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 Post subject: Move I've played for a few years without understanding it.
Post #1 Posted: Mon May 02, 2011 12:27 pm 
Gosei
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When I play handicap games, a lot of times I like to play the two-space high approach against the 4-4, like such:
Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . b . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . c . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . a . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]

I realize that, in comparison to the standard approach against the 4-4, this approach is lighter. However, after Black plays a move such as :b1: , which is common, I find myself with the strange task of trying to making good use of the move that I just played. To me the move I played already feels out of place and sometimes I try to mess the situation up by playing a move like 'a'. Usually though I just take tenuki and play elsewhere, but a lot of times I find the stone just doesn't work for me and it irks me that I let Black play a cash move like :b1: in exchange for a move I don't know how to use.

I feel that trying to make an extension along the side with a move like 'b' is incorrect, since B can slide and suck the base away with 'c' anyways. To be honest, I think the only reason I even play this approach move is because a lot of times I've noticed the opponent react slightly perplexed to it, as if it's a move they haven't seen much of before (which I suppose is also why I enjoy playing hamete, or unusual openings). That and because I've seen it in a lot of high-level handicap games...don't copy moves you don't understand, they said.

So I'd like to ask:

1. What is the follow-up to this move if Black responds with :b1: , and how does it make the approach move meaningful?
2. Is :b1: even the strongest response to the high approach?
3. Why is this move typically seen in handicap games, but not in even games? <- Highest priority question.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #2 Posted: Mon May 02, 2011 1:12 pm 
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Araban wrote:

1. What is the follow-up to this move if Black responds with :b1: , and how does it make the approach move meaningful?
2. Is :b1: even the strongest response to the high approach?
3. Why is this move typically seen in handicap games, but not in even games? <- Highest priority question.


Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . a . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . B . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . b . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


I think this is the strongest response, given an empty board, but when I've seen this in handicap games, I don't think I've usually seen it as the first move.

It seems to me, that the use of this move is that it lets you come back in and hammer the corner with a move like b, while still getting a presence on the outside.

It seems like move 2 for white should generally just be tenuki. The slide at "a" is good, but you can let it go if you can take out the corner behind it, and you're light enough that they'd have to play 2 moves on the second and 3rd line to consolidate just the side.

EDIT:

Basically:
3. it's a fast way to get a presence, and still leave invasions behind. But if we're in an even game,
we're less likely to screw up a response to a corner invasion, and we wouldn't attack the light stone in the same way.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #3 Posted: Mon May 02, 2011 1:53 pm 
Gosei
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Click Here To Show Diagram Code
[go]$$Wc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . 2 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . B . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


I just know this move as a follow-up to :w1: . Idea is most likely to "attack" the marked black stone and to play a non-standard-move for broader and unkown variations.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #4 Posted: Tue May 03, 2011 2:10 am 
Oza

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Quote:
I realize that, in comparison to the standard approach against the 4-4, this approach is lighter.


No. A move is not light or heavy. It is the resulting group that may be light or heavy. To say a move is light is to imply you have decided in advance that you want a light group. Horses and carts and all that.

What the approach move is above all else is a probe. Once you see how Black responds, then you decide whether that makes your stones light or heavy.

Black 1 is OK locally but a White pro will be content to see it (for the reasons shapenaji mentioned, plus the fact that it does not relate easily to any other stones or exploit the inherent attacking nature of the 4-4 stone). Having made Black play a submissive move here he will typically play elsewhere now. The same sort of thinking applies when Black plays 5-2 to the 6-3 approach.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #5 Posted: Tue May 03, 2011 2:39 am 
Oza
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GoGoD has more than a thousand examples of the 2-space high approach. Ota Yuzo used it against Shusaku in 2-stone games in the 1840's and all sorts of people have used it in the mean time. There are only 20-some examples of Black answering with the diagonal move and its winning percentage is poor. Since the 2-space high approach does not threaten to slide into the corner, the diagonal play protects against a threat that does not exist and still leaves the corner wide open from the other side. It is clearly inconsistent. White can consider the initial play a successful kikashi and play elsewhere. The normal response by Black is a simple 1-space jump. It appears in about half the examples in GoGoD. The most severe choice by Black is a pincer. Again, this is related to the lack of a corner threat for the initial approach. If Black prevents White from making something on the side by pincering, what really is the purpose of the original approach? Basically in a handicap game the initial approach play is just a probe. It has no compelling, natural follow up. I think the point is normally to test Black and then play elsewhere, without worrying too much that Black will be able to punish such a light stone before White comes back to it later.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #6 Posted: Tue May 03, 2011 4:03 am 
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I think that the strongest response is this:

Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . a . . |
$$| . . . X . . . . . , . . . 1 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


This is actually a development for Black, as it works with the centre and lower left stone. In contrast, `a` would just be getting forced.

White will now be very inclined to add another move on the right, to build a base. In answer to 'a', on the other hand, he could treat this stone as kikashi.

I think that the comparison of :b1: and 'a' is important for the assessment of this situation.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #7 Posted: Tue May 03, 2011 4:09 am 
Honinbo

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I would say that the benefit of playing a two space high approach is to use it later to attack a group. It's obvious to say it, but the move is clearly not territorial. In order to get as much benefit as playing territorially, then, it seems natural that you just need to use the stone for fighting and/or central power.

If you are worried about black slides and such, just play a more territorial move to begin with.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #8 Posted: Tue May 03, 2011 4:47 am 
Tengen
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i think i have more experience in handycap game than most here.
1. IMO, knight approach is better move locally.
but since it is a handycap game it really doesnt matter what you play.
if i was white i would answer as below to leave 3-3 invasion open.
Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . 4 . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . b . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . c . |
$$| . . . . . . . . . . . . . . . . 2 . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . X . . . . . , . . . 3 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]

or as below.
Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . b . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . c . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . X . . . . . , . . . 2 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]

2 & 3. yes it is the strongest move but i wouldnt play that if i was black.
im pretty sure that i would fall behind if it was an even game playing such move.
it is effective in handycap game because it simplify the board and limit the variation.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #9 Posted: Tue May 03, 2011 1:06 pm 
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Magicwand wrote:
If I was White, I would answer as below to leave the 3-3 invasion open:
Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . 4 . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . b . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . c . |
$$| . . . . . . . . . . . . . . . . 2 . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . X . . . . . , . . . 3 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]



I do not like this :w2: because it gives Black the opportunity to play :b3: after all. It feels to me like this time it is White who got forced by the :b1: -- :w2: exchange. Also, the marked white stone looks misplaced now---imagine having played :w2: first, Black kicks, and White plays... kosumi?!

Quote:
or as below:
Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . b . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . W . c . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . X . . . . . , . . . 2 . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]



This follows the proverb "the enemy's point is my point". I think that it is a strong move, but perhaps it is better to play somewhere different altogether for now, as it is unclear that you want a second high and light move in this part.

Quote:
2 @ 3: yes, it is the strongest move, but I wouldn't play that if I was Black.
I'm pretty sure that I would fall behind if it was an even game playing such a move.


If it is the strongest move, then you would not fall behind (but you might intend a different meaning of "strong", as in "aggressive" or "forceful").

Anyway, I do not think that you can compare this board with a non-handicap board. The situation is just fundamentally different. I think that in most early situations on an even-game board, the one-point jump is still the strongest (as in "best") answer. However, the two-point high approach move would most likely be a special measure for an uncommon case, so one cannot generalize this.

Quote:
It is effective in handicap games because it simplifies the board and limits the variations.


You seem to imply that it is conceding points for security, relying on the handicap to scrape out a victory despite suboptimal moves. I do not think so.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #10 Posted: Tue May 03, 2011 1:13 pm 
Judan

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I have only looked at the diagrams so far and they all miss the point of the position.

Click Here To Show Diagram Code
[go]$$Bc
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . d . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . c . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . b W . . . |
$$| . . . . . . . . . . . . . . a . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


The big moves are a, b, c or d. In high handicap games, forget about joseki and small corners. What matters is global thinking. Let White have the corners and the sides - Black wins big. Or play elsewhere in the greater empty part of the board - Black wins big.

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 Post subject: Re: Move I've played for a few years without understanding i
Post #11 Posted: Tue May 03, 2011 1:43 pm 
Tengen
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Harleqin wrote:
If it is the strongest move, then you would not fall behind (but you might intend a different meaning of "strong", as in "aggressive" or "forceful").

Anyway, I do not think that you can compare this board with a non-handicap board. The situation is just fundamentally different. I think that in most early situations on an even-game board, the one-point jump is still the strongest (as in "best") answer. However, the two-point high approach move would most likely be a special measure for an uncommon case, so one cannot generalize this.

i will rephrase: "aggressive" then you should rephrase also to "optimal" to avoid confusion.

if you are playing 5 stone handycap..it really dont make any differece what you play in the beginning long as it is good.

IMO my selected move is fine in this case. YES! that is how i play. i play my opponent not looking for optimal move.

Harleqin wrote:
You seem to imply that it is conceding points for security, relying on the handicap to scrape out a victory despite suboptimal moves. I do not think so.

yes that is what i am saying. and i bet you do same upto certain degree.

how about i challenge you to Markovich game? even game.
i will give you chance to prove that you are stong enough to comment on my game.

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The greater the unknown"

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 Post subject: Re: Move I've played for a few years without understanding i
Post #12 Posted: Tue May 03, 2011 3:40 pm 
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Magicwand wrote:
Harleqin wrote:
You seem to imply that it is conceding points for security, relying on the handicap to scrape out a victory despite suboptimal moves. I do not think so.

yes that is what i am saying. and i bet you do same upto certain degree.

how about i challenge you to Markovich game? even game.
i will give you chance to prove that you are stong enough to comment on my game.


This is a logical fallacy, from wikipedia:

Argumentum Ad Verecundiam:

Source A says that p is true.
Source A is authoritative.
Therefore, p is true.

Whether or not you are a strong player has only a limited connection to this particular position. I recommend arguing with logic rather than rank.

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Post #13 Posted: Tue May 03, 2011 5:02 pm 
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I agree with what Shapenaji writes, but I intend to take you up on that game offer anyway, Magicwand (not that it would prove anything about what I have written). However, I do not have much regular time to devote to this game at the moment, and I will be on vacation end of may till mid of june. It should be better after that, but if you think that frequent pauses are OK, we can start tomorrow.

Playing the board has the advantage that I need not care who sits on the other side. This also holds for discussions, by the way. ;-)

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Post #14 Posted: Tue May 03, 2011 5:50 pm 
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shapenaji wrote:
...

This is a logical fallacy, from wikipedia:

Argumentum Ad Verecundiam:

Source A says that p is true.
Source A is authoritative.
Therefore, p is true.

Whether or not you are a strong player has only a limited connection to this particular position. I recommend arguing with logic rather than rank.



I can see your point, but I think it's worth considering WHY "source A" is authoritative in a given situation. It's possible that there's a connection between authority and knowledge of board positions in this situation.

The fact that someone has authority, in itself, doesn't show anything. But in this case, the authority is an earned rank. It could be worth it to consider what they are saying against your own thoughts.

For example, just because a pro says something is true doesn't mean it is. But I have faith in a pro's ability, so I should still consider what they have to say. That's because their "authority" is the result of having proved themselves to be knowledgeable on the go board.

That's because, in my opinion, the authority is the result of knowledge/skill.

I think that "Argumentum Ad Verecundiam" is better applied when someone is given authority by a totally unrelated reason (eg. Obama doesn't play go, but he's president of the USA, so let's listen to his advice on tsumego).

Again, I don't think that what a pro says is necessarily gospel when it comes to go, but at my current rank, it's more likely that I am wrong than they... So it is more flexible of me to analytically evaluate the opinion of a higher ranked player (of course, accepting such advice blindly can't be logical).

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Post #15 Posted: Tue May 03, 2011 8:12 pm 
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Kirby: I considered posting a similar point that while the argument from authority is a logical fallacy, it's not always unreasonable.

But in the present context, what's gained by it? We have several players of various strengths commenting on the position. Even if Magicwand is stronger than Harlequin, why cut off the discussion?

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Post #16 Posted: Tue May 03, 2011 8:32 pm 
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Well, magicwand's comment seemed to suggest that good ideas can't come from a lower rank, or that more experienced players can't be wrong about these sorts of things. In that case, he is using his authority as someone who has a proficiency for winning games to justify his particular view on this position. In that case, the authority is misplaced.

It was primarily that MW seemed to be cutting off discussion. He is welcome to say "This move has this problem..." or "Here's what I see...", but simply saying "If you can beat me then you can consider alternatives to my judgment on this matter" just seems incredibly wrong-headed.

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Post #17 Posted: Tue May 03, 2011 8:38 pm 
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Kirby wrote:

The fact that someone has authority, in itself, doesn't show anything. But in this case, the authority is an earned rank. It could be worth it to consider what they are saying against your own thoughts.

For example, just because a pro says something is true doesn't mean it is. But I have faith in a pro's ability, so I should still consider what they have to say. That's because their "authority" is the result of having proved themselves to be knowledgeable on the go board.

That's because, in my opinion, the authority is the result of knowledge/skill.



I don't think it has an effect on my thoughts at all. My experience should lend itself to explaining my position. I don't need to resort to my rank to prove something, but rather to the knowledge that I gained in getting that rank.

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Post #18 Posted: Tue May 03, 2011 8:45 pm 
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Appeal to authority is *never* a valid argument, even if the authority is knowledgeable in the domain; if the authority has an argument, then you can evaluate the argument. If the authority does not have an argument, then what reason do we have to consider them an authority?

However, given that this is go, a lot of knowledge strong players have is not really available to them in a form that enables them to express it to us. It's like driving a stick; you can explain feathering the clutch all day long but people won't actually understand it (even if they parrot back everything you said) until they go out and learn to do it. High-speed cameras in sports have shown that athletes aren't actually doing the things they say they are doing. So I don't think it's necessarily fair to accuse magicwand of an appeal to authority.

It certainly sounds like he's playing irrationally to me. But it also sounds like he's claiming that such play is optimized for beating players a few stones weaker than him, at a higher handicap than they really should have. And I don't find that too hard to believe.

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Post #19 Posted: Tue May 03, 2011 8:49 pm 
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Post #20 Posted: Tue May 03, 2011 10:06 pm 
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Click Here To Show Diagram Code
[go]$$W
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
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$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . 1 . . . . . X . . . . . 2 . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . O . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . X . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


Now the white stone is heavy and the previous exchange has become aji keshi. Therefore tenuki was wrong.

Click Here To Show Diagram Code
[go]$$W
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . O . . . |
$$| . . . . . . . . . . . . . . 2 . . . . |
$$| . . . . . . . . . . . . . . . . X . . |
$$| . . . X . . . . . , . . 1 . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


Even if White plays the lightest double approach, Black cuts and gets a double attack with which he uses his handicap stones. Therefore W cannot do that.
Click Here To Show Diagram Code
[go]$$W
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . , . . . . . X . . . . . , . . . |
$$| . . . . . . . . . . . . . . . 2 . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . O . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . X . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


Defending the stone is correct but overextending means Black can cut and gets a double attack using his handicap stones well. So 1 is wrong.

Click Here To Show Diagram Code
[go]$$W
$$-------------------------------------
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . 1 . . |
$$| . . . , . . . . . X . . . . . a . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . O . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . X . . |
$$| . . . X . . . . . , . . . . . X . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$| . . . . . . . . . . . . . . . . . . . |
$$-------------------------------------[/go]


This is the farthest extension White can play without making an overplay. So this or a is correct.

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