# BasicEndgameTheory/old content

Path: Endgame =>
Sub-page of BasicEndgameTheory

# Gote plays are worth half of sente plays

Bill: The point of this saying is the comparison of sente and gote plays. Most go players use what is called deiri counting. With deiri counting you cannot compare sente and gote plays directly, but must halve the value of gote plays to compare them with sente plays. Doing so produces what are called miai values. The examples below show why this is done.

Why you halve the deiri value of gote plays

Simple 3 point gote (deiri)

1 1/2 point gote

If Black cuts off the White stone, the local score is 3 points (for Black). If White saves it, the local score is 0. We may represent this position like this:

```    {3 | 0}
```

On average, this position is worth 1 1/2 points. On average, a move gains 1 1/2 points. The miai value of a play is 1 1/2 points, but the deiri value is 3 points. The deiri value is the difference between 3 and 0, which are separated by 2 plays, not 1 (1 play for Black, 1 for White). If you want to add and subtract plays, you must use miai values, and to convert the deiri value of a gote to its miai value, you divide by 2. It's no more complicated than that.

Why you do not halve the deiri value of sente plays

Simple 3 point sente

3 point sente

If Black cuts off all the White stones, the result is 10 points. If White connects to the single stone and Black cuts off the rest, the result is 7 points. If Black lets White save all of them, the result is 0. We may represent this position like this:

```     {10 | {7 | 0}}
```

The average value of this position is 7. If Black plays his reverse sente, he gains 3 points (on average). If White connects to the single stone, her threat is worth 3 1/2 points, which is more than Black's reverse sente. When the biggest play elsewhere is worth more than 3 points but less than 3 1/2 points, White will normally be able to make this play with sente, and Black will not be able to afford to play the reverse sente first. So we call it White's sente.

It turns out that the deiri value of a sente is the same as its miai value, because there is only one net play between the sente result and the reverse sente result. No conversion is necessary. For instance, the deiri value of our example is 3 points (10 - 7), the same as the miai value (10 - 7)/1.

# Play double sente points first

In double sente points, it is first come, first served. Often, the 'threat' behind the sente play is much larger than the value of the play if answered, so you can count on your opponent answering the sente play, even though the actual value of the sente play is smaller than the overall goban 'hotness'.

Bill: Double sente can look misleadingly small, so their "apparent" value may be smaller than the ambient temperature. However, if their actual value is not greater than that, they are not double sente (as a rule).

See types of endgame sente plays.

# Play sente points which have a large 'threat'

Since sente is important, you may find that your opponent does not always answer what you consider a sente play, but plays a sente play of his own. If the 'threat' behind his sente play is larger than yours, you will have to answer his sente play. You have then given him sente, and he can play the sente plays in his order. Of course, he will have to finish in sente to come back and answer your original play.

In general, a sente move can be said to be 'absolute sente' if the threat behind it is larger than the overall goban 'hotness'. I.e., in the endgame, when moves are worth around 10-12 points, say, a sente move (although itself only worth 2 points) which threatens a follow up larger than 15 points, will be 'absolute sente' and will always be answered. Therefore, these moves can be played long before the goban 'hotness' sinks to the actual value of the move (2 points).

# Play gote points which have a sente follow-up

The value of gote points can be larger if the follow-up to a gote play is sente. You should play these before you play 'purely' gote plays. (The concept of sente is of course relative and not always black/white). A slightly related topic is Reverse Sente.

Bill: The extra potential lies in the fact that the sente follow-up may be used as a ko threat.

Other than that, when choosing among plays of about the same size, it is typically better to pick one with a sizable follow-up over one without one. See Infinitesimals.

# Captures which are rarely worth taking

The simplest capture is a stone in a ko which does not threaten the group - this stone has no value but one half a point and is not worth taking.

Anonymous: Actually, isn't this only a third of a point?

A white stone string ( fills up)

A white two-stone string

The two-stone string has also a deceptively low value of only 1 point.

If Black captures at the circled point, White does not have to respond. Black can then connect (in gote) and make one point of territory plus two stones captured for a total of three points, but both moves are gote! 1.5 points in gote per move is not very good.

Bill: The average value of the original position is 1 point. Black gains 1 point by taking, and another point by connecting.

A white three-stone string

The three-stone string may look big, but is only worth around 5 points with 2 gote plays - 2 and a half points gote per move is again not very good. -- MortenPahle

Bill: The original position is worth slightly less than 2 points. Taking is worth slightly less than 2 points. Connecting after that is worth a bit more than 1 point.

Using Ogawa's endgame theory, this would be the way to evaluate the move in order to prioritize: (Ogawa uses miai counting)

makes 3 provisional points. If Black follows up with ...

... 3, he makes an additional 2 points in gote.

Follow-up moves to gote moves are counted half their value. So the total value would be 3 + 2/2 = 4.

If, however, White answers with 2, Black has taken three stones and lost one stone, but he did so in sente ...

Bill: For counting, we do not assume an immediate reply.

He can follow up with , making one point in gote.

This is a follow-up move to a sente move, and should be counted its proper value. Moreover, he can steal another stone in ko later, but the added value of that is already close to zero (1/4 AAMOF). So in total, the move is now worth (slightly more than) 5 points (= (3-1)x2 + 1). This already tells us that White will recapture not too soon.

Bill: After , the local score is 3 1/3 points on average. (Black took three stones, lost one, and can claim 1/3 of White's ko stone, in addition to one point of territory.) If White plays at , the local score is 2 points. So the local score after White takes back is 2 2/3 points.

For White to recapture means: 2 points in gote + 1 point in gote (= 2.5 points).

Bill: If Black plays at the result is 5 points, and if White plays there it is 2 2/3 points. The miai value of a play at is thus 1 1/6 points, and the local count after is 3 5/6.

If White saves her stones, the result is 0, of course. So is worth 1 11/12 points, and the count of the original position is also 1 11/12.

I have added some precision, but Dieter's analysis is certainly close enough for practical play. :-)

These values only serve to prioritize when a lot of moves are available. When only a few (3 to 5) endgame moves are available, it is far easier and more accurate to imagine the several orders in which the moves can be played, still keeping the basic endgame theory in mind.

Authors

Tom: I have an Endgame Question

tapir: The "value" of gote and sente. It should be stated more clearly that the gote is worth half or sente double and double sente infinity is as a heuristic for move choice only. While somewhat clear that you may lose a game even if you get a double sente, it is kind of confusing for the other moves. Another idea is whether one should start with counting or with sente gote. I feel like sente gote is more important (losing sente in macro-endgame is probably more crucial than losing some points in micro-endgame through wrong sequence of moves) than counting.

Path: Endgame =>
BasicEndgameTheory/old content last edited by HermanHiddema on March 25, 2010 - 18:55