at S5 more often, then N5 O4 L6 tenuki or N5 O4 N7 Q7.As for evaluation, this is an irresistable example.
answer1:
B has 2 stones more locally, taking gote after having 2 more stones originally. B expects 14*2=28 more stones.
counting N5 to T1 is 7*5 = 35. Plus P6 to T6 is 35+5=40 stones.
W has 4 stones only. However, with one move, the influence helps surround side territory, especially after M3. M3 is also supported by the option of N4 sente, which is more important than it looks, otherwise, the boundary is too thin to make territory with one move. After that, W will have an extra 3 lines of "head" as well as perhaps a 2*2 block of K5 to L4 extra compared to a normal 3rd line more. And B has little more than the line of N already counted. The main question is whether W's potential is territory or not and how much W can get from the attack. On an even board, we often count each extra line of head as 3 stones worth, which decreases to zero if the opponent is alive nearby (since the value is counterbalanced by the opponent's potential stones). In this case, we have in part already counted this in the 2x2 block, and not fully counted W's weak points either. However, the extra centre stone should surely help by "curling" around to counterattack if B comes near. This won't matter if B is alive enough nearby. But if B is weak, it may bring a kill half a move closer. Or push them away, so that W expects B to prepare with 1/2 move before, so perhaps we count 1-1/sqrt(2)=0.293 of W's potential rather than 1/2. At the same time, the local temperature is higher if there are weak points, so for example, B at K3 threatens both M2 and L4, so we give a larger portion to B before halving and so on.
It looks as though an integral could help here, but the corridor principle seems quite general. Assume in your opponent's area that you have influence corresponding to the value of your first move. This is strict if it is sente, and less if gote.
For now, B can at the least get M2 in semi sente, so lets estimate W as gaining control of K6 to M1 with a bit more, but subtracting 3 stones around M2.
What about B's influence? Note this is reduced by W's centre stones which are relatively light even if B is strong on both sides, because W's stones are relatively worthless if undermined. This means that by the time the temperature is low enough that capturing them is big, connecting them is likely also big.
It seems L3 is best locally, after which W M4 is likely (eventually) sente for N3. Then, B gets as extra perhaps only half of the M1 to M4 line at best and then perhaps with K2, 7 stones on the outside solid with potential for at least 3 more.
Then averaging between these, and cancelling the "at least", it seems we should count around K6, K5, L5, M5, M4 for W locally with half more on 7 others. This is 8.5 stones. Adding N6, O6 (not M6 due to weak point), it is around 11 stones.
Probably should be less because W isn't yet alive, and even locally, B has moves like M4.
This sort of analysis points out to me how much I underestimate strength on the 2nd line. It makes moyos much less interesting for either side, reducing temperature greatly.
On the other side, W can peep Q7 eventually say with O8 or R9 support. I am unsure how to count it as W has reasonable potential with both O8 and R9. And if W R9, then B cutting around P8 isn't really high temperature, so it seems plausible for W to get both. It seems that counting the usual 2 extra stones for B's 5 line wall is usual here. subtracting 1 from height due to Q7. However, if so, then it seems we should expect W gets O8 in sente or so, which is perhaps also a line of 2 extra from W's 5 stone centre wall. Presumably B's side wall counts for more, but I don't know how to judge W's shape. Perhaps count 4 extra stones for B from this?
This comes to 40+4-11=36 stones more for B.
This is 8 stones over expected, which is quite surprising. I can only conclude that the difference is made up for by W's centre potential, and that quite a bit can be gained by threatening to make territory on the sides, even after B spends a move. Basically I counted a height up to 6 on the lower side and a width of 5 from horizontally. However, there is also potential curving around in the J7 direction.
If this justification for the discrepancy is correct, my komi calculation is also missing something serious here. In that case, komi is expected to be exponential rather than polynomial in dimension number.
counting N5 to T1 is 7*5 = 35. Plus P6 to T6 is 35+5=40 stones.
W has 4 stones only. However, with one move, the influence helps surround side territory, especially after M3. M3 is also supported by the option of N4 sente, which is more important than it looks, otherwise, the boundary is too thin to make territory with one move. After that, W will have an extra 3 lines of "head" as well as perhaps a 2*2 block of K5 to L4 extra compared to a normal 3rd line more. And B has little more than the line of N already counted. The main question is whether W's potential is territory or not and how much W can get from the attack. On an even board, we often count each extra line of head as 3 stones worth, which decreases to zero if the opponent is alive nearby (since the value is counterbalanced by the opponent's potential stones). In this case, we have in part already counted this in the 2x2 block, and not fully counted W's weak points either. However, the extra centre stone should surely help by "curling" around to counterattack if B comes near. This won't matter if B is alive enough nearby. But if B is weak, it may bring a kill half a move closer. Or push them away, so that W expects B to prepare with 1/2 move before, so perhaps we count 1-1/sqrt(2)=0.293 of W's potential rather than 1/2. At the same time, the local temperature is higher if there are weak points, so for example, B at K3 threatens both M2 and L4, so we give a larger portion to B before halving and so on.
It looks as though an integral could help here, but the corridor principle seems quite general. Assume in your opponent's area that you have influence corresponding to the value of your first move. This is strict if it is sente, and less if gote.
For now, B can at the least get M2 in semi sente, so lets estimate W as gaining control of K6 to M1 with a bit more, but subtracting 3 stones around M2.
What about B's influence? Note this is reduced by W's centre stones which are relatively light even if B is strong on both sides, because W's stones are relatively worthless if undermined. This means that by the time the temperature is low enough that capturing them is big, connecting them is likely also big.
It seems L3 is best locally, after which W M4 is likely (eventually) sente for N3. Then, B gets as extra perhaps only half of the M1 to M4 line at best and then perhaps with K2, 7 stones on the outside solid with potential for at least 3 more.
Then averaging between these, and cancelling the "at least", it seems we should count around K6, K5, L5, M5, M4 for W locally with half more on 7 others. This is 8.5 stones. Adding N6, O6 (not M6 due to weak point), it is around 11 stones.
Probably should be less because W isn't yet alive, and even locally, B has moves like M4.
This sort of analysis points out to me how much I underestimate strength on the 2nd line. It makes moyos much less interesting for either side, reducing temperature greatly.
On the other side, W can peep Q7 eventually say with O8 or R9 support. I am unsure how to count it as W has reasonable potential with both O8 and R9. And if W R9, then B cutting around P8 isn't really high temperature, so it seems plausible for W to get both. It seems that counting the usual 2 extra stones for B's 5 line wall is usual here. subtracting 1 from height due to Q7. However, if so, then it seems we should expect W gets O8 in sente or so, which is perhaps also a line of 2 extra from W's 5 stone centre wall. Presumably B's side wall counts for more, but I don't know how to judge W's shape. Perhaps count 4 extra stones for B from this?
This comes to 40+4-11=36 stones more for B.
This is 8 stones over expected, which is quite surprising. I can only conclude that the difference is made up for by W's centre potential, and that quite a bit can be gained by threatening to make territory on the sides, even after B spends a move. Basically I counted a height up to 6 on the lower side and a width of 5 from horizontally. However, there is also potential curving around in the J7 direction.
If this justification for the discrepancy is correct, my komi calculation is also missing something serious here. In that case, komi is expected to be exponential rather than polynomial in dimension number.
using the usual extra 2 stones for each line of the wall, we have 5*8 -4 + 10 = 46 stones for B. W has perhaps 5 * 3 + 4 = 19. By this crude estimate, B+27 is expected which is reasonable as B is out on both sides and W isn't alive. If we ignore W's local life and death, it seems that locally B can threaten either from P7 and Q8, or from S7, (or R6/R7 with support).
The meaning of overconcentration is that extra defences don't help until the last boundary is sealed. Basically B always has at least R6 unless blocked. Although W can block, B still has 2nd line strength. This means 1 stone jumping S7 can go ahead 2 spaces with 2 lines of territory minus one weak point is 3 stones. Then 1st line and 2nd line development are miai, so opp has to play further to surround, after which B normally has at least the equivalent of another 2nd line move. Probably we just add 3-4 stones without halving for this potential, and maybe another for W not being alive.
However, W also expects a little more than this on the lower side perhaps because M3 threatens P2. Perhaps we subtract a (3*3-2)/4 (if W can play M3 with just 2 moves) and another 6/16 for P2 as that probably needs another move even if M3 is there to be played securely. This is then another 2 stones.
Overall B+28 seems about right.
The meaning of overconcentration is that extra defences don't help until the last boundary is sealed. Basically B always has at least R6 unless blocked. Although W can block, B still has 2nd line strength. This means 1 stone jumping S7 can go ahead 2 spaces with 2 lines of territory minus one weak point is 3 stones. Then 1st line and 2nd line development are miai, so opp has to play further to surround, after which B normally has at least the equivalent of another 2nd line move. Probably we just add 3-4 stones without halving for this potential, and maybe another for W not being alive.
However, W also expects a little more than this on the lower side perhaps because M3 threatens P2. Perhaps we subtract a (3*3-2)/4 (if W can play M3 with just 2 moves) and another 6/16 for P2 as that probably needs another move even if M3 is there to be played securely. This is then another 2 stones.
Overall B+28 seems about right.
I think this has something to do each other. How to evaluate marginal expected profit from an area. If aggressive, it seems taking 4th line can be a good idea, trying to attack 3rd line with it "working".
Such areas are most "interesting" because the least moves have the highest mistake value. that is, they are close enough to death that it is valuable if the opponent makes a mistake.
I think this means allow the opponent weakish stones to give you strong but eyeless shape, then counterattack or kill when they attack your stones.
Such areas are most "interesting" because the least moves have the highest mistake value. that is, they are close enough to death that it is valuable if the opponent makes a mistake.
I think this means allow the opponent weakish stones to give you strong but eyeless shape, then counterattack or kill when they attack your stones.