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Dieter: First, I really like how you have worked out a simplified treatment of the endgame. Then I wondered if it even mattered just that bit. The BOSE in this example helps to reduce the risk of making a 1 point error, avoiding the full calculation of the endgame. Games hinging on a 1 point error are rather rare. The error is wider on the gote side, so the safe and quick argument is "reverse sente first", unless the swing points included in the reverse sente are wide off the swing points in the gote.
So, sente first, big reverse sente next, big gote next, small reverse sente next, small gote last, looks like a very useful heuristic. The difficulty of judging sente remains anyway, especially when calling in mutual damage.
I think efforts in the endgame should be directed as much as possible towards endgame tesuji, which make at least 1 point difference per situation. This truly yields points regardless of the whole board. I think if one consistently applies good endgame technique, one can afford a couple of errors in the order of execution.
My meta advice would sound like this:
Agreed, endgame tesuji is a much more effective way of gaining points that optimizing the move order.
Even then, knowing (or at least having a hunch of) the value of getting sente is useful when deciding which tesuji to apply in a given situation; for example you may sometimes have to choose between a 10 point gote move and a 4 point sente tesuji, which makes the 10 point move disappear. Without knowing the value of tenuki, it is really hard to say whether it is a good idea to throw away the 6 points in order to get sente.
--Bass
... in which case BOSE says: if half the next gote is larger than (10-4)=6 , play the sente tesuji. But that would make the next gote 12 points, 2 points larger than the current gote. So, the sente tesuji only comes into consideration if it reduces the 10 point gote to something bigger than 10/2=5, which reverts to the old sente = 2*gote rule of thumb.
Tesujis which turn a big gote into a small sente, are not necessarily tesuji. Turning a big gote into a slightly smaller sente, or into a bigger gote, those are truly tesujis which make a difference. I was thinking of those.
Don't get me wrong: I like the exercise and your ideas a lot.
Well, despite heavy editing on Endgame Tesuji (everyone, please add some more!) I believe that the struggle over initiative is the single most important issue for improving your endgame (and I am happy that Basic endgame theory reflects this). After all the problem with a "sente first" heuristic starts with "sente": Which move is sente when?
But back to BOSE, it boils down to the question how much is sente worth given all the simplification... and isn't it: 1st move size (with an odd number of plays remaining) - 2nd move size (odd number of plays remaining) + 3rd - 4th etc. that is a value between 0 and the current move size. As the number of remaining moves is supposed to be random, from here you go with statistics, reaching the half value of largest gote sentence. (Please note the relation to komi and supposed first move value.)