Life In 19x19

looks fishy, but I can't totally explain it to me why, but taking on right (so, B's move is 1 sente and not 3 gote, so to say) may change how the game ends... But can't figure out the fundamental reasoning it may be so, doesn't seem right.

I believe the mistake is playing at d5 instead of taking at j4, though j4 could also be played instead of d1, since if black takes d1 white plays at d6. J4 nets one point and takes from black a move for one point whereas d5 nets white nothing but takes away a 2 point move. The first is better than the second because white has two moves at f8 and a5 that have follow up moves, so after black plays d5 white can do a sequence of three moves for one point instead of 2.

<Tenb> White 3 should make the one point at d6 instead [04\:01]
<Tenb> That way white gets the tedomari and wins by one point
<Tenb> d1 and j4 are miai so no need to hurry to them

Seems like move 7 should be played on the left edge.

This is too late, as the rest of the board is Miai now.

Change move 3 from D1 to D6. Then D1 and H5 pair off, and playing through some variations seems like white always gets the last move instead of black.

This took disappointingly much time for me, partly because I tried to do most of this in my head.

Yay!

Okay, useful fact learned: two 0.75 moves of the flavor where white leaves an 0.5 move but black terminates it immediately, plus an 0.5 move, equals miai.

Play D1. By the useful fact, A4, F9, and F3 add up to miai. So white wins because now he can get the last non-miai move by simply responding locally to black on each of the 1-point moves, since in both situations if black plays first he leaves behind a 1-point move that white then eats and leaves nothing.

Some further thinking about it results in the following things that I think are true:
* Compared to "fair", getting tedomari at temperature T prior to a drop in temperature to T' gives (T-T')/2 extra points. Useful for calibrating a sense of how bad you should feel when your opponent steals a big move right out from under you.

* Meaning that compared to "opponent gets tedomari" at temperature T, getting tedomari prior to a drop in temperature to T' gives T-T' extra points.

* Going back over the variations in both puzzles, indeed in the jigo variations, black gets the last 1-point move *and* the last 0.75-point move, *and* the last 0.5-point move. Whereas in the white-winning variations, white gets the last one of all of these. Indeed, this sums to a difference of 1 point.

* So to rephrase, when all moves of temperature less than T are miai and your opponent gets the last move of temperature T, you get the maximally bad case. Because due to miainess, he also gets the last move of temperature T' for all T' < T. If instead of that you got one more final move of temperature T, you get all of them instead. Then, you can either do the accounting of the gain by adding T more points immediately because all the miai below cancels out, or you can do the accounting by adding (T-T') + (T'-T'') + (T''-T''') + ... + (T'^n - 0) points for winning every subsequent tedomari, which also sums up to T.

* Wait a minute. The game's score aside from komi has to be an integer...

* Okay, I think this means (absent any kos) you can completely ignore all moves whose values are less than 1 point for any possible endgame puzzle like this and focus only on who gets the last 1-point or greater move. This shortens the necessary reading a little bit.

Why is this? Well, the only case where you gain a whole point from getting the last 1-point move is when it also switches every smaller-than-1-point tedomari from against-you to favoring-you. Which is precisely when everything below is miai. Anything short of this fails to produce a whole point of improvement, meaning that it must produce 0 points of improvement since the difference in final outcomes must be an integer.

But of course, by the very fact that it's a puzzle, we know that it must matter. A puzzle where your choice can have no effect on the result would be boring. So it must be the case that the puzzle is set up so that everything below 1 point is miai.

Moreover, the integerness of the game's score also means that if you want to verify that it does matter who gets the last 1-point move (that is, you don't want to rely on the knowledge that the puzzle is a puzzle), all you have to do is play through *one* of the possible variations of moves with values less than 1 point and watch who gets the last move of each temperature. If both players share in the 1-point-or-smaller tedomari to any degree, then by integerness every other variation necessarily gives the same result and it doesn't matter. Otherwise it does matter.

Of course, ko could still mess this up.

Yay! Okay, time for bed.