Endgame proverbs

[topazg]

In general, to get the last play at the level of the plays,

For instance, suppose that the last two plays are a gote that gains 1 point and a reverses sente that gains 1 point. If you take the reverse sente, you gain 1 point, but then the opponent takes the gote to gain 1 point, as well. Net result: 0. But if you take the gote, you gain 1 point, and then the opponent takes his sente, for no gain. Net result: 1 point for you. Note that in the second line of play you get the last play (the reply to the sente).

I can understand the reasoning, but I can't make the reasoning work in practice. If there are the two plays you mention above, then there is no gain. 1 point reverse sente is still worth 1 point, so if he got it in sente the net difference is still 0 points for either side, but because he gets it in sente he would have got the third play if there was one. However, if you take the reverse sente, he takes the gote, and you get the third play? Why am I wrong?

[Bill Spight]

For instance, suppose that the last two plays are a gote that gains 1 point and a reverses sente that gains 1 point.

I'm sorry, I still don't understand. If black can choose a 1 point gote or a 1 point reverse sente, I do not see how gote could be better.

Case 1: If black takes the gote, he gets a point, white gets a point for the move that is his sente, then black blocks. It's 1-1 and white's turn.

Case 2: If black takes the reverse sente, and white takes the gote, it's 1-1 and black's turn.

The only difference that I see is that in case one, black agrees to let white keep sente when white plays the sente move. Would you please explain this a bit more? The only situation in which I can see case 1 be better is in rules like AGA rules, and then only if this would cause white to have to pass first.

Here is an example:

(;GM[1]ST[2]SZ[19]AP[GOWrite:2.2.21]FF[4]CA[ISO8859-1]C[Black has a reverse sente that gains 1 point and a gote that gains 1 point.]PB[ ]AW[dc][cc][bd][ec][ea][ce][eb][ad][fb][gb]PM[2]FG[259:]PW[ ]GN[ ]AB[bb][aa][cb][bc][ac][db][fa][ha][hb][hc][gc]
(
;C[Black plays the reverse sente.]B[da]
;C[White gets the gote. Net local score: +1]W[ga]
)
(
;C[Black takes the gote.]B[ga]
;C[White gets ]W[da]
;C[Net local score: +2

One point better for Black.]B[ca]
)

)

[Chew Terr]

Oh, you're calling it a one-point gote after halving its value? Okay, that makes sense, I've seen that done before. I was comparing one-point reverse sente with what you would call a half-point gote, I think? Yes, I could see that a gote that by itself nets two points could be preferable to a one-point reverse sente. Thanks for clearing it up (unless I'm still misunderstanding =D).

[kokomi]

If the opponent has no gain from a sente move, was it really sente then?

A sente move that does no good to yourself, or even benefits your opponent is called 'Su Shou'.

[Bill Spight]

why gote is preferred to reverse sente?

In general, to get the last play at the level of the plays,

For instance, suppose that the last two plays are a gote that gains 1 point and a reverses sente that gains 1 point. If you take the reverse sente, you gain 1 point, but then the opponent takes the gote to gain 1 point, as well. Net result: 0. But if you take the gote, you gain 1 point, and then the opponent takes his sente, for no gain. Net result: 1 point for you. Note that in the second line of play you get the last play (the reply to the sente).

I'm trying to understand this.

Let's say we modify the situation a bit and say that there are two gote plays left and two reverse sente plays left, all equally valuable.

Then the two gote are miai and tend to cancel out. (They may cancel out exactly.) That leaves the reverse sente.

It seems to me that if you play gote in this situation, your opponent will play the two sente plays and then the last gote play, but if you play reverse sente, your opponent will play sente, then gote, leaving you to get the last gote play. So, we should play reverse sente to get 2/4 of the available points instead of 1/4. Is my thinking wrong somewhere here, or is this a situation where the guideline is inverted? And in that case, what's so exceptional about the above situation that the guideline is still a good guideline?

Thanks. I should have made miai higher priority than the preference:

Rule of Thumb 2) In general miai will be shared,

Edit: here's an illustration of how I imagine this situation, possibly clarifying where I'm confused.

(;GM[1]FF[4]AP[Drago:4.01]SZ[19]CA[UTF-8]C[Black to play. Reverse sente along the top, gote along the bottom. Ignore the center.]AB[aa][bb][bc][ac][cb][db][sa][rb][rc][sc][qb][pb][ar][br][cr][dr]
[bs][ds][rr][qr][sr][rs][pr][ps]AW[ad][bd][cd][cc][dc][eb][ec][ea][oa][oc][ob][pc][qd][qc][rd][sd]
[aq][bq][dq][cq][eq][fq][gq][hq][iq][ir][is][gr][gs][hs][fs][jq]
[lq][kq][mq][nq][oq][pq][qq][rq][sq][kr][ks][js][ns][ms][ls][jr]
[mr]
(;B[er]C[Black prefers to play gote first.];W[da];B[ca];W[pa];B[qa]
;W[or]C[Black has two points in each corner; 8 points. White has 3 points (including the eyes along the bottom).])
(;B[da]C[Black prefers to play reverse sente first.];W[pa];B[qa];W[er]
;B[or]C[Black has 9 points, white has 3 points. Black is better off by one point.]))

The gote are not only exact miai, they gain less than the reverse sente (1/2 point instead of 1 point).

[Bill Spight]

In general, to get the last play at the level of the plays,

For instance, suppose that the last two plays are a gote that gains 1 point and a reverses sente that gains 1 point. If you take the reverse sente, you gain 1 point, but then the opponent takes the gote to gain 1 point, as well. Net result: 0. But if you take the gote, you gain 1 point, and then the opponent takes his sente, for no gain. Net result: 1 point for you. Note that in the second line of play you get the last play (the reply to the sente).

I can understand the reasoning, but I can't make the reasoning work in practice. If there are the two plays you mention above, then there is no gain. 1 point reverse sente is still worth 1 point, so if he got it in sente the net difference is still 0 points for either side, but because he gets it in sente he would have got the third play if there was one. However, if you take the reverse sente, he takes the gote, and you get the third play? Why am I wrong?

There is no third play in the example. The SGF I posted should clear things up.

[John Fairbairn]

Does "endgame" always have to wait until the "middle game" in over?

No-one has answered this part of the OP's question, but it represents the real problem succinctly. The real problem is one of terminology, and even the Basic Endgame Theory page on SL manages to start off on entirely the wrong foot.

The first point is that it is more correct to talk about "boundary plays" (= yose) and these can occur even in the opening. They are common in the middle game. Conversely, the endgame can include plays (e.g. ko fights) that are not boundary plays.

The second point is that discussion of the topic is riddled with confusing usages of terms such as count, size, move, point, tally, etc. It is usually futile to start reading anything, even by an expert, about counting boundary plays unless you know for certain how these various terms are being used. It is not just that writer A may use one term and writer B another. It is that writer A may use the same term in two ways even in the same sentence. For example, with count you need to know whether the de-iri count or the miai count is being referred to. Context can help, but as the earlier posts in this thread show, it is unsafe to make assumptions about the context.

Even if you do come to terms, so to speak, with counting you need to remember that this is just one part of boundary play study. For instance, you need to be familiar with the many tesujis for this aspect of the game - not so very different from middle-game or life-and-death tesujis, but instead of good shape or life the goal is to gain extra points.

A further aspect of study is really for dan players, and that is thickness (i.e. solidity). Often you will want to play the most secure move rather than the one that looks biggest. This applies usually to boundary plays in the middle game (and ability here is one of the markers for very strong players), but it can occur quite late in the game, too, for example when there are still ko fights lurking.

There are also other kinds of boundary play strategy. One centres round the tedomari - getting the last move of a certain level. Just as in the opening where, say, there are three big 20-point big points you will usually try to improvise a plan to get two out of three of these, so with boundary plays: if there are three 2-point gote plays you will want to ensure you get two of them (this is often where thickness comes in). Timing is general is an important element of boundary play strategies.

Proverbs don't really cope with such a wide range of requirements, although sayings such "the monkey jump is worth 7 (or 8) points" are useful in various ways. I think the most unuseful advice is to stress the importance of sente. It is often plain wrong - usually the biggest move is best, often the thickest move is best, and often the tedomari is your goal. Sente is just a means. The end (or boundary ) matters more than the means.

When you see a pro described as "good at the endgame", remember that this should be "good at boundary plays". In fact it really means he is good at the middle game. It does not mean he is good at counting local positions - all pros can do that and they have very many standard counts stored in their heads. It means rather that he is good at evaluating boundary plays, potential as well as actual, at an early stage and so can make the right decisions as regards timing or thickness.

[topazg]

There is no third play in the example. The SGF I posted should clear things up.

In your .sgf example that's a two point gote move, not a one point gote move. There's a capture and a point of territory afterwards, so it's a 2 point swing. The reverse sente is 1 point, so if there are only two plays remaining, the gote point is bigger because White can't get more than the 1 point in sente. If there's even a 1 point gote move left as well, he can get parity because he takes the one point and keeps sente for the 3rd play. The only reason the gote is bigger in that .sgf is because the reverse sente is 1 point and the gote is 2 points and there are no plays afterwards.

[Bill Spight]

I also don't get this, and it wasn't my understanding at all. Saying this, I'm not the 5 dan, so I'm probably wrong, but Chew's analysis is exactly how I saw it:

Assume there's a 2 point gote move, a 2 point reverse sente move, and a 1 point gote move left.

Then it does not matter, if the gote values say how much it gains.

Line 1) Take gote, gaining 2 points, then the opponent takes the sente and the 1 point gote, gaining 1 point. Net result: a gain of 1 point.

Line 2) Take reverse sente, gaining 2 points, then the opponent takes the top gote, gaining 2 points, and finally you take the last gote, gaining 1 point. Net result: a gain of 1 point.

The assumption in the initiative will be worth the next biggest move, which presumably is smaller than the ones taken.

The initiative is worth, on average, 1/2 the gain of the largest remaining play. (Consider the extremes. The most the initiative gains (except for ko) is how much the largest play gains. The least is 0. The average is 1/2 the gain.)

It seems like reverse sente is worth half a move more than gote for the same point value plays?

Because of privilege, we make the usual assumption that sente are played. Then we can regard the rest of the board besides the reverse sente as a number of gote. Let's call the reverse sente R and the top two gote G0 and G1. G0 gains at least as much as G1. We assume that either player will play G0 before G1.

Line 1: Take R, then the opponent has the initiative and takes G0. Estimated result: v(R) - v(G0)/2

Line 2: Take G0, then the opponent takes the sente and then has the initiative and takes G1. Note that the result will be the same as if the sente had already been played. Estimated result: v(G0)/2

Comparison: v(R) - v(G0)/2 vs. v(G0)/2
IOW: v(R) vs. v(G0)

If the reverse sente and the gote gain the same, this comparison does not decide between them. But let's include v(G1) in the analysis. That gives us this comparison:

v(R) - v(G0) + v(G1)/2 vs. v(G0) - v(G1)/2

IOW: v(R) + V(G1) vs. 2*v(G0)

If v(R) = v(G0), that gives us this comparison:

v(G1) vs. v(G0)

Since v(G1) <= v(G0), that gives the edge to the gote.

PS As an aside, Ogawa Tomoko and James Davies give reverse sente as double the value of gote plays as a rule of thumb in The Endgame book, which doesn't seem consistent with taking gote first.

All that does is allow a comparison. It says nothing if the comparison is equal.

[Bill Spight]

There is no third play in the example. The SGF I posted should clear things up.

In your .sgf example that's a two point gote move, not a one point gote move.

A play gains 1 point. At the start the stone in atari is worth -1 point (for Black). If Black saves it she gains 1 point, for 0; if White takes it he gains 1 point, for -2.

White can't get more than the 1 point in sente.

Sente gains nothing. (On average.) White has the privilege in the sente, which means that we expect that White will play the sente, and assess territory accordingly. Before White takes the sente we count 2 points in the corner, which is the local score afterwards. Net gain from the sente = 0.

We call it a 1 point sente, but what we call a play does not say how much the play gains. It is the reverse sente that gains 1 point.

The only reason the gote is bigger in that .sgf is because the reverse sente is 1 point and the gote is 2 points and there are no plays afterwards.

To call a gote a 2 point gote does not mean that it gains 2 points. Remember that to compare swing values you multiply the reverse sente value by 2 to compare it to a gote value. That tells us that the two plays are equal (on average). The key in the example is who gets the last play, not that the gote is somehow bigger than the reverse sente.

[topazg]

In your .sgf example that's a two point gote move, not a one point gote move.

A play gains 1 point. At the start the stone in atari is worth -1 point (for Black). If Black saves it she gains 1 point, for 0; if White takes it he gains 1 point, for -2.

I see where you are coming from, but I find it very counter-intuitive. For the purposes of the game, you can identify a reverse sente as "one you'd respond to". In the example you gave, the swing value of the reverse sente is 1 point, and the gote is 2 points. If they are the only two points remaining, it is better to take the gote as White cannot use his sente for a 3rd play. If there was a 3rd play at 1 point gote remaining, there would be no difference in which you took. If there were 2 one point gote moves remaining after the original two, it would be better to play gote again because it's a point bigger. However, if the gote move was 1 point the reverse sente would always be better because it kicks the initiative chain the other way. i.e. if there were only those 2 plays (but at 1 point each), there would be no difference as the 3rd play you get from taking the reverse sente move would be dame or pass. However, if there was an odd number of remaining plays you would benefit from taking the 1 point reverse sente play over the gote, as you then have sente for play 3.

I have a feeling we have a different definition of a 1 or 2 point gote move

I know that the Davies / Ogawa book refers to that single atari as a 2 point gote move, so I suppose I'm biased as that's been my reference for endgame evaluation, but it feels more intuitive to evaluate the point value as the swing value.

[Bill Spight]

Oh, you're calling it a one-point gote after halving its value? Okay, that makes sense, I've seen that done before. I was comparing one-point reverse sente with what you would call a half-point gote, I think? Yes, I could see that a gote that by itself nets two points could be preferable to a one-point reverse sente. Thanks for clearing it up (unless I'm still misunderstanding =D).

The gote does not net 2 points. It is not bigger than a 1 point reverse sente. The whole point is getting the last play.

[HermanHiddema]

I have a feeling we have a different definition of a 1 or 2 point gote move

The difference between deiri (swing) counting and miai (average gain) counting, it seems. See http://senseis.xmp.net/?BasicEndgameTheory for a basic explanation.

[Bill Spight]

In your .sgf example that's a two point gote move, not a one point gote move.

A play gains 1 point. At the start the stone in atari is worth -1 point (for Black). If Black saves it she gains 1 point, for 0; if White takes it he gains 1 point, for -2.

I see where you are coming from, but I find it very counter-intuitive. . . .

I have a feeling we have a different definition of a 1 or 2 point gote move

Actually, I talk about how much a play gains (on average). What you are calling a 2 point gote gains 1 point.

I know that the Davies / Ogawa book refers to that single atari as a 2 point gote move, so I suppose I'm biased as that's been my reference for endgame evaluation, but it feels more intuitive to evaluate the point value as the swing value.

For purposes of simple comparison, there is nothing wrong with swing values, along with the necessary multiplications and divisions. However, I have observed for many years that people assume that the swing value tells you how much a play gains. That is not so. Since questions that go beyond simple comparison, such as whether to play gote or reverse sente, pretty much require saying how much a play gains, I just talk about that.

[Bill Spight]

The second point is that discussion of the topic is riddled with confusing usages of terms such as count, size, move, point, tally, etc. It is usually futile to start reading anything, even by an expert, about counting boundary plays unless you know for certain how these various terms are being used. It is not just that writer A may use one term and writer B another. It is that writer A may use the same term in two ways even in the same sentence. For example, with count you need to know whether the de-iri count or the miai count is being referred to. Context can help, but as the earlier posts in this thread show, it is unsafe to make assumptions about the context.

I hope that count, move, point, and tally are not being used in confusing ways, at least in the literature. Charles Matthews introduced the term, tally, for the net number of plays between two positions. That is clear, I think. I hope that people are not confused. As for count, OC it is regular English, but Berlekamp introduced it as a technical term to refer to the assessed territory (along with dead and captured stones) in a local region. I am unfamiliar with its use to refer to the value of plays (which is what makes it a good term for something else ). I hope that people will not start using it that way.