Endgame Question 1

According to my understanding of endgame theory, a play at a is a three point sente play for Black (miai value three). On the other hand, a play at c is a five and a half point double gote play (miai value two and three quarters).

I make errors all the time with evaluating these things. Does it get easier with practice?

Have I got this one right?

I calculated these values using thermographs, but this is quite difficult to do in one's head. I feel sure that there must be a traditional technique for doing it, but I can't quite get it from the Ogawa book or from the pages here.

With the knowledge that a is Sente for black, the value of a is easy to deduce, you just assume that if Black plays a, White has to respond at b giving White seven points compared to the ten she would have got from playing a. The difference of the ten and the seven gives the three point value for a.

Similarly, with the knowledge that c is gote, its value is easy to deduce. If Black gets it, then you count the average of the two scores:

1. for if Black gets d too
2. for if White gets d.

This is the average of zero and five points for White. That is, two and a half for White. Contrarywise, if White plays c she gets eight points. The difference of the eight and the two and a half gives the five and a half point value for c. However, since this move is Gote, you have to divide by two to give a miai value of two and three quarters if you want to compare it to the value calculated for a.

However, if you apply the Sente calculation to the Gote move, or the other way around, you get the wrong answer. I realise that this answer will not be very inaccurate for moves that are close to the Gote / Sente divide.

Goodness, what a lot of waffle. My question is: I can work out the value of moves (sometimes) if I know whether they are Sente or Gote. However, in order to work out which they are, I have to draw thermographs in my head. Is there an easier way?

Thanks.

Jono I'm also trying to work this out, however using area scoring. Which brings us to EndgameQuestion2.

evand: I believe the easier way is to calculate it both as sente and as gote, and whichever gives a smaller value is correct. Take the play at a, for example: if we assume sente, it's a 3 point miai value. If we assume gote, the a B play at a gives a score of W + 3.5 (average of 7 and 0), or a W play at a gives a score of W + 10, for a gote value of 3.25. Since the value is smaller if W answers than if not, it is correct play for W to answer; that is, the play is in fact sente. If the values are the same, then the play is ambiguous. Perhaps someone more versed in CGT theory can tell me whether this is always correct or not.

Bill: Tom, you got these values right. Evand, your way works. (With caveats. See below.) :-)

Another approach is to assume one way or the other and check it. If you are wrong, you will find out. For instance, let's assume that both plays are 3 point sente plays. To check that, figure the size of the followup after Black takes. The play at b after Black plays at a is worth 3.5 points, which checks, since it is larger than 3. The play at d after Black plays at c, however, is worth only 2.5 points, which is less than 3, and shows that Black's play is gote.

One thing you have to watch out for is a reverse. For instance,

This is the well known 1 point hane-tsugi. If you work things out, you will find that is a larger play than , and assume that is sente. It is, in a way, but it is a losing sente. Black has to play at , and the whole thing is gote.

Another caveat is that you cannot use the lower value method to compare different options. For instance, a losing sente option can give you a lower value than the correct gote option.