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In the 8th game of the series1 between AlphaGo Zero and AlphaGo Lee the following position with a double ko at {A,C}×{13,14} arises: Position at start of double ko play On the next move AlphaGo Lee (Black) plays the double ko exchange A14-C13 before its next effective move at T15 and subsequent three effective moves; then AlphaGo Zero joins in the fun and also makes double ko exchanges before its effective moves. This continues until move 272; after 276 Black resigns.

I do not see the benefit in these exchanges as against immediately playing at T15 etc. Are these exchanges useful or merely something that their respective training never taught them how to do? If they are useful, what purpose do they serve?

1 See the article in Nature at https://www.nature.com/articles/nature24270#t1; the full text is not free but selected game records are, in the download at https://media.nature.com/original/nature-assets/nature/journal/v550/n7676/extref/nature24270-s2.zip

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There is a difference between the two semi-stable double ko positions, although a rather small one. C14 reduces the immediate number of liberties of the G13 leg. This means that black will have a free tempo when G13 runs out of liberties, if we assume that black can find a big enough ko threat to answer the C13 capture with C14 in order to force the B15 gote.

Assuming black still has a big enough ko threat when G13 runs out of liberties, the value of keeping the one liberty at C14 filled is most likely 1 point (turning a one point sente for white to a reverse-sente, as we can infer from what happens later in the game), so the two-move sequence of capturing the double ko at C13/C14 followed by an answer as A13/A14 has a (ko-related) miai value of 1 for both players. That explains why both players take the opportunity to capture this double ko whenever they can.

An other way to put it is to attribute an average of 4.5 liberties to the G13 group (alternating between 4 and 5), with white being able to force it up when they need it if black can't find a big enough ko threat.

  • Thanks, you have made some things a little clearer to me, though there is a lot I still do not understand, I fear, not least why Black resigns when he does, but also why Black is in a better place after 239@A14, 240@C13, 241@T15 than he would be with 239@T15 – after all, it (temporarily) gives White an extra liberty at C14. I note that White taking half the double ko threatens to remove a point at B12 and make points at A14, C14 and B15, while Black threatens to do the opposite. Of course, if Black connects at A13 or C13, B15 is not a point for White either way. – PJTraill Feb 27 '18 at 22:33
  • Ok, I realize I didn't pay close attention to what happens in the game. Playing 247 and canceling it with 251 does indeed seem useless, even though it does no harm. But B5 which comes right after that wastes a ko threat. So, I think black already realized the situation was hopeless and was just delaying the end of the game for all the other moves seemed closer to defeat. – Stéphane Gimenez Feb 28 '18 at 14:29

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