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Wood with a vertical load is in compression, and a joint that has shoulders like a lap or a finger joint will be best, since strength is not relying entirely on the glue bond.

A member that is under shear, or side loading, is more difficult to make secure, but again, a long lap joint or finger joint will be best since the long grain glue bond is stronger in shear. I disagree, a half lap has only half board thickness in 2 places, and makes a weaker member for side load. we'll just agree to disagree.

End grain to end grain joinery has very little strength, if any and that would be from the glue alone, not from the wood structure. So minimize the end grain condition and increase the long grain area for a stronger joint.
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