
We've had some fun with numbers in recent posts. Here is an example from Japan where numbers are used to mark the degree of risk associated with 39 common formations.
The book is アマの知らない打ち込み対策事典 or "Catalogue of countermeasures to invasions that amateurs don't know". It is by Awaji Shuzo 9-dan (ISBN 978-4-8399-2610-6, Mainichi Communications, 2007; 223 pages, about 1400 yen).
For each position, Awaji gives a percentage, which is meant as a guide to the likelihood of the territory or base of that position being disrupted in actual play. The figure is supported by a brief supporting comment (e.g. "Don't think of this shape as territory" or "This territory is worth about 10 points"). The numbers, of course, are largely decorative, but seem to be in the right ballpark. I did a small survey with the GoGoD database. This confirmed that the positions were indeed common (typically of the order of 100 games upwards) and that the percentages were reliable enough. E.g. for a position marked 60% risk, I looked at 10 games. In 5 the position was indeed later disrupted, in 4 it wasn't, and 1 case was borderline.
The real meat of this book, however, is in the explanations of the weak points of each position. In each case, a Black position is invaded by White, and the book shows various results, ranging from the typical duffer's response to Awaji's recommended response. Sometimes the recommended response kills the invader, sometimes it just minimises damage. In some cases there is more than one recommended line. For some positions Awaji also shows best next move for Black - the mamori (pre-emptive defence) move.
Only the corner positions are shown - there are no game or full-board examples - but this part is excellent, ausgezeichnet, A1, whizzo, just dandy, the bee's knees, well worth a shufty, on the money, spiffing, not bad at all, cushty. You might even end up saying, "Cor, love a duck!"
Below I give a selection of positions from the book, where you may wish to make your own assessment of the risk factor in each case, assuming White plays next (0% means it's totally safe; units of 10% only). A low figure means you see little risk that Black loses his base or the bulk of his territory and that White gets away scot free. Obviously (I hope), this also assumes that White's various possible invasions are well timed in terms of the rest of the board. The White positions here are partly just indicative of outside strength. Awaji's figures are given at the end, but I won't hide the answers or delay them. Instead, I'll bury them in a solid paragraph and trust you to keep your eyes on the road.
The test here is not meant to be taken too seriously - it's just a coffee-break moment. The real point of the examples is to give a notion of the sort of positions covered by the book.
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[go]$$ Diagram 1
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$$ . O . . O . X . . . . . |
$$ . . , . . . . . X X . . |
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$$ . . . . . . . . . O . . |
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 2
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$$ . . . . . . . . . . . . |
$$ O . . O . X . . . . . . |
$$ . . , . . . . . X X . . |
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$$ . . . . . . . . . O . . |
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$$ . . . . . . . . . O . . |
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$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 3
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ O . . O . X . . . . . . |
$$ . . , . . . . . X . . . |
$$ . . . . . . . . . X . . |
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$$ . . . . . . . . . O . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , O . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 4
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . X . . . . . . . . . |
$$ . . , . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 5
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$$ . . . . . . . . . . . . |
$$ . . X . . . . . . . . . |
$$ . . , . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 6
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . X . . . . . . . . . |
$$ . . , . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 7
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . O . X . . X O . |
$$ . . , . . . . . X . O . |
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$$ . . . . . . . . . O . . |
$$ . . . . . . . . . . . . |
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$$ . . , . . . . . O . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 8
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . X . . . . |
$$ . . , . . . . . , X . . |
$$ . . . . . . . O . . . . |
$$ . . . . . . . . . O . . |
$$ . . . . . . . . . . . . |
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$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 9
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . O . . O . X . . . . |
$$ . . , . . . . . , X . . |
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$$ . . . . . . . . . O . . |
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$$ . . . . . . . . . O . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 10
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$$ . . . . . . . . . . . . |
$$ . . . . . . . X O O . . |
$$ . . O . X . O X X O . . |
$$ . . , . . . . . X O . . |
$$ . . . . . . . . X . . . |
$$ . . . . . . . . . O . . |
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$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 11
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ O . X . . . X O O . . . |
$$ . . , . . . X X , O . . |
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$$ . . . . . . . . . O . . |
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$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 12
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . O . X . . . . X X O . |
$$ . . , . . . . X , O . . |
$$ . . . . . . . . . . O . |
$$ . . . . . . . . O . . . |
$$ . . . . . . . . . . . . |
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$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 13
$$ -------------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . O . X . . . X X O . |
$$ . . , . . . . X , O . . |
$$ . . . . . . . . . . O . |
$$ . . . . . . . . O . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 14
$$ -------------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ O . . O . X . . X . . . |
$$ . . , . . . . . , . . . |
$$ . . . . . . . . . X . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . O . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , O . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 15
$$ -------------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . X . O . . O X . . . . |
$$ . . , . . . O . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , X . . |
$$ . . . . . . . . . . . . |[/go]
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[go]$$ Diagram 16
$$ -------------------------
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . X . O . . O X . . . . |
$$ . . , . . . O . X . . . |
$$ . X . . . . . . . . . . |
$$ . . . . . . . . X . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |
$$ . . , . . . . . , X . . |
$$ . . . . . . . . . . . . |[/go]
Awaji's risk factors are as follows: 1 = 0%, 2 = 60%, 3 = 40%, 4 = 20%, 5 = 30%, 6 = 40%, 7 = 50%, 8 = 20%, 9 = 60%, 10 = 60%, 11 = 40%, 12 = 50%, 13 = 5% (yes, I lied about 10% units, but this is the only exception), 14 = 10%, 15 = 30%, 16 = 10%.
Your eyes may pop at some of the figures, not just in absolute terms but relative to each other. The book's text may still not convince you but will teach you a lot. One especially useful side benefit is that when you compare one position against another that differs by just one stone, you get a surprisingly new insight into the effect of that extra stone.
Do you need to read Japanese to get value from this book? No. Perhaps the only two phrases you really need are オススメ!(Recommended) and 守り方 (How to defend pre-emptively). These appear as luggage labels under the relevant diagrams.