(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2] RU[Japanese]SZ[19]KM[0.00] PW[White]PB[Black]C[Copyright Steve Fawthrop, 2003, 2013 =============================== Over the last three lessons we have develop some rules of thumb to help us determine who is ahead. It is now time to start implementing these and tying them together. In the remain lessons we will be doing this. We will do very little actual counting tonight, relying more on the "feel" for the count which I hope you have developed in previous lessons. However, I encourage you to review the lesson later and perform the actual counts yourself. If you have not yet developed the feel then you are probably not yet ready to study this lesson. In this lesson we will be looking at two things: 1. Reevaluating the count at vital points 2. Basing play on an evaluation of the count. The most important principle we have discussed so far is that the absolute score of each individual is not important. Only the difference matters. This means that when the board situation changes locally we only need to determine the net change locally. The count in other parts of the board has not changed. Actually, that is not exactly true as the effect of thickness and influence elsewhere may have changed. But as these lessons are aimed at mid-kyu players and below we are not going to consider that. Anyone capable of accurately evalauting such a change is already a strong kyu player. Let's start off by looking at some examples, all starting with the first variation. At the end of the lesson go to the variation on move 1 to get a summary. ] (;B[] ;W[] (;B[qd]CR[qd] ;W[dc]CR[dc] ;B[pq]CR[pq] ;W[dp]CR[dp] ;B[oc]CR[oc] ;W[po]CR[po] ;B[qo]CR[qo] ;W[qn]CR[qn] ;B[qp]CR[qp] ;W[pm]CR[pm] ;B[nq]CR[nq] ;W[qi]CR[qi]C[This position occurs in professional games so let us assume it is even. What we are going to do is play some different joseki in the top left corner and reevaluate the score after each one. Because joseki are expected to produce equal results we will all look a couple of non-joseki to show how counting can indicate that a mistake was probably made. However, we will not reevaluate the whole board - that takes too long. We will only reevaluate the top corner. So, we first need to know the estimated value of the stones in that corner. From our earlier lessons we saw that a single stone in a corner contributes an estimated 10 points to the count. So let's continue.] (;B[de]CR[de] (;W[ce]CR[ce] ;B[cf]CR[cf] ;W[cd]CR[cd] ;B[df]CR[df] ;W[fc]CR[fc] ;B[cj]LB[fc:A][cj:B]TR[df]C[Looking at the top corner only: W has about 15 points of secure territory B has about 8 points. 'A' and 'B' each have influence along the sides and so can be considered to cancel out. How about the influence of the triangle stone? From a previous lesson we can say that this is worth an extra 5 points to B. It appears, then, that W has only 2 points more than Black , an apparent loss of some 8 points from the initial position. However, B has played an extra move. From lesson one we saw that sente in the early part of the game is worth about 5 points. That means that W gains an extra 5 points and his total loss is only 3 points. In fact, sente is worth a little more than 5 points (the Nihon Kiin recently made komi 6.5) and so W's loss is more like 1-2 points. Since all of our values are approximate we can say that this result is about even as far as kyu players are concerned.]) (;W[cg]CR[cg] ;B[cc]CR[cc] ;W[cd]CR[cd] ;B[dd]CR[dd] ;W[ce]CR[ce] ;B[cf]CR[cf] ;W[df]CR[df] ;B[bf]CR[bf] ;W[bc]CR[bc] ;B[cb]CR[cb] ;W[be]CR[be] ;B[ec]CR[ec] ;W[bg]CR[bg] ;B[ef]CR[ef] ;W[dg]CR[dg]LB[bb:A][ee:B]C[Here the number of points depends on who gets to play 'A'. It is a fairly sizable endgame move but not one to be played in the fuseki. For the sake of estimating the count at this stage let us assume that neither player gets it. So, W has about 8 points of definite territory to B's 4. B has thickness facing along the top and W has thicknessalong the side. W's thickness is actually significantly better than B's because there is a cutting point at 'B' in B's shape, so tell us say that these are not quite equal. It is hard to put an exact value on this sort of thing but if you imaging W curtting at 'B', B connecting and W extending, then I would say that W has at least 5 points more when you consider the extra influence W has. In actual fact it is probably more than that, but W will have played an extra move so let's just leave it at 5pts This makes it W 13 pts to B 4 pts. Black played here first and W last so there are no extra points to be factored in for sente. So we see that, within our tolerance for estimation, the count has not changed - W is still about 10 pts ahead.]) (;W[cd]CR[cd] ;B[ce]CR[ce] ;W[fc]CR[fc] ;B[ck]CR[ck] ;W[be]CR[be] ;B[bf]CR[bf] ;W[bd]CR[bd] ;B[cg]CR[cg]LB[fc:A][ck:B]C[This sequence is NOT joseki. W has about 15 pts in the corner and B has about 12 pts on the side. 'A' and 'B' cancel as far as influence along the sides is concerned. W has sente (one fewer stone) which is worth about 5 points B has far more influence towards the center, say about 5 points. All this adds up to W 20 pts, B 17 pts., so W is only about 3 points ahead. He was originally 10 points about so he has lost out in a big way in the sequence. We will not evaluate the moves as this is a lesson in evaluating positions, not sequences, but it is an interesting exercise for you to try to figure out what went wrong.])) (;B[cf]CR[cf] ;W[cd]CR[cd] ;B[ci]LB[dc:B][ci:A]C[Here W has about 10 points in the corner and B has about 4 points on the side. B has played an extra move which gives 5 points to W. B 'A' may have a little more effect on the side than W 'B' but it is small -- 2 or 3 points at most. Add all this together an we see than it is about 10 points in favor of W. That is, the count is unchanged and so this is a fair sequence.]) (;B[cd]CR[cd] ;W[dd]CR[dd] ;B[ce]CR[ce] ;W[cc]CR[cc] ;B[bc]CR[bc] ;W[bb]CR[bb] ;B[ad]CR[ad] ;W[de]CR[de] ;B[cf]CR[cf] ;W[dh]CR[dh] ;B[ch]CR[ch] ;W[ci]CR[ci] ;B[dg]CR[dg] ;W[bh]CR[bh] ;B[cg]CR[cg] ;W[di]CR[di] ;B[eg]CR[eg] ;W[gd]LB[gd:B][eg:A][ci:C]C[This is just simply an awful sequence for B, but one which may be seen in a low-kyu game. W has about 15 points at the top, B has at most 5 points on the side (if he lives). It is hard to assigned any value to the influence of 'A becasue there are W stones on both sides of it. W 'B' & 'C' defintely have influence along their respective sides, worth at least 5 points each Both sides have played the same number of moves so there is no points adjustment for sente. This all adds up to W being over 20 points ahead locally. This is a disaster for B who was only 10 points ahead before this sequence. Given the B still is not alive -- we must take gote to live -- the difference is, in reality, even greater.])) (;B[pd]CR[pd]C[This move starts the discussion of our second topic -- basing the play on an evaluation of the count. By this we mean that you should determine who is ahead using the counting methods we have discussed and base your play on this. If your count shows you to be ahead, then you do not need to do anything dangerous. You should find a good move which maintains your lead. You should not make any bad invasions, rather you should make light reductions. You should not overextend and create a weak group. You should defend cutting points rather than cut your opponent. All of this is, of course, based on an evaluation of the count AFTER your move. You must visualize your move and the probable followup sequence on the board and readjust the count after those moves. If they do not lose any points then take the simple route to victory. If, on the other had, your count shows you are behind then you must be more aggressive. Maybe you need to invade instead of reduce. Maybe you need cut in order to create a weak group of your opponents. If the count shows you are behind, playing steady moves will not tilt the count in your favor and so you must do something to change that. So let's have a look at a couple of positions. I am going to deliberately play a few bad moves in order to create a suitable situation for discussion.] ;W[dc]CR[dc] ;B[pp]CR[pp] ;W[cq]CR[cq] ;B[pj]CR[pj] (;W[co]CR[co] ;B[jp]CR[jp] ;W[ce]CR[ce] ;B[jd]CR[jd] ;W[gc]CR[gc] ;B[eq]CR[eq] ;W[eo]CR[eo] ;B[gp]CR[gp]LB[qf:C][dj:A][jj:B][qn:D][np:E][nq:F]C[We will not bother actually doing the count in this simple example because it obvious W is way behind. This means that W must be aggressive. Playing a simple move like 'A' is likely to get a resposne of 'B' from B. This is no good -- the balance of the count shifts even more to B. So W must be far more agressive. A deep invasion is called for. The exact point is not important to this discussion. What is important is that you understand this, visualize the next few moves and try to determine how this has affected the count. For the record, I would play at 'C'. Why? Because if W responds at the top his potential territory is undercut from the left. That would not the true if W played at the bottom. In this game, 'D' would be wrong because it prompts B 'E' which helps a lot at the bottom. In this game W is so far behind that he should try to aim at playing 'F' himself later. Let's change the postion some by moving some of these stones.] ;AE[gc][jd][co][eo][gp][jp]AW[jc][cj][do]AB[md][hp][kp]LB[je:A]C[Now we have the same number of stones , but W has played far better. The balance here is much more even. There is no rush for W to invade. Playing at 'A' is good enough. Althought these two example may have been obvious without appealing to the count I wanted to start with a couple of easy ones to show how actually going through the mechanics of evaluating the could gives a pretty foolproof method of determining strategy. Not let's look as a more complex example.]) (;W[de]CR[de] ;B[fp]CR[fp] ;W[cn]CR[cn] ;B[jp]CR[jp] ;W[jc]CR[jc] ;B[dq]CR[dq] ;W[dp]CR[dp] ;B[eq]CR[eq] ;W[cr]CR[cr] ;B[pn]CR[pn] ;W[nc]CR[nc] ;B[pf]CR[pf]C[Where should W play next? Or to be more accurate, from our point of few: what should W play next? Is it time to be agressive or passive? I throw out 4 moves for consideration. You may think of others, but we only have time to consider 4.] (;LB[qc:C][cj:A][jj:B][nq:D]C[Let us discuss these four moves. But first, how do we evaluate the game? Before continuing let us evaluate the position, look at the sequences, then return here. When you have looked at the sequences come back to the variation on this move for a summary. ] ;W[]TR[na][nb][ec][fc][gc][hc][ic][kc][lc][mc][dd][ae][be][ce][an][bn][co][cs]SQ[ra][rb][qc][rc][pe][pg][ph][pi][pk][pl][pm][po][gp][hp][ip][kq][lq][mq][nq][oq][pq][er][es]C[As a rough estimate let us count all territories behind these lines: W has 43, B has 58. B is way ahead in territory. This, of course, is not absolute territory, but if W does not invade B, for example, then it wil become territory. How about infleunce and thickness? W certainly has more potential for extra territroy along the sides, but B has stones on the 4th line, whereas W's are all on the third line. B definitely has more potential in the center. All in all, it seems that B is comfortably ahead. So let's look at the 4 moves. ] ;B[] (;W[cj]CR[cj]LB[pb:A][jj:C][oq:B]C[This move clearly will not be enough. It does add more secure territory on the side but it is on the 3rd line. Almost any move B comes up with will gain as much for B as this move did for W. Imagine a B stone at any one of the points marked. Clearly the exchange of this W move for any of this will NOT change the balance at all towards W, probably the opposite. As W was way behind before this move, it cannot be the right answer.]) (;W[qc]CR[qc]C[This move certainly looks like it has potential, but before we can evaluate it we must lay out the probably follow up sequence on the board and then count.] ;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[qd]CR[qd] ;B[of]CR[of]C[This is the most common sequence. There are others but we will just look at this one. How has the count changed. If you refer back to the original count B has lost about 10 points in the corner and W has gained about 9, for a swing of 19 points. However, W can no longer expect and territroy between K17 and O17 -- a lost of 8pts. In addtion, B has solidify the upper right side and has gained huge influence towards the center. This, altogether, cannot be worth less than 10 points. So, adding all this together we find that W really has not gained much at all by his invasion. The one thing that can be said for this is that he has sente to play elsewhere, but that is not guaranteed if B plays some other sequence. All-in-all, it has to be said that this has not made a huge dent in B's lead.]) (;W[jj]CR[jj]C[How about this? This does not affect the territories we sketched out but it does effect the influence in a big way. By just applying the rule of influence -- all points within 2 of this stone there is an immediate gain of 12 points for B. Adding in a half value for all points closer to W than to B adds in a few more. To evaluate this move better, let us look at a couple of possible B responses and see how the count if affected. ] (;B[oq]CR[oq]LB[fm:A]C[This is a very valid response by B. It is solid, but it is a little slow. W will likely answer at 'A'. In that case W will have a huge moyo and has shifted the balance into his favor. He would even be ahead so this exchange is worth over 20 points -- B would not make it. So let's look at another B response.]) (;B[cg]CR[cg]C[B needs to invade. The one move by W shifted the balance from B have a superior position to B having to invade. Of course, this is not bad for B.] ;W[cj]CR[cj] ;B[eg]CR[eg] ;W[fe]CR[fe] ;B[gg]CR[gg] ;W[he]CR[he] ;B[ej]CR[ej] ;W[dl]CR[dl]C[Let us just hypothesize something like this. B's position has not changed from our original count. What about W? W has gained about 10 points around B8 and an extra two lines of territory around G17, for a total of about 20 extra points. The B group is weak but probably cannot be killed so let us say that it is worth about 5 points of territory and it undermines the W corner so W is going to loose maybe 5 points there from the original count. However, the W stone at tengen is still worth more than that in terms of influence. When we factor in the 5 points for sente to B we see that all of this adds up to a net gain of around 15 points for W. W has definitely count up quite a bit, but is still a little behind.])) (;W[nq]CR[nq]C[This is our last move to consider. Let's look at a possible followup.] ;B[oq]CR[oq] ;W[lq]CR[lq] ;B[kq]CR[kq] ;W[lp]CR[lp] ;B[kn]CR[kn] ;W[np]CR[np] ;B[nn]CR[nn] ;W[mr]CR[mr]C[W is alive. So let us see how the count has changed. Remember, we do not count the whole board, only the local change. B has lost all his original territory between K4 and Q4 for a loss of 20 points and W has gained 2 pts. W's territory to the top and left is unchanged, so it would seem that W is ahead. But B has gained extra influence in the center which, according to our two point rule is worth around10 points. All-in-all, W seems to have gained about 10 points from this sequence. So let us return to out original position and decide what to do.])) (;LB[qc:C][cj:A][jj:B][nq:D]C[So let's have some discussion about the best move here. 'A' is clearly wrong, but what can be said of the rest? On the surface it appears as though 'B' is the best move and there is nothing can be said against it. However, there may be a better sequence. Note that the sequences show after both C and D will reduce the effectiveness of 'B', so playing 'B' in conjunction with either of these may not be so great. But, how about playing 'C' in sente, followed by 'D'? This seems to give the optimal gain. So let's return to the beginning and see what we have learnt today. ])))) (;C[Summary of this lesson: Tonight we have discussed two things: 1. Reevaluating the count at vital points 2. Basing play on an evaluation of the count. The first topic brought together all the information from the previous lesson and showed us how to use it in a local situation. Because only the difference in score is important we can calculate the local change to determine by how much the local battle has affected the overall score and then we can add this figure to our previous estimate to get and updated score estimate. This saves us from having to recount the whole game every time something happens. Of course, counting local battles is more error prone than counting whole boards and so several times thoughout the game we should stop and recount the whole board. As your strength increases you should see that the accumulated error gets less and that your incremental counts become more and more accurate, but even so it is always necessarily to recount the whole board as critical points. The second topic told us how to use the count to determine our actions. If the count tells us we are ahead then we can play more conservatively than if we are behind. If we are way behind we may have to invade. If we are way ahead we may be able to let the opponent's invasion live and still win the game. No major action should ever be undertaken without consulting the count of the game. ]))