W wouldn't want to throw in to start the ko in any case; he knows that B will have to start the ko eventually (W can win by filling outside liberties, so eventually B will have to throw in at A9 and W will get to make the first capture without making a ko threat).

The ko is always direct for W, since W can ignore one threat and capture at B7. On the other hand, if B throws in at A9 immediately he has an approach ko and has to ignore two threats; if he plays D9 first, he only has to ignore one threat. -- So I can't figure out why the first solution would ever be better for B.

It seems to be the most favorable way and if white tries to set up ko with A8 instead of E5 as you suggest then white needs to find the first ko threat which seems to be to be a waste. (White will win if he fills all the outside liberties so black has to start the ko, if white starts, the ko is easier for black since white uses 1 more threat than he otherwise would).

Just FYI this thread will most likely be moved since this is Game analysis. (Study room is appropriate I think).

But perhaps that reasoning would only apply when black's A5 group would be unconditionally alive (or at least having sufficient liberties on the outside to kill white from the inside).

But if A5 were alive or has superfluous liberties, then Black kills unconditionally with A8. No need to risk a ko at all.

I did some counting in order to reproduce Bill magic.
From his diagrams we get:
B gets 15 points if B starts and B wins the ko b = 15
W gets 28 points if B starts and W wins the ko w₁ = -28
W gets 28 points if W starts w₂ = -28
So, maybe accidentally, here applies w₁=w₂=w
Bill has count c = -13_2/3 and temperature t = 14_1/3.
We find: b = c + 2t and w = c - t or inversed:
t = (b-w)/3 and c = (b + 2w)/3 = t + w
I won't try to explain the concept temperature. Too hot for me! Nor what if the w's are unequal.
edit: I don't care to much but the study group is the best place for this topic IMHO.

.... So when White is komaster the corner is worth 29 pts. for White.

:)
Understood. But I am trying to decypher your magics and it seems you only used 15 and -28 to calculate count and temperature.
BTW Are count and miai value the same concept?

When White is komaster Black is effectively dead. But when Black is komaster White takes one net move to kill (3d variation above), for a score of -28. Or Black takes two net moves to make and win the ko (1st variation), for a score of +15.

Each move in the ko gains on average (15 - (-28))/(2 + 1) = 43/3 = 14 1/3. The local count is -28 + 14 1/3 = -13 2/3.

Es claro?