An 8 to 1 ratio scarf joint will give the strength of the original wood. However, it is hard to cut an accurate flat bevel at an 8:1 slope, and even harder to clamp while gluing. In reality, a stepped lap joint is usually used. For your situation, four 1/8" deep steps, each 1 1/4" wide, will give the right ratio and provide plenty of glue surface for strength. Joining two 18" boards would result in one 31" board (5" overlap for a 5/8" thick board).
A lot of work to stretch the boards, but may be worth it if they are going to be door stiles, frame/panel construction, etc. Do the deepest step first to give the most stable surface for the next cut.
If you are going to use them for face frames, etc, where a lot of end-to-end strength is not important, then a 1" lap joint would probably suffice.
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