Priority of plays

Patrick Traill: 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.

Patrick Traill: 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.

Patrick Traill: 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).

Table of contents The opening (stub) The middle game (stub) The endgame The basic endgame rule The mathematics of the endgame: infinitesimals ⅓-point yose kos See also Notes

The opening (stub)

1. Corners:
   1. Claim open corners first
   2. Approach/enclose corners
2. Sides (biggest side first)
3. Center moves: Caps, shoulder hits..

The middle game (stub)

See also Strategic timing in the article on Timing.

The most important rule in the middle game is:

• Play urgent points before big points.
  • Go is ruled by minimal play – play something only because it is required – so the essence of timing is 'recognition of necessary plays'.

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. (Known as ‘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]

For a more comprehensive article on this site, with examples, see Infinitesimals - Optimal Play

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?
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

See the article half-point ko for the value of the remaining kos and other details

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). As stated above, these should not be played until there is nothing else left but dame.

The priorities for playing them are unaffected by which ko/superko rules are in force; they are:

1. Connect any ko in which you lead.
   • Since any in which your opponent leads is miai with this, there can be no point taking that.
2. Take a ko in which your opponent leads.
3. Make a threat (which the opponent should answer) to contest the very last ko.

The result is that miai pairs of opposite kos cancel, and if one player leads in ``n`` kos, the ``2n`` debatable points yield them a net area score of approximately ``{:2n:}/3``; an exact formula is given at Half-point Ko.

See also

The following articles are relevant:

• Whole board thinking
• Direction of play
• Positional judgement
• Fuseki
• Priority – (though that article is more about rules of thumb)
  • Play urgent moves before big moves
  • Sequencing questions – (as of 2018-11-05 this is simply a list of articles)
  • Timing – Rules of thumb for strategic timing & examples of local timing
• Kikashi – Forcing moves, especially played out of sequence
• Premature – Moves played to early
• Probe – A move forcing the opponent to commit to a choice, ideally when you have good answers to all his options
• Order of play alias Order of moves – (though that is more about local considerations)
• Endgame coupling – (though that is also more local, being about positions where plays are not, in fact, independent?)
• Urgent point – (though that refers to a more unambiguous / less finely balanced situation)
• Sente, gote and counting – These are essential to the priority of plays in the endgame, and sometimes sufficient to answer the question of priority completely (as in the section The endgame rule above)
• Combinatorial game theory (CGT) – Deals with sums of games and generalises the concepts of sente, gote and value. In theory, once your reading of all remaining active positions is complete, the question of priority is purely a question of CGT, though the basic form of CGT excludes loopy games and hence kos.

Notes

• [1] For instructions on the correct order of play for infinitesimals, see Figure E.9 in Appendix E: Summary of Games (p. 194) and the text on p.26. The table is also shown as Figure 2.12 (p. 24), but without the instructions for ⅓-point yose kos.