(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2] RU[Japanese]SZ[19]KM[5.50]TM[60]OT[25/600 Canadian] PW[DrStraw]PB[DrStraw]DT[2002-09-042002-09-04]PC[The Kiseido Go Server (KGS) at http://kgs.kiseido.com/The Kiseido Go Server (KGS) at http://kgs.kiseido.com/]C[Copyright Steve Fawthrop, 2002, 2013 =============================== This lesson is aimed at mid kyu players. Some higher ranked players may not find much new. I do include some original ideas of my own, but others have probably also come up with them independently. The target audience is around 3-10k, but anyone lower should also benefit. As this is a lesson on counting, perhaps we should start with a short discussion of when to count. If you are a pro you probably count on almost every move. High dan players in a tournament will count every 10-20 moves, more often in a difficult situation. Everyone should count as follows: 1. At the end of the fuseki 2. At least one in the middle game and preferably after each local battle 3. At the start of the endgame You should count at least 3 times in a game. The fuseki stage requires a different counting technique to the rest of the game and we will get to that later. Also, if you think the position have changed significanlty then count. The more you count the easier it gets, so count often. So, let's start the lesson. There are five main topics to be discussed, as follows: 1. Basic counting techinques and tricks. 2. Definite, probable, & possible territory. 3. Estimating points for thickness and influence. 4. Evaluating the count for changes. 5. Balancing the count. I do not intend to get through them all tonight, for two reasons. One is that there is probably not enough time. The other is that I think it important to practice the first two before we discuss the last three. The last three will be done in future lessons. INSTRUCTIONS: GOTO VARIATION ON MOVE 274 AT END OF GAME TO START ITEM ONE. (Note. this lesson jumps around within the game. If you are instructed to move to the end of a variation make sure you step back one or two moves to catch all the comments.) ] (;B[qd]CR[qd] ;W[qp]CR[qp] ;B[dc]CR[dc] ;W[cp]CR[cp] ;B[ce]CR[ce] ;W[od]CR[od] ;B[oc]CR[oc] ;W[nc]CR[nc] ;B[pc]CR[pc] ;W[md]CR[md] ;B[qf]CR[qf] ;W[ic]CR[ic] ;B[gc]CR[gc] ;W[ie]CR[ie] ;B[ep]CR[ep] ;W[gq]CR[gq] ;B[gp]CR[gp] ;W[hp]CR[hp] ;B[hq]CR[hq] ;W[fp]CR[fp] ;B[go]CR[go] ;W[eq]CR[eq] ;B[fo]CR[fo] ;W[fq]CR[fq] ;B[ip]CR[ip] ;W[hr]CR[hr] ;B[ho]CR[ho] ;W[ir]CR[ir] ;B[co]CR[co] ;W[bo]CR[bo] ;B[bn]CR[bn] ;W[cn]CR[cn] ;B[do]CR[do] ;W[bq]CR[bq] ;B[ao]CR[ao] ;W[bp]CR[bp] ;B[bm]CR[bm] ;W[en]CR[en] ;B[eo]CR[eo] ;W[cm]CR[cm] ;B[cl]CR[cl] ;W[em]CR[em] ;B[dk]CR[dk] ;W[ek]CR[ek] ;B[ej]CR[ej] ;W[fk]CR[fk] ;B[fj]CR[fj] ;W[hk]CR[hk] ;B[gj]CR[gj] ;W[hm]CR[hm] ;B[gm]CR[gm] ;W[gl]CR[gl] ;B[fm]CR[fm] ;W[el]CR[el] ;B[im]CR[im] ;W[il]CR[il] ;B[jm]CR[jm] (;W[bk]CR[bk] ;B[bl]CR[bl] ;W[dj]CR[dj] ;B[di]CR[di] ;W[cf]CR[cf] ;B[cj]CR[cj] ;W[cd]CR[cd] ;B[de]CR[de] ;W[be]CR[be] ;B[dd]CR[dd] ;W[bc]CR[bc] ;B[cc]CR[cc] ;W[bd]CR[bd] ;B[bg]CR[bg] ;W[cb]CR[cb] ;B[db]CR[db] ;W[ca]CR[ca] ;B[bf]CR[bf] ;W[ab]CR[ab] ;B[gk]CR[gk] ;W[fl]CR[fl] ;B[hn]CR[hn] ;W[hl]CR[hl] ;B[ne]CR[ne] ;W[nd]CR[nd] ;B[ke]CR[ke] ;W[kc]CR[kc] ;B[kk]CR[kk] ;W[jj]CR[jj] ;B[kj]CR[kj] ;W[jh]CR[jh] ;B[if]CR[if] ;W[ki]CR[ki] ;B[ii]CR[ii] ;W[ji]CR[ji] ;B[he]CR[he] ;W[je]CR[je] ;B[jf]CR[jf] ;W[jl]CR[jl] ;B[kl]CR[kl] ;W[km]CR[km] ;B[jo]CR[jo] ;W[kn]CR[kn] ;B[ko]CR[ko] ;W[mn]CR[mn] ;B[mj]CR[mj] ;W[mi]CR[mi] ;B[ni]CR[ni] ;W[mh]CR[mh] ;B[nl]CR[nl] (;W[lo]CR[lo] ;B[lp]CR[lp] ;W[mp]CR[mp] ;B[jn]CR[jn] ;W[nh]CR[nh] ;B[oi]CR[oi] ;W[oh]CR[oh] ;B[pi]CR[pi] ;W[lq]CR[lq] ;B[kp]CR[kp] ;W[qm]CR[qm] ;B[mf]CR[mf] ;W[ph]CR[ph] ;B[qh]CR[qh] ;W[qi]CR[qi] ;B[qj]CR[qj] ;W[ri]CR[ri] ;B[rj]CR[rj] ;W[qg]CR[qg] ;B[rh]CR[rh] ;W[rg]CR[rg] ;B[si]CR[si] ;W[pf]CR[pf] ;B[pe]CR[pe] ;W[oe]CR[oe] ;B[of]CR[of] ;W[pg]CR[pg] ;B[rf]CR[rf] ;W[kf]CR[kf] ;B[kg]CR[kg] ;W[lf]CR[lf] ;B[lh]CR[lh] ;W[lg]CR[lg] ;B[mg]CR[mg] ;W[le]CR[le] ;B[li]CR[li] ;W[kh]CR[kh] ;B[lj]CR[lj] ;W[hf]CR[hf] ;B[sg]CR[sg] (;W[pd]CR[pd] ;B[qe]CR[qe] ;W[hg]CR[hg] ;B[qq]CR[qq] ;W[pq]CR[pq] ;B[rp]CR[rp] ;W[qr]CR[qr] ;B[qo]CR[qo] ;W[rq]CR[rq] ;B[pp]CR[pp] ;W[qq]CR[qq] ;B[pn]CR[pn] ;W[ro]CR[ro] ;B[rn]CR[rn] ;W[sp]CR[sp] ;B[qn]CR[qn] ;W[ff]CR[ff] ;B[eg]CR[eg] ;W[op]CR[op] ;B[no]CR[no] ;W[mo]CR[mo] ;B[nn]CR[nn] ;W[nb]CR[nb] ;B[pb]CR[pb] ;W[hb]CR[hb] ;B[mq]CR[mq] ;W[mr]CR[mr] ;B[nq]CR[nq] ;W[np]CR[np] ;B[lr]CR[lr] ;W[kq]CR[kq] ;B[jq]CR[jq] ;W[kr]CR[kr] ;B[jr]CR[jr] ;W[ls]CR[ls] ;B[js]CR[js] ;W[oq]CR[oq] ;B[dq]CR[dq] ;W[dr]CR[dr] ;B[dp]CR[dp] ;W[cr]CR[cr] ;B[gb]CR[gb] ;W[sn]CR[sn] ;B[rm]CR[rm] ;W[fg]CR[fg] ;B[fh]CR[fh] ;W[ef]CR[ef] ;B[df]CR[df] ;W[gh]CR[gh] ;B[gi]CR[gi] ;W[eh]CR[eh] ;B[dg]CR[dg] ;W[fi]CR[fi] ;B[ij]CR[ij] ;W[jk]CR[jk] ;B[ge]CR[ge] ;W[mm]CR[mm] ;B[hc]CR[hc] ;W[ib]CR[ib] ;B[ih]CR[ih] ;W[ig]CR[ig] ;B[cq]CR[cq] ;W[ar]CR[ar] ;B[ks]CR[ks] ;W[nr]CR[nr] ;B[nm]CR[nm] ;W[fn]CR[fn] ;B[iq]CR[iq] ;W[oa]CR[oa] ;B[pa]CR[pa] ;W[da]CR[da] ;B[ea]CR[ea] ;W[gn]CR[gn] ;B[hs]CR[hs] ;W[gr]CR[gr] ;B[is]CR[is] ;W[gs]CR[gs] ;B[me]CR[me] ;W[kd]CR[kd] ;B[ng]CR[ng] ;W[ee]CR[ee] ;B[ed]CR[ed] ;W[fe]CR[fe] ;B[fd]CR[fd] ;W[oo]CR[oo] ;B[on]CR[on] ;W[ml]CR[ml] ;B[mk]CR[mk] ;W[fa]CR[fa] ;B[eb]CR[eb] ;W[ga]CR[ga] ;B[fb]CR[fb] ;W[ha]CR[ha] ;B[gf]CR[gf] ;W[hh]CR[hh] ;B[ae]CR[ae] ;W[ad]CR[ad] ;B[af]CR[af] ;W[hd]CR[hd] ;B[gd]CR[gd] ;W[id]CR[id] ;B[lm]CR[lm] ;W[ln]CR[ln] ;B[ll]CR[ll] ;W[an]CR[an] ;B[am]CR[am] ;W[dl]CR[dl] ;B[dn]CR[dn] ;W[ck]CR[ck] ;B[dj]CR[dj] ;W[dm]CR[dm] ;B[bj]CR[bj] ;W[dh]CR[dh] ;B[ch]CR[ch] ;W[sm]CR[sm] ;B[sl]CR[sl] ;W[so]CR[so] ;B[rl]CR[rl] ;W[po]CR[po] ;B[ak]CR[ak] ;W[ap]CR[ap] ;B[ob]CR[ob] ;W[na]CR[na] ;B[an]CR[an] ;W[fh]CR[fh] ;B[hi]CR[hi] (;W[jg]CR[jg] ;B[] ;W[]TW[aa][ba][ia][ja][ka][la][ma][bb][jb][kb][lb][mb][ac][jc][lc][mc][jd][ld][ke][if][jf][kg][fm][gm][pp][rp][aq][mq][nq][sq][br][er][fr][lr][or][pr][rr][sr][as][bs][cs][ds][es][fs][ms][ns][os][ps][qs][rs][ss]TB[qa][ra][sa][qb][rb][sb][ec][fc][qc][rc][sc][rd][sd][re][se][sf][ag][ah][bh][sh][ai][bi][ci][qi][ri][aj][bk][ck][lk][al][in][io][hp][jp]) (;W[]C[This is our starting point. Look over the board for a minute or two and see what you think, then we will count it. I will count it myself, using the techniques I will show you and the board will disappear as soon as I am finished. If you get the riight answer before I do you do not need this part of the lesson. Our first item to learn is: "ALWAYS COUNT DEFINED POSITIONS IN PAIRS" This means that you count one pair for each prisoner and one pair for every two points This is a well know trick so there is not much to say. Let's look at an example. Move forward to the next move with comments. ] ;B[]TW[aa][ba][ia][ja][ka][la][ma][bb][jb][kb][lb][mb][ac][jc][lc][mc][jd][ld][ke][pp][rp][aq][mq][nq][sq][br][er][fr][lr][or][pr][rr][sr][as][bs][cs][ds][es][fs][ms][ns][os][ps][qs][rs][ss]TB[qa][ra][sa][qb][rb][sb][ec][fc][qc][rc][sc][rd][sd][re][se][sf][ag][ah][bh][sh][ai][bi][ci][qi][ri][aj][bk][ck][lk][al][in][io][hp][jp] ; ;LB[qa:6][ra:1][sa:1][qb:6][rb:2][sb:2][ec:20][fc:20][qc:7][rc:3][sc:3][rd:4][sd:4][re:5][se:5][nf:8][sf:7][ag:24][cg:21][og:8][ah:22][bh:22][sh:10][ai:23][bi:23][ci:24][qi:9][ri:9][aj:26][nj:17][oj:13][pj:13][sj:10][bk:25][ck:25][lk:21][nk:17][ok:14][pk:14][qk:12][rk:11][sk:11][al:26][ol:15][pl:15][ql:12][om:16][pm:16][in:18][io:18][hp:19][jp:19]C[Let's count Black's territory. First, ignore prisoners and count in pairs as indicated here. Do NOT count as 2-4-6-8. Counting pairs in this diagram we find we have 26 pairs. Notice how, as much as possible I tend to go down pairs of columns to keep it simple. Also note that the point M9 was not counted along with the right side territory. Why? Because it was an odd point so I keep a mental flag that there is one point to still count. When I find another odd point (at C13) I add it in then and reset the flag. Remembering this odd point is very simple with a bit of practice. NEVER think of this as 52 points - that is irrelevant and it only confuses you. Always think in pairs. ] ;LB[cf:37][pf:30][pg:29][qg:28][rg:27][mh:34][nh:33][oh:32][ph:31][mi:35][qm:36]C[Now we have 26 pairs of territory for B, so let's add in the prisoners. Each prisoner counts as one pair -- one for the captive and one for the territory underneath. And we see that B has a total of 37 pairs. The big advantage of counting in pairs, apart from speed, is so that you don't have to count prisoners double, since you gain the point for (1) the prisoner and (2) the territory in a single pair. ] ;W[]LB[aa:1][ba:1][ia:11][ja:6][ka:5][la:4][ma:3][bb:2][jb:6][kb:5][lb:4][mb:3][ac:2][jc:7][lc:8][mc:8][jd:7][ld:9][ke:9][if:27][jf:26][jg:A][kg:25][fm:10][gm:10][pp:16][rp:19][aq:24][mq:12][nq:12][sq:19][br:23][er:21][fr:20][lr:11][or:14][pr:15][rr:18][sr:18][as:24][bs:23][cs:22][ds:22][es:21][fs:20][ms:13][ns:13][os:14][ps:15][qs:16][rs:17][ss:17]C[Now we do the same for White and get 24 pairs of territory plus 3 pairs for prisoners. Note that A is not a point because White must eventually play there. In addition, W had 10 prinsoners and B had 7, for a surplus of 3 to W. Also, we must add in komi which was 5.5 to W Adding these in we get that W has 31 pairs (ignore the half point komi for now). ] ;B[]C[ OK - so now - how many did Black have? Don't remember? Not surprising? Most people forget frequently and have to recount. So here is the second item: ONLY THE DIFFERENCE IN SCORES COUNTS Why bother to calculate two separate numbers when only one is needed. So after getting the first player's score round it to 50 Occasionally there will be so much territory you have to round to 100, but that is rare. You may also be able to round to 25 in a low scoring game. For example, if B has 37 pairs, as here, round to 50 by adding 13. Then start counting White's score at 13. In this game his actual score was 31, so starting at 13 results in a score of 44. This 44 does not represent anything on the board, but it DOES represent a score relative to 50 By doing this you do not need to remember Black's score -- it is ALWAYS 50 So when you get a score for White of less than 50 you know White has lost. Only if the White score is also 50 do you worry about that odd 0.5 komi which results in a W win. This is a trick I came up with myself years ago, but I am sure others use it. and have saved a lot of time since by not having to recount. ] ;W[]C[ So in this game the scoring steps are: 1. B has 37 pairs 2. Round this to 50 by adding 13 3. Start counting W from 13 4. W has less than 50 pairs so he lost. One other thing. If B ends up with a half pair (ie an odd number of points), take care of that first when counting W, by finding an odd point by itself to count. OK - That completes the first item in the lesson: Basic counting techinques and tricks. Now onto the second one: Definite, probable, & possible territory. INTRUCTIONS : TO CONTINUE THE LESSON GOTO TO THE VARIATION OF MOVE 58 ])) (;TR[aa][ba][ka][la][qa][ra][sa][bb][jb][kb][lb][qb][rb][sb][ac][jc][lc][mc][qc][rc][sc][kd][ld][rd][sd][ke][re][se][if][jf][pf][sf][jg][kg][pg][qg][rg][ah][bh][ch][mh][nh][oh][ph][sh][ai][bi][ci][mi][qi][ri][aj][bj][dj][ak][bk][al][am][in][io][ar][br][er][fr][gr][as][bs][cs][ds][es][fs][gs][hs]SQ[ja][ma][mb][ec][fc][ad][ed][fd][jd][cf][cg][dg][dh][nj][oj][pj][sj][mk][nk][aq][cr][dr]C[Let's evaluate the position here: We see that B is ahead in both definite territory and probably territory. But there is a large part of the board which is not marked. A lot of this is definitely more likely to fall to one player or the other. ] ;TR[eb][fb][gb][ec][fc][ed][ee][fe][df][ef][ff][dg][eg][fg][eh][fh][ei][fi]SQ[ia][ib][ig][jg][rn][sn][po][qo][ro][so][np][op][pp][rp][sp][nq][oq][pq][qq][rq][sq][mr][nr][or][pr][qr][rr][sr][ms][ns][os][ps][qs][rs][ss]C[Here we see that W has much more possible territory than B and it is his move. Let's see what the score is for each type of territory. Definite: B:25.5, W 20 (inc. komi) Probably: B 7.5, W 4 Possible: B 9, W 17.5 Total: B: 42, W:41.5 This game is very close IF W can convert all the potential territory into definite territory. So we can conclude that IF everything goes W's way he can expect to lose by one point. If W tries to stop B from getting all the triangle points he will not get all the square points, so it is not looking good for W. In this game White needs to come up with somethng extra to win. ] ;W[]C[So let us look more closely at these three concepts. 1. Clearly the player who is ahead in definite territory has an advantage, but it may not be enough. 2. If the other player has more probable territory then he may be ahead. 3. You must learn to decide how secure the probable territory is and judge who is ahead. 4. Finally, you must look at potential territory. If one player has a lot more potential territory then he may be able to overcome a disadvantage, but he will usually have to fight hard for it. In this positition, if W gains all his potential territory then there is a good change B will gain all his -- after all, it is give and take. In order to stop B from gaining all his potential territory, W will probably have to give upo some of his potential. Usually, it is not possible to get all of the potential territory. We can see then that in this game W is not only behind in definite and probable territory, but that he probably cannot find enough possble territory to win this game. INSTRUCTIONS: TO CONTINUE THE LESSON GOTO THE VARIATION ON MOVE 108 ])) (;W[]C[This is the position a bit earlier in the game. Let's evaluate it. ] ;B[]TR[aa][ba][ka][la][qa][ra][sa][bb][jb][kb][lb][mb][qb][rb][sb][ac][mc][rc][sc][rd][sd][cf][cg][ah][bh][ch][ai][bi][ci][aj][bj][dj][ak][bk][al][in][io][ar][br][er][fr][gr][as][bs][cs][ds][es][fs][gs][hs]SQ[ia][ja][ma][na][ib][nb][ec][fc][jc][lc][ad][ed][fd][ee][re][se][df][ef][rf][sf][kh][lh][nj][oj][mk][nk][ok][am][gn][ro][so][rp][sp][qq][rq][sq][cr][dr][pr][qr][rr][sr][is][ps][qs][rs][ss]TB[hp]C[First, definite territory (triangles). Black is ahead by 2 pairs. Then probable territory (squares): White is ahead by 4 pairs plus komi We see that in terms of territory W is about 9 points ahead. (2pairs + 5 komi) so it looks like W is ahead in this game. Let's look further. ] ;TR[pa][eb][fb][pb][fd][fe][ff][gf][dg][eg][fg][gg][qg][rg][sg][dh][eh][fh][gh][qh][rh][sh][ei][fi][gi][qi][ri][si][pj][qj][rj][sj][ok][pk][qk][rk][sk][ol][pl][ql][rl][sl]SQ[pn][qn][rn][sn][po][qo][ro][so][pp][mq][nq][oq][pq][kr][lr][mr][nr][or][ks][ls][ms][ns][os]C[We see that Black has a lot more possible territory than White. (Approx 19 points more) So even if Black can convert only half of this excess into territroy he will win. And that does not take into consideration the relative strengths of the groups. ] ;LB[gl:2][go:1]TR[ni][kj][mj][kk][kl][nl][km][kn][mn]C[In addition to the excess in possible territory, the balance of weak groups is in Blacks favor. Ignoring the odd stone here and there (which can be considered as yose) the only potentially weak stones he has are marked. The black group marked "1" is 90% alive and not likely to die. White has a few weak stones as shown, but the group marked "2" is potentially very weak. So in this position, we conclude that, although White appears to have an edge on the board, Black is probably in the lead. INSTRUCTIONS: TO CONTINUE THE LESSON GOTO THE END OF THE VARIATION OF MOVE 1 ])) (;W[] ; ;B[]TR[aa][ba][ca][ra][sa][ab][bb][cb][qb][rb][sb][ac][bc][cc][qc][rc][sc][ad][bd][rd][sd][ae][be][af][bf][ag][bg][ah][bh][ai][bi][aj][bj][ak][bk]SQ[ka][la][kb][lb][jc][kc][lc][mc][jd][kd][aq][ar][br][er][fr][gr][as][bs][cs][ds][es][fs][gs][hs][is]C[DISCUSSION OF: Definite, probable, & possible territory. Ok - here is a position after 57 moves of this game. It is White's move, but that it irrelevant to counting. There are three types of territory: 1. Secure or definite territory, which the opponent cannot do anything about unless you choose to let him. 2. Possible territory: areas where you expect to get territory but the boundaries are not yet secured. In this case there is room for potential invasion but for one reason or another you do not expect that the opponent is likely to invade. 3. Potential territory: area where you have influence, but it is far from secure. In this case you can expect the opponent to sucesfully invade. But when he invades you also expect to get something in return. Let's look at this position. Count the squares: W has 12.5 pairs + komi. B has 17.5 pairs. Is all of this definite territory? The UR, UL, LL corners can all be considered definite. The top for W is almost definite so we can count that. The left side is pretty close to definite although there is a little potential for invasion. However, in that case, Black will almost certainly get compensation elsewhere. So B has a lead in definite territory of about 5 points, but it is W's move. So we can same that, counting definite points only the game is very close. ] ;TR[da][ea][fa][db][eb][fb][re][se][cf][rf][sf][cg][dg][ch][dh][ci][di][ei][cj][dj][ck][al][bl]SQ[ja][ma][na][ib][jb][mb][nb][ld][je][ke][ro][so][rp][sp][qq][rq][sq][pr][qr][rr][sr][ps][qs][rs][ss]C[ Now, what about probable territory? We see that B has 11.5 pairs to W's 12.5 pts Again the balance is fairly even. It takes experience to decide how much probable territory a player has and that is not the subject here. The best way to learn is to be conscious during a game of where you expect to make territory and see if you are right. If you are wrong ask yourself why. It may be that you did not get the territory for some reason but that you got compensation elsewhere of equal value. Also note that conventional wisdom says that a single stone in a corner in worth 10 pts. So why do we assign 15 pts to the lower right. The point is that we are talking here about probable territory. 10pts can normally be considered definite, either directly or in compenasation if the opponenet invades, but he will probably get more so for current purposes we count more. So in this game, if we look at definite and probably territory wefind it is fairly close. It is the rest of the board, that which is unmarked, which will determine the outcome. This is referred to as possible territory. Some possible for either players, some for both To look at possible territory let's move forward in the came INSTRUCTIONS: TO CONTINUE TO THE LESSON GO TO THE VARIATION ON MOVE 148 ])) (;B[pd]CR[pd] ;AB[dp] ;W[cd]CR[cd] ;B[qp]CR[qp] ;W[oq]CR[oq] ;B[ec]CR[ec] ;W[ic]CR[ic] ;B[lp]CR[lp] ;W[np]CR[np] ;B[pn]CR[pn] ;W[qr]CR[qr] ;B[qj]CR[qj] ;W[nc]CR[nc] ;B[pf]CR[pf] ;W[dc]CR[dc] ;B[ed]CR[ed] ;W[df]CR[df] ;B[he]CR[he] ;W[jd]CR[jd] ;B[le]CR[le] ;W[if]CR[if] ;B[hf]CR[hf] ;W[ig]CR[ig] ;B[hg]CR[hg] ;W[ih]CR[ih] ;B[lc]CR[lc] ;W[qc]CR[qc] ;B[pc]CR[pc] ;W[pb]CR[pb] ;B[ob]CR[ob] ;W[qb]CR[qb] ;B[oc]CR[oc] ;W[re]CR[re] ;B[rf]CR[rf] ;W[qe]CR[qe] ;B[qf]CR[qf] ;W[pe]CR[pe] ;B[oe]CR[oe] ;W[of]CR[of] ;B[og]CR[og] ;W[nf]CR[nf] ;B[ne]CR[ne] ;W[ng]CR[ng] ;B[nh]CR[nh] ;W[mg]CR[mg] ;B[oh]CR[oh] ;W[qd]CR[qd] ;B[ie]CR[ie] ;W[je]CR[je] ;B[mh]CR[mh] ;W[lg]CR[lg] ;B[kf]CR[kf] ;W[me]CR[me] ;B[md]CR[md] ;W[nd]CR[nd] ;B[mf]CR[mf] ;W[lf]CR[lf] ;B[me]CR[me] ;W[kh]CR[kh] ;B[nb]CR[nb] ;W[ke]CR[ke] ;B[hh]CR[hh] ;W[nn]CR[nn] ;B[hi]CR[hi] ;W[fq]CR[fq] ;B[dn]CR[dn] ;W[ip]CR[ip] ;B[ch]CR[ch] ;W[bf]CR[bf] ;B[eh]CR[eh]C[Here is a position from another game. Let's look at the relative importance of the three types. ] ;W[]TR[aa][ba][ra][sa][ab][bb][mb][rb][sb][ac][bc][mc][nc][rc][sc][ad][bd][nd][od][rd][ae][be][jf][kf][jg][kg][pg][qg][ph][qh][rh][sh][qi][ri][si][rj][sj][or][pr][os][ps][qs][rs]SQ[ia][ib][qk][rk][sk][ql][rl][sl][qm][rm][sm][qn][rn][sn][ro][so][hq][iq][gr][hr][ir][gs][hs][is]C[First lets look at definite and probably territory: Definite Territory: B - 9, W - 14 Probably Territroy: B - 7, W - 5 Total: B- 16, W - 19 We see that, on this count, W is ahead. ] ;TR[fe][ge][ff][gf][fg][gg][fh][gh][ai][bi][ci][di][ei][fi][gi][aj][bj][cj][dj][ej][fj][gj][ak][bk][ck][dk][ek][fk][al][bl][cl][dl][el][am][bm][cm][dm][em][an][bn][cn][ln][mn][ao][bo][co][do][ko][lo][mo][ap][bp][cp][jp][kp][lp][mp][aq][bq][cq][jq][kq][lq][mq][nq][ar][br][cr][jr][kr][lr][mr][nr][as][bs][cs][js][ks][ls][ms][ns]C[But looking at possible territory we have: B - 28.5, W - 11.5 Let us suppose that B gains only half of this surplus of 17 pairs, that is 8.5. That would mean than his deficit of 3 in definite and probably points has turned into a 5.5 advantage. Thus, it is not unreasonable for B to win this game by at least 11 points. In fact, this is a professional game and Black won by 16 points. So now we have a rule of thumb we can follow: ADD TOGETHER THE DEFINITE POINTS,THE PROBABLE POINTS AND HALF THE POSSIBLE POINTS TO GET AN ESTIMATE OF THE TOTAL SCORE. Of course, this is far from final, but it gives an idea of who it ahead. As you gain more experience you are able to evaluate these positions more accurately. For example, some positions are more possible than others and you can allow more than half. You may ask why should we take half of the possible but all of the rest. No definite answer, just a good rule of thumb for kyu players. It probably would not work for dan players, who need a more accurate estimate. You have to concede that you will not get all your possible territory. but neither will the opponent. You may not get all your probable territory, but in that case te opponent will probably lose some of his. You will invade some of his and he will invade some of yours. If you have more to invade than he does then you stand to lose more of it than he does, but you also stand to gain more of it. So we take half of it as a compromise. That is the end of part two of this lesson. Before continuing to part three you should play several games and practice these concepts. Try to play slower and make sure you count at least three times in every game. I will close with the following comment: YOU CANNOT DETERMINE THE CORRECT STRATEGY IN A GAME IF YOU DO NOT KNOW THE SCORE. ]))