house any.