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 Post subject: benson rules
Post #1 Posted: Mon Apr 05, 2021 4:13 am 
Lives with ko

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Hi, I've been starting to read some maths papers on Go recently, such as lambda search, Wolfe. I'd pretty much only read Feldmann's bestiary before and a Berlekamp -?-Spight paper on thermography and skimming a few others. I hope to read more.

I have come to Benson's classical paper on unconditional life: ... benson.pdf.

In '6. Safety is Best', he adds 'Rule 3 (scoring)': (my wording)

At the end of the game, all groups without two (pass-alive) eyes are considered dead and become the opponent's prisoners.

A nice advantage of this rule is his lemma 5 and paragraph following it. Though I don't think the paragraph following is actually a proof that it is unhelpful to kill your own living groups. Note that his next paragraph comments that in certain (I think most) rulesets, sometimes best play is to kill your own unconditionally alive groups (e.g. in order to kill the opponent's moonshine life).

Do I understand correctly that under this rule, seki stones are dead? In fact, they are still "seki" in the sense that it is a mistake for either player to add a move there, but they are very different in terms of scoring. All the stones involved are treated as prisoners for the other side. If you have more stones in the seki, you lose points.

(NB Benson uses territory scoring. In area scoring, you get an essentially equivalent result (as usual) by not counting the stones nor dame involved in such a seki. The parity of neutral seki points affects the score though.)

1. Is this difference to standard rulesets why we don't use Benson rules or even discuss them?
2. Is there a nice way to modify Benson rules to keep both seki and the "no point killing own groups" ?(I don't see a way)
3. What else do you suggest I read?

NB: Also, as far as I can tell, he has proved safe = unconditional life (in his definition). This means each unsafe block can be captured if you keep passing. But I don't think he has proved that the set of all unsafe blocks can be captured simultaneously if you keep passing, which despite sounding obvious, took me a page to (I think) prove (but it is only true if ko situations are ignored). Though I can probably shorten it with a better understanding.

NB: blocks (Benson)=chains

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