Joining two 10 ft 6x6s of dry pressure treated with half lap (not tapered) and 3/8" lag bolts with washers (not machine bolts). For strength, what is the optimal length of half lap and what is the optimal ratio of thicknesses? Would it be different for 4x4s?
In a "half" lap joint, the thickness should always be half of the material for the most strength. You're reducing the strength of the board because you're removing thickness, and the joint will only be as strong as the weakest piece. If you made the thickness ratio 25%/75%, then the 25% side would be the weakest.
Lap joints are used often for 90 degree joints, and in this case, the length of the joint is equal to the width of the board so all the edges match up. In a end-to-end joint, the same ratio can be used to provide adequate gluing, nailing, or bolting area. Less length might not provide enough area for bolts, and more area isn't going to add more strength because the weak point still comes from the fact that you just cut out half the thickness of the board.