# Priority of plays

Difficulty: Intermediate   Keywords: Strategy
PJTraill: This article seems to me to be wanted (e.g. for the reference in The Endgame, chapters 4 & 5), and I could not find it, which seems odd for such a vital skill. I would expect there to be a Japanese go term for it, but could not find one in the entire list! If anyone knows of a page that handles this, they are welcome to make this an alias, perhaps moving any useful parts of this content there.
PJTraill: This is also about Timing of plays, though with a change of emphasis: there one has a possible play and is waiting for the right point in the game, here one is looking for the right play at a given point in the game.

Priority of plays may refer to the global strategic problem of selecting which part of the board to play in, once one has read out the possibilities of the various positions as well as one can. The depth of reading will, of course, depend on ones ability and the stage of the game.

PJTraill: This article should in my opinion give much more in the way of guidelines, rather than just the list of articles (See also), which is all I have felt capable of supplying, apart from the standard endgame rule (as of 2018-11-05).

## The middle game (stub)

The most important rule in the middle game is:

The middle game is typically a time of concurrent fights, and the priority of plays in them is a matter of nice judgement.

## The endgame

### The basic endgame rule

In the endgame, once one can read out all remaining positions completely and calculate their values, the basic rule is:

1. Play out the valuable moves by repeating the following sequence:
1. (Ignore ⅓-point kos and dame).
2. Make any double sente plays.
3. Identify the largest remaining (double) gote play.
4. Make all sente (if any) plays that are at least half the size of the largest gote.
5. If you have one, make the largest reverse sente play that is at least half the size of the largest gote.
6. Play the largest gote.
• Once you finish, your opponent will be able to do the same until only ⅓-point kos and dame remain.
• Note that in this process:
• The sente/gote status of positions can change as the value of other remaining positions changes.
• This is because sente moves are those that make a threat greater than the value of other possible moves; as their value changes, so does the status.
• Your opponent may be able to interrupt you by playing a sente move of his own with a larger threat than yours. (Kiki??  see note by DaveSigaty in Kikashi/Discussion.)
• If there is a ko in the offing, you may need to retain some sente moves as ko threats; moves of little to no value with large threats are ideal for this.
2. Play ⅓-point kos as in the section below
3. Fill in the dame.
• Take care not to get into shortage of liberties, it is probably wise to make any remaining needed internal connections first.

### The mathematics of the endgame: infinitesimals

For a more complete mathematical analysis of the endgame, see Mathematical Go Endgames. This includes instructions on the correct order of play for infinitesimals.[1]

1. Ignore miai pairs, i.e. pairs of infinitesimals with sum 0.
2. Attack long corridors and/or defend attacks on tinies
• Attack shorter corridors before longer!
• To expand: The priorities are in Figure 2.12.
• Also to do: mention these priorities on other relevant pages; was there already a page with this rules?
3. Play the remaining infinitesimals, which should all be positive.
4. To expand: Play numbers.

Note that this method can gain at most one point more than traditional methods!

### ⅓-point yose kos

To do: simplify here, move details to half-point ko
These are also treated in Mathematical Go Endgames, in § 5.3 Kos (p. 106) and the instructions for playing infinitesimals[1].

At the end of the game, there are often a number of ⅓-point kos (also known as half-point kos).

The priority for playing these is:

1. Connect any ko in which you lead.
• Since any in which your opponent leads is miai with this, there is no point taking that.
3. Make a threat (which the opponent will answer) to contest the very last ko.
• These rules are unaffected by which ko/superko rules are in force.

The result is that miai pairs of opposite kos cancel, any excess falls in triplets ⅓ to the player leading and ⅔ to the one trailing. Then there may be 1 or 2 left; if 2, they cancel; if 1, it is connected by the leader if they have sente or if they have more threats available than their opponent, who starts the ko.

The resulting net area score on the debatable points to the player who is leading in more kos is (PJTraill thinks, please correct if necessary and remove this annotation):

```2 * ( ⌊k/3⌋ + ( k % 3 ≠ 1 | 0 | s > 0 | 1 | m > 0 | 1 | -1 ) )
```

where:

• k is the excess of kos led by one player,
• s = ±1 according as the leading player has sente after 3⌊k/3⌋ moves or not,
• m = the excess or deficit of ko threats available to the leading player over the other,
• % is the minimal positive residue operator,
• (||) is the if-then-else operator.
• ⌊⌋ is the floor (greatest integer not greater) operator,

The resulting net territory score is (PJTraill thinks, please correct if necessary and remove this annotation):

where symbols are as above, and:

• to be added number of captives originally taken in the kos by either player