(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2] RU[Japanese]SZ[19]KM[0.00] PW[Counting]PB[Counting]WR[7d]BR[7d]DT[2002-12-05]PC[The Kiseido Go Server (KGS) at http://kgs.kiseido.com/]C[Copyright Steve Fawthrop, 2002, 2013 =============================== In this lesson we will be discussing how to evaluate a position in the early middle game. In particular we will concentrate on how to evaluate thickness and influence. We are going to look at three positions and evaluate them. In the first two lessons we created rules for use in specific situations. Because the middle game does not lend itself so easily to rules we will not be creating any definite rules in this lesson, but will be offering some guidelines. Let's make sure we know what we mean by "thickness" and "influence"? Are they the same thing? Thickness is where there is a strong position, invulnerable to attack, facing the center of the board. Influence is not as strong. It refers to a situation where one player has more stones in an area than the other. Usually they are not subject to attack, but they can be. In the previous lessons we have talked about how to evaluate definite and probably territory. We will not talk about that tonight. All we will be interested in is the potential and how to get estimates of the score for it. All three positions tonight are taken from a book: Positional Judgment by Cho Chikun I will not actually be agreeing with everything he says. Not because i disagree, but because i want to put a different emphasis on it. This is aimed at mid-kyu players or weaker: stronger players will possibly disagree, and so they should becasue they have learnt when to recognize exceptions After the lesson is complete go to the last, one-move, variation for a summary. ] (;B[pd]CR[pd] ;AW[fb][fc][ed][kd][ie][ef][gf][bm][cm][dn][en][pn][qo][dp][op][pp][lq][mq][nq]AB[dc][ec][cd][hd][df][dg][pg][cl][dl][dm][bn][cn][bp][qp][oq][pq][qq][mr][nr]C[Here is the first position. Look over this first and form your own opinion with reference to the value of the thickness and influence A few observations: White has some influence on the upper side White is thick in lower right. Black has influence in upper right. The white position in the lower left could be atacked sometime, therefore it is not thickness, but it is influence. A good way to define thickness, proposed by John Stephenson, is "Look at the stones and ask whether they will be uncomfortable if the opponent comes near". If not, then they are thick, it so then they are thin, even though they may have some influence associated with them. So, in this position how much territory should White expect from the lower right thickness? Let us assume, for the moment, that this is an even joseki. That means that a pro playing this would think that the black territory is equal to white's thickness in terms of points. The is a useful thing to remember when studying a joseki. In this case, if we agree that it is equal then the white thickenss must be worth around 12-15 pts, maybe a little more because black presumably got sente from an invasion So we propose a rule for evaluating thickness. However, this is not going to be hard and fast rule like in earlier lessons, but more of a guideline which you can agree with or not as you wish. It is for the benefit of beginner and lower kyu players who do not have any definite tools to use otherwise. ] ;W[]CR[pk][ol][ql][nm][rm][ln][mn][sn][ko][jp][iq]TR[pm][on][qn][oo][po][ro][lp][mp][np][kq]SQ[pl][om][qm][nn][rn][lo][mo][no][so][kp][jq]C[ Rule: If a position is thick then count all points within 3 points of the stones as territory. Within 3 points means count from any stone along the lines of the board. Thus, all triangle moves in the above diagram are within one point, all square stones within two points, and all circle stones are within three points. For obvious reasons, however, we do not count points unless they are closer to White than black, so there are several points on this diagram (S4 for example) which are within 3 but not coutned. These points are NOT necessarily going to turn into territroy, BUT White can expect to get about this amount from this position, either here or elsewhere. In this case, using this method of counting, W can expect to get more than the 15 mentioned earlier. So why would this be considered equal if played in a professional game? Remember that we are trying to create a WHOLE BOARD guildine. This method does not work in isolation, but as you evalaute more position on the same board the errors tend to cancel and the overall evaluation is pretty good. As you get stronger, about 4k maybe, you will learn that this method is not that accurate, but at say 10k you will find that it is fair good. So remember, this is only a GUIDELINE. It is not accurate in any single position. But, if you use it on several different positions over the board then the error will tend to cancel out and you will get a useful approximation for who is ahead if you are not comfortable with your counting abilitiy. . Let us look at the other positions on this board which show us how to count for influence, not thickness. We agree that influence in not as strong so obvious it is worth less. So, how do evaluate the influence for W at the top? for the answer see the next move? ] ;B[]LB[kg:A]C[Black can play at 'A' all W's influence is nullified, but if B gets much closer he may end up attacked. So let's say that B can get within 3 points of W but no closer. (Again, this is a rule of thumb that will not actually happen in the game) So for influence we need a different guideline, which is: Count all points within 2 pts of influence and count them as territory. So in this case i would add about 8-10 pts for the influence at the top. Remember, again, this is not a rule but a guideline. As you get more comfortable withthe idea you will realize that positions vary and some are worth more, some less. So, for now, as a newcomer to counting estimate within 2 points of influence and 3 points of thickness. This will give a rough idea of who is ahead. Remember, this is the count for influence and thickness only. We talked about counting for definite territory in earlier lessons. Let me point out something before we continue. These muber are estimates only: some will be over, some will be under. Some will give overlapping points between B and W but in the last case, both count them and neither gets them but the different is the same. Remember the cardinal rule: only the difference in scores counts ] ;C[You should not expect you to start counting 2 or 3 points from every stone to see what the total is. This method is just a way to eyeball it, so to yourself " i think there is about 15 pts there within 3 of my stones" ]) (;B[qd]CR[qd] ;AW[cc][qc][dd][df][oi][oj][ck][pk][cl][pl][dm][pm][dn][mn][do][lo][dp][dq][jq][mq][nq][cr][dr]AB[db][fc][ic][oc][pd][pf][ph][pi][pj][qk][bl][ql][cm][bn][cn][qn][cp][np][op][cq][pq][br]TR[oi][ck]SQ[dm][lo]C[Here is the second position. Let's just concentrate on W here. Clearly W is all thickness and no influence.in the bottom half of the board Look at the two triangle stones. It would not be unreasonable for W to get everything behind the line between these, but we cannot count all those points according to our method. But we CAN count amost all of those behind the line between the square stones as they are within 3 points of a W stones. ] ;W[]SQ[ch][ci][di][li][mi][ni][cj][dj][ej][lj][mj][nj][dk][ek][fk][mk][nk][ok][dl][el][fl][ll][ml][nl][ol][dm][em][fm][gm][km][lm][mm][nm][om][en][fn][gn][jn][kn][ln][nn][eo][fo][go][io][jo][ko][lo][ep][fp][gp][hp][ip][jp][kp][lp][eq][fq][gq][hq][iq][kq][lq][er][fr][gr][hr][ir][jr][kr][lr][mr][ds][es][fs][is][js][ls][ms]C[So we count all the square stones as points. What about all the remaining points which are in the trough formed by these stones. Clearly they are far more likely to all to W than to B, but because they are not within 3 points of W we cannot say for sure that they will. What we do then, for estimating purposes, is to take all those points which are closer to W than to B and count HALF their total. This is merely an acknowledgement that they are more likely to end up as W territory, but that it is not cetain.] ;B[in]CR[in]C[Let's look at an example of what happens if B invades here. This is right on the section line which defined W's secure territory according to our methods. Let us say right away hat this is too deep. Counting should show us why. According to our guidelines, a lot of points which were closer to W are now closer to B and so it appears that W has lost a lot of points using these methods. So suddenly our count is completely different. How can one move make such a difference? The point is that NOTHING WE HAVE SAID ABOUT COUNTING SO FAR TONIGHT APPLIES IN THE MIDDLE OF A BATTLE. B has invaded so a local L&D fight is on and all counts are suspended temporarily. However, the count before the fight should give some idea of the expected outcome. In order to count we have to finish the local battle. There are two continuations shown with the resulting count analysis. ] (;W[hp]CR[hp] ;B[ik]CR[ik]C[The first thing many W players would consider would be this. And it is immediately obvious from the count that W has, indeed, lost a lot. But this defensive move by W is wrong. and if we understood the concept of counting thickness and influence we would immediately see this and realize the move is bad. It is bad becasue it gives a drastically different count on the game. Before you play a move you should try to guess the continuation and see if it drastically alters the count. If it does, then it probably is a bad move. If this is not so then you probably misestimated early and need more practice at this lesson. ]) (;W[il]CR[il]C[This is the correct move. Let's see how the count looks after just one possible variation.] ;B[iq]CR[iq] ;W[ip]CR[ip] ;B[hp]CR[hp] ;W[hq]CR[hq] ;B[ir]CR[ir] ;W[hr]CR[hr] ;B[jp]CR[jp] ;W[io]CR[io] ;B[jo]CR[jo] ;W[ho]CR[ho] ;B[hn]CR[hn] ;W[go]CR[go] ;B[kq]CR[kq] ;W[jr]CR[jr] ;B[kr]CR[kr] ;W[is]CR[is] ;B[lp]CR[lp] ;W[mp]CR[mp] ;B[jm]CR[jm] ;W[kk]CR[kk]C[B is having a hard time living. If B dies our original estimate is right because all the points we counted previously did, in fact, turn into W territory. So let's continue and assume B does live. ] ;B[jl]CR[jl] ;W[jk]CR[jk] ;B[kl]CR[kl] ;W[lk]CR[lk] ;B[ll]CR[ll] ;W[mk]CR[mk] ;B[lm]CR[lm] ;W[ml]CR[ml] ;B[hm]CR[hm] ;W[hk]CR[hk] ;B[hl]CR[hl] ;W[gk]CR[gk] ;B[gl]CR[gl] ;W[fl]CR[fl] ;B[fm]CR[fm] ;W[em]CR[em] ;B[gn]CR[gn] ;W[fo]CR[fo] ;B[fn]CR[fn] ;W[ln]CR[ln] ;B[kn]CR[kn]C[Say that it goes like this. (Yes it is a silly sequence but just played to make the point.) Let's recount. W gained much more than B in definite territory and that is added in to the total score. For the outside we have a new areas of thickenss and influence. If we recount according to these methods we find that W still has a lot of points due to thicknes on the outsdide. in actual fact it is not as many as it was before, but that is because i put down bad moves to illustrate a point in a situation where B probably should have died. However, despite bad moves by W, the count does not change significantly. So, counting points in one place gives a good score ESTIMATE. it does NOT guarantee points in those places, but it is a good indicate of acheiving points SOMEWHERE. ])) (;B[qc]CR[qc] ;AW[pb][dc][kc][nc][ld][de][ci][dn][dp][cq]AB[pd][je][pf][jh][pj][op][qp][fq][iq][dr]C[This is our final position, which we will look at briefly. We are looking to count influence and thickness only. The lower left B group is thick, it cannot be attacked. The upper right W group is the same. The rest of the board is probably only influence, although the upper right B group is fairly strong. R4 and P4 are not thick: Q3 spoils them. Same in upper left, but they are influence. I am not going to give an answer to this one, but based on the principle we have talked about in this lesson use it as an exercise. After completing the exercise so to the end of this variation and reevaluate the count after 5 extra moves. See if your original estimate is close to the new one. ] ;W[jp]CR[jp] ;B[jq]CR[jq] ;W[kp]CR[kp] ;B[ho]CR[ho] ;W[jm]CR[jm]C[Now reevaluate. Did you about the same? If not, why not? Ask yourself whether you miscounted or whether the moves for one side or the other were not optimal. Don't leave the lesson until you understand. If you got the same each time then you probably feel that the moves were reasonable and you understand the lesson. Don't be so sure! Think about it and make sure you really are correct. Next lesson we will be talking about balancing the count. ]) (;C[Here is the summary of this lesson. Influence and thickness are hard to evaluate so we need a rule of thumb to help new players to estimate who is ahead. We have previously learnt how to evaluate definite territory and that must be added in to all figure derived from tonight's lesson. tonght we present only guidelines, not rules, because they are too vague to be accurate for anyone who has reached the hugh kyu levels. However, for weaker players they will provide a quick and easy method for determining if you are ahead or not. Step 1: Determine which stone are thick and which have influence. Step 2: Count all points within 3 of thickness as full value points in your score. Step 3: Count all points within 2 of influence as full value points in your score. Step 4: For all remaining points on the board coutn them as HALF value to the play with the nearest stone. These steps do NOT show you which territory you expect to get, or where. They do not even show you how much territory you will get. However, they will give a good estimate of the DIFFERENCE in the final score, and this is all that matter. If you try to apply them to only a single situation on the board and try to extract that number of points out of that area you will probably find an large error. However, if you apply it to all areas of the board at once and take the total you will find that errors tend to cancel out and that the final difference in the total score will be fairly accurate. Or, to be more exact, it will give you a very good indication of who it ahead, and whether it is a large margin or not. However, the reliablity of these methods as an accurate assessment decrease as you reach the high kyu levels. ]))