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Joseki 4-4, low approach, low extension, contact variation

https://www.lifein19x19.com/viewtopic.php?t=16191

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Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 9:38 am
by Kirby
dfan wrote: Others are allowed to think differently!
Thanks. I do, and you are free to disagree as well :-)
Uberdude wrote: Plus, isn’t the success of AlphaGo, LeelaZero etc evidence this approach works?
It's different. These AIs are not calculating winrate from a single localized position. They calculate from an entire board position.

If the local situation was good for black, but black died across the rest of the board, the winrate wouldn't be good.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 9:44 am
by Kirby
To be clear, if Elf says a> b on an otherwise empty board (maybe it does), I think the evidence is much stronger than some ad hoc stats on a few hundred human games with varying global positions.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 9:58 am
by Uberdude
Kirby wrote:
Uberdude wrote: Plus, isn’t the success of AlphaGo, LeelaZero etc evidence this approach works?
It's different. These AIs are not calculating winrate from a single localized position. They calculate from an entire board position.
I'm not talking about how, when running AG/LZ, it can give you a winrate for a whole board positon. I am talking about the training process: how does information about what moves are good and what moves are bad get fed into and update the neural networks? The basic premise of AG/LZ is:
- here's a game I played against myself
- pick a random move, say 67
- Did player of move 67 win this game?
- - Yes: 67 was more likely to be better than the average goodness of moves I play, update network to do more like it
- - No: 67 was more likely to be worse than the average goodness of moves I play, update network to do less like it
This only works if the assumption there was a causal link, however faint, between the goodness/badness of move 67 and whether or not the player of it won the game, is valid.
Kirby wrote: If the local situation was good for black, but black died across the rest of the board, the winrate wouldn't be good.
Do you think it is more likely for black to have died somewhere else on the board when black descends at 'a', compared to when black pushes at 'b'? On the absence of any evidence to believe such a bias, my default position is to think those are equally likely.

Bayesian Bill to the rescue?!

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 11:05 am
by Kirby
I agree with what you say here, Uberdude, but I don't think it's a fair comparison to take AlphaGo, which has trained on thousands or maybe millions of games to build up a sophisticated network that can give you win rates, and to then compare it to the OP here, which only does an analysis on a single local position, and notes a small statistical difference across a few hundred games.

Making AlphaGo would have been a lot simpler if the model were that dumb.

Last week, when I skipped going to the gym, I was 100% more likely to eat at the Mexican restaurant down the street. It must mean that skipping the gym means I'm destined to eat Mexican food on that day. My sample size is 1.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 11:14 am
by Gomoto
Kirby wrote:8% win rate difference from a handful of human games doesn't seem like much evidence to make much of a point about a single move out of hundreds that determined the result of the game.
And what is your take on the choice between a and b? :)
Click Here To Show Diagram Code
[go]$$B
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . O O O . . . . .
$$ | . a X O X O . . . .
$$ | . . . X X b . . . ,
$$ | . . . . . . . . . .
$$ | . . X . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 11:15 am
by Kirby
Gomoto wrote:
Kirby wrote:8% win rate difference from a handful of human games doesn't seem like much evidence to make much of a point about a single move out of hundreds that determined the result of the game.
And what is your take on the choice between a and b? :)
What is the rest of the board like?

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 7:15 pm
by MikeKyle
On the theoretical discussion:
Are the points being made here muttually exclusive?
Can't we say that a big swing observed in a tool like waltheri is a really interesting observation that suggests that b is a move that we should take a closer look at, but also that we need to do more work because the method has validity issues that stop it being conclusive?
As ever in go, getting closer to the answer seems to require a lot of work.
On a vs b:

First, I didn't see anyone address this:
Kirby wrote:To be clear, if Elf says a> b on an otherwise empty board (maybe it does), I think the evidence is much stronger than some ad hoc stats on a few hundred human games with varying global positions.
Personally I don't really like this methodology. I know it's the clasical way of formulating joseki, but it doesn't seem quite relevant/what the bots were built to do. The bots really really like the first few moves in each corner, which means that i think joseki questions posed to bots in this way will get answers that are dominated by trying to take sente at all costs. As a result, I think that studying joseki with bots on an empty board would give you different patterns to real games.
It's easy to do though:
Elf v1 wants to tenuki instead of a or b.
a is a -13.4% mistake
b is a -3.1% mistake
(both on just over 35k playouts)
The reason for this seems to be that in this specific unusual case, a is not sente (white will take an empty corner), but b is. In many real game whole board situations a seems pretty sente though
My default response to a problem is "How can I throw some data at this problem".
I've built some automation that uses patern searching and GRP to gather data to answer the question 'When a human pro chooses to play this move in a game, how does AI feel that it effects the win%'. I set it to work on both a and b
Method:
I sampled 50 recent games featuring a and 44 recent games including b (supposed to be 50 of each, my error). Still small samples, but ritcher data from each if you trust elf. Grp allows me to skip straight to the relevant moves of the relevant games where these paterns happen, estimate the win% with elf before the move, estimate the win% after and output all this into a nice spreadsheet. I also get to look through the alternative moves.
for a:
Sample size: 50
(ie. 50 different whole board positions in which a human pro chose to play 'a')
average swing: -1.63%
elf agreed with the pro move: 32/50
elf thought that 'b' was a better move than 'a': 11/50
Win % before Win % after swing
56.66% 53.10% -3.56%
65.79% 50.26% -15.53%
9.82% 8.50% -1.32%
56.28% 55.92% -0.36%
48.00% 46.23% -1.77%
49.11% 46.91% -2.20%
54.92% 54.40% -0.52%
44.15% 44.67% 0.52%
42.38% 42.14% -0.24%
42.63% 40.41% -2.22%
53.89% 53.16% -0.73%
52.30% 52.50% 0.20%
51.27% 51.88% 0.61%
73.36% 70.54% -2.82%
53.69% 53.98% 0.29%
0.22% 0.21% -0.01%
45.53% 42.91% -2.62%
55.43% 55.22% -0.21%
51.40% 52.06% 0.66%
55.98% 56.22% 0.24%
39.47% 40.00% 0.53%
42.74% 42.63% -0.11%
58.98% 58.50% -0.48%
36.19% 36.54% 0.35%
99.61% 99.57% -0.04%
48.43% 45.03% -3.40%
99.67% 99.65% -0.02%
56.32% 56.78% 0.46%
47.39% 45.32% -2.07%
52.67% 52.21% -0.46%
22.91% 19.38% -3.53%
47.36% 46.62% -0.74%
47.21% 45.35% -1.86%
50.80% 43.49% -7.31%
52.02% 51.45% -0.57%
54.15% 52.92% -1.23%
50.52% 49.88% -0.64%
40.40% 32.34% -8.06%
45.24% 45.32% 0.08%
49.80% 49.22% -0.58%
51.06% 49.45% -1.61%
16.50% 15.99% -0.51%
44.66% 44.85% 0.19%
36.08% 29.67% -6.41%
59.21% 54.58% -4.63%
53.77% 54.78% 1.01%
51.84% 48.68% -3.16%
51.28% 50.36% -0.92%
52.64% 52.32% -0.32%
49.69% 46.07% -3.62%
for b
Sample size: 44
(ie. 44 different whole board positions in which a human pro chose to play 'b')
average swing: -2.43%
elf agreed with the pro move: 19/44
elf thought that 'a' was a better move than 'b':18/44
Win % before Win % after swing
99.63% 99.60% -0.03%
37.00% 34.52% -2.48%
37.00% 34.10% -2.90%
38.86% 36.96% -1.90%
58.10% 51.14% -6.96%
36.22% 32.73% -3.49%
14.15% 14.47% 0.32%
82.28% 82.02% -0.26%
72.07% 72.35% 0.28%
64.86% 58.24% -6.62%
61.06% 55.65% -5.41%
49.61% 49.15% -0.46%
40.49% 39.44% -1.05%
50.18% 48.12% -2.06%
44.00% 43.98% -0.02%
62.17% 62.37% 0.20%
50.85% 50.06% -0.79%
55.04% 46.31% -8.73%
63.03% 54.25% -8.78%
39.82% 38.60% -1.22%
47.50% 46.33% -1.17%
50.83% 50.21% -0.62%
49.03% 48.14% -0.89%
65.17% 58.93% -6.24%
40.11% 37.13% -2.98%
51.48% 47.69% -3.79%
52.19% 50.04% -2.15%
57.21% 54.54% -2.67%
60.21% 56.66% -3.55%
52.37% 47.89% -4.48%
53.89% 53.07% -0.82%
61.67% 60.83% -0.84%
29.73% 29.76% 0.03%
63.51% 58.62% -4.89%
88.80% 79.16% -9.64%
52.36% 51.24% -1.12%
64.18% 61.42% -2.76%
55.48% 55.39% -0.09%
52.29% 52.00% -0.29%
70.54% 70.15% -0.39%
52.56% 49.97% -2.59%
46.21% 46.18% -0.03%
56.13% 54.16% -1.97%
68.15% 67.61% -0.54%
I'd say that the degree to which elf agrees with pro's judgement on a vs b is pretty impressive (Elf is highly opinionated). which suggests to me that elf thinks that pros often make the right choice here and that the game is won or lost elsewhere.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Mon Nov 05, 2018 10:30 pm
by Gomoto
Thanks for taking a closer look.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 7:11 am
by topazg
Click Here To Show Diagram Code
[go]$$B
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . O O O . . . . .
$$ | . 1 X O X O . . . .
$$ | . . . X X . . . . ,
$$ | . . . . . . . . . .
$$ | . . X . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . a . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . O . . . . . . .[/go]
Click Here To Show Diagram Code
[go]$$B
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . O O O . . . . .
$$ | . . X O X O . . . .
$$ | . . . X X 1 . . . ,
$$ | . . . . . . . . . .
$$ | . . X . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,
$$ | . . . X . . . . . .[/go]
(Actually I'd play "a" in the first diagram over either .. probably, depending on what was below the White stone, but I couldn't move the white stone up a position without clearly separating from the original dia)

This reminds me greatly of a chess video of Peter Svidler's when he was criticising why "this thematic way of playing a very common opening is simply bad here because this pawn is on that square and therefore the bishop can't do this" ... I'm paraphrasing and rather too lazy to look up the video (I think it was one of his banter blitzes though as opposed to his dedicated opening repertoire material).

Honestly I'll play what feels right in this sort of position, and I suspect that comes down to a comfort zone thing and a "I think I know how to play on from here more than in the other line" sort of thought process. Of the remaining 100 moves I make, at least 80 of them will probably be sub-optimal anyway, so I'd rather play with something I think I understand than go on a % stat that I definitely don't understand the intricacies behind.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 10:35 am
by Gomoto
That is a line of thought I am also considering right now. When a is the stronger play in a certain position, even the pros seem to have difficulties to handle the continuations in an efficent way.

Another important aspect are the possible/available follow up moves in the near vicinity that are strongly connected to this joseki. I started to review related pro games and will post my thoughts later, but this will take some time.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 10:41 am
by Bill Spight
Gomoto wrote: And what is your take on the choice between a and b? :)
Click Here To Show Diagram Code
[go]$$B
$$ --------------------
$$ | . . . . . . . . . .
$$ | . . O O O . . . . .
$$ | . a X O X O c . . .
$$ | . . . X X b . . . ,
$$ | . . . . . . . . . .
$$ | . . X . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]
Looking over the games at Waltheri, I have a few observations.

1) The choice of where to play generally occurs late in the opening. Which means that the rest of the board is definitely relevant.

2) Both "a" and "b" are normally sente, with "c" as the usual response to "b" and "b" as the usual response to "a".

3) Tenuki is definitely an option. "a", "b", and tenuki are chosen roughly equally. After tenuki, White seldom plays first locally.

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 12:15 pm
by Gomoto
Cho Chikun 9p - Paek Seongho 9p, W+5.5 (Komi 6.5)
3rd Korea Senior Baduk League, final, round 2, 2018-10-23

Paek Seongho chooses move a (move 1) in this game.
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X X X . . . . . . . . . . . . . . |
$$ | . 1 O X O X . . . . . . . . . . X . . |
$$ | . . . O O 2 . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . O O . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . O . . . . . X . . . . X , X . . |
$$ | . . . . . X . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In this position move a seems to be better than b because it is possible to aim at this continuation (not the game):
Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X X X 2 1 . . . . . . . . . . . . |
$$ | . O O X O X . . . . 3 . . . . . X . . |
$$ | . . . O O X . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . O O . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . O . . . . . X . . . . X , X . . |
$$ | . . . . . X . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In the game Cho tries to resist with H17. (But in this position it would have been probably better to just connect at F18.)
Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X X X . 1 . . . . . . . . . . . . |
$$ | . O O X O X . 2 . . . . . . . . X . . |
$$ | . . . O O X . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . O O . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . O . . . . . X . . . . X , X . . |
$$ | . . . . . X . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 2:01 pm
by Gomoto
Cho Hanseung 9p - Choi Cheolhan 9p, W+Resign (Komi 6.5)
year 2018 Korean League, round 14, 2018-10-05

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . a . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . . X b . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In this game Choi went for move b in an early game state.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . . X W . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Variation (not the game):
Move b seems to be the better option in this game because after move a these follow up moves are not attractive yet (too small and 4 is too good of an answer).
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . W . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . 2 X B . . . . . . . . . . . . . . . |
$$ | . 1 . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 4 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 4:03 pm
by Bill Spight
dfan wrote:
Kirby wrote:8% win rate difference from a handful of human games doesn't seem like much evidence to make much of a point about a single move out of hundreds that determined the result of the game.
I would agree more with this if we were talking about a few dozen games rather than a few hundred. I did some simulations to ask the question "If Black won 153 out of 323 games in total and we break it into groups of 202 and 121 games, what are the chances that he won 90 or fewer games in the group of 202?" and the answer is around 11.6%. So I think that it is fair to say that it is not proof but it is solid evidence.

Of course, there are all sorts of things that confound this. Maybe Black usually makes his decision based on a situation elsewhere on the board, and that other situation is really the thing contributing to the difference in win rate.
Ceteris are seldom paribus. :)

Re: Joseki 4-4, low approach, low extension, contact variati

Posted: Tue Nov 06, 2018 7:19 pm
by Kirby
Gomoto wrote:Cho Hanseung 9p - Choi Cheolhan 9p, W+Resign (Komi 6.5)
year 2018 Korean League, round 14, 2018-10-05

Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . a . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . . X b . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In this game Choi went for move b in an early game state.
Click Here To Show Diagram Code
[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . . X W . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Variation (not the game):
Move b seems to be the better option in this game because after move a these follow up moves are not attractive yet (too small and 4 is too good of an answer).
Click Here To Show Diagram Code
[go]$$W
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . W . . . . . . . . . . . . . . . . |
$$ | . X O . . O . . . . . . . . . . . . . |
$$ | . X X O . . . . . , . . . . . X . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . 2 X B . . . . . . . . . . . . . . . |
$$ | . 1 . . . . . . . . . . . . . . . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 4 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
I like these kinds of posts. We have several examples and can discuss various *reasoning* for various alternatives. The OP seemed more like a very generalized statement that said "win rate is X%, therefore b > a". I fight back against this kind of generalization, even if it's true in many cases.

Going over reasoning and seeing the limits of when "b > a", when "a > b", when "a ~= b", etc., is interesting and valuable. The win rate of a few hundred pro games is also interesting in some regard, but it's kind of like a novel piece of knowledge than any sort of true understanding.
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