I agree with what everyone else has already suggested.
Pit finder gets 1st pick, and then alternate picks back and forth, unless for example the non pit finder secured the permission, or did most of the work, or drove you two hours to the site, or some other reason that you might want to give them a crack at first pick, by flipping a coin or some other way of determining who picks first.
If your intent is to try to get the finds divided as evenly as possible, I would also suggest that you alternate who gets 1st pick each "picking round" so to speak. It goes without saying that the lower the number the pick, the better it is (eg. 1st pick is lower and better than 2nd pick). For example, in a scenario where you find 10 pickable items, if you were to take 1st pick and then alternate back and forth with one other person, you would be getting picks number 1,3,5,7,9, and your buddy would be getting 2,4,6,8,10. Your picks add up together to a total of 25, and your buddies to 30. If you were to alternate the 1st pick each picking round you would get picks 1,4,5,8,9 and your buddy would get 2,3,6,7,10 this way your total is 27 and your buddies 28. This really comes into play when you have more than two people involved in a dig and split. I have been on a few digs where we had to split everything 6 ways, and I can tell you that when the first person in a six way split gets picks number 1, 7, 13, 19 etc. and the sixth person gets picks 6, 12, 18, 24 etc. the disparity is obvious, and alternating who picks first each round helps even things out.
Good luck in the fire pit!
