# Discussion Of The Value Of Sente And Gote Plays

BillSpight: The following discussion occurred before I posted the explanation in Basic Endgame Theory. In it, people are struggling with the reasons, which are *not* well explained in most yose books.

It seems apparent that people want to assess the gain and loss of plays with the deiri values. But you use miai values for that. The rule is about converting between deiri and miai values.

A general saying says that gote plays are worth half the value of sente plays. The reason for this is that, while you play a gote play, your opponent gets to play twice elsewhere. In order for you to not lose points, your gote play must have been twice as valuable as his two plays.

Hmm. That's maybe not quite clear.

Comment: Confusing. But that's not your fault. -- BillSpight

Let's try again: if in general the overall 'hotness' of the goban has been reduced to plays which have a value of, say, 4 points, then, if you keep sente, you can play two of these plays before losing sente. A sente play worth 4 points followed by a gote play of 7 points makes 11 points before losing sente. If you play the gote play at 7, your opponent takes sente after only 7 points and he can then play the sente play at 4 points and the gote play at 4 points, for a total of 8, 1 point more than you have gained with your sente turn.

Comment: *Sente plays gain nothing, on average.* I assume that you are using deiri values. Then the 7 point gote has a miai value of 3 1/2.

For this kind of analysis you should consider the value of sente (playing first). On average it is half the ambient temperature, which is the value of the largest gote aside from the plays you are focusing on.

If you play the 4 point sente, followed by the 3 1/2 point gote, you gain 3 1/2 points minus 1/2 the ambient temperature (on average). If the temperature is almost 3 1/2, your gain is a bit more than 1 3/4 points (on average). If you play the 3 1/2 point gote and your opponent plays the 4 point reverse sente, you lose 1/2 point but gain 1/2 the ambient temperature (on average). Making the same assumption, that comes to a bit less than 1 1/4 points.

-- BillSpight

Let's try an example.

There are three plays left on the board: 'A' is a 7 point gote play, 'B' is a 4 point sente play and 'C' is a 4 point gote play.

You need to provide the value of the threat behind the sente play though. If this 4 point sente play threatens to only gain 5 points (total) if the opponent tenukis, then since this is less than the 2 other plays, it is actually gote. ~srn347

If White plays 'B', she gains 4 points and keeps sente, so she can play 'A' and gain 7 more points, but she lets Black play 'C', which gives him 4. All in all White has gained 4+7-4 = 7 points more than Black.

If White were to play the largest (gote) point at 'A' first and gain 7 points, Black would play the sente point at 'B' for 4 points and keep sente to play 'C' for 4 more points. All in all White has lost 1 points to Black.

BillSpight: Again, I assume you are using deiri values. Converting to miai values, A is worth 3 1/2 points and C is worth 2 points. You don't say whose sente it is, so let's say that it is Black's sente. Playing in order of size, White plays B (- 4), Black plays A (+ 3 1/2), White plays C (- 2). Result: -2 1/2. If White starts with A (- 3 1/2), Black plays B and White replies (0), then Black plays C (+ 2). Result: -1 1/2. White does 1 point better to make the biggest play first.

GoranSiska - Oops, better check this again. You have just proven your second proverb not first (B seems to be double sente); in addition in the first run White made 7 points more than Black and in the second Black made 1 point more than White. The difference of points is 8 points for Black, due to White's incorrect play%%% MortenPahle - Hmm. I was trying to show that if White assumes that 7 points gote are worth more than 4 points sente, White is wrong, and I think that the example shows it. Maybe it also shows the second 'proverb', why not? But if the example is unclear to others, then we should try to think of a better one.

(GS)- What the proverb states in my opinion is this: if Black defends against White's sente play (for 4 points) and there are two times larger gote plays, he made an incorrect play. Therefore for the sake of kos, and for optimal play, you should keep the position open to allow your opponent to play incorrectly.

(MP)- I think it is against the spirit of Go (and the proverbs) to hope for your opponent to make mistakes, and I also think that move value evaluations do not normally take into account ko-threats etc. - that is another issue. (Of course, in a real game, that may be a consideration, but the basic proverb applies even in the absence of kos.) But I could be wrong.

(GS)- Actually you might want to rethink much of the text on this page... Sorry!

(MP) - :-)

I should hope so. It would be surprising if a 10 kyu could write a text on the endgame which was complete and unambiguous. This is why this is a wiki :-)

(GS)- To go a bit further if your problem was stated so that B is only sente for White then the correct sequence would be:
White A (7pts), Black B or C(4pts) and White the remaining B or C (4pts) giving White 11 pts to Black's 4 pts.
Or even White B, White A, Black C.

(MP)- If A = 7 points gote, B = 4 points sente for White, C = 4 points gote, then I see the correct sequence for White as White B, White A, Black C (White: +7 and has sente afterwards). If White plays A, Black B, White C, the result is the same but Black has sente afterwards. (Black should always play B (reverse sente) before C).

For Black the correct sequence will be B (reverse sente before gote), White A, Black C (Black:+1). If Black plays A, the gote point first, the sequence will end with White B and C, leaving total value Black:-1.

To me, this shows that sente (or reverse sente) points are worth twice the gote points. But I could be wrong.

BillSpight: If B is White's sente, then White's normal sequence is that White plays B and Black replies (0), White plays A (- 3 1/2), and Black plays C (+ 2). Result: -1 1/2. Or White plays A (- 3 1/2), Black plays B (+ 4), and White plays C (- 2). Result: -1 1/2. All same same. :-)

(GS)- The proverb only makes sense if there are further plays along the way as then the issue who gets sente is important:
1. White A (7 pts), Black B (4 pts reverse sente), White C (4 pts) and Black to play - is worse than
2. White B (4 pts sente), White A (7 pts), Black C (4 pts) and White gets to play.

(MP)- Exactly :-)

(GS)- The thing is sente plays are judged by their follow-up so in a way if a 1 point sente play is absolute sente (kills a group of 20 stones in endgame if Black doesn't respond, and Black has no bigger move) then it doesn't matter when White plays it if she doesn't care about the correct order of play (see before) and if there's no possibility of a ko. As far as the result is concerned it just doesn't matter. Hope this helps.

(MP)- See below.

GoranSiska - Let's make an example then. A = 9 points gote, B = 7 points gote, C = 4 points sente for White (and only White!), D = 5 points gote, E= 4 points gote, F = 3 points gote. White to play.

1. A,C,B,D,E,F gives White 20 Black 12, and White to play 2. A,B,CD,E,F gives White 21 Black 11, and Black to play.

So White gained 2 points but lost sente - that is why the proverb states you should play (reverse) sente moves at 1/2 the value of gote moves. If there are further sente plays below the value of F then the optimal sequence for White changes - is this helpful? To prove the other point... 3. C-A,B,D,E,F gives White 21 Black 17, Black to play again. This is the same result as 2 in case C is an absolute sente move. The only difference is Black has a bigger chance of making a mistake in the second sequence than in the third. Hoping for your opponent's mistakes is not a violation of go ethics but is in fact a part of it. I'm not talking about overplays here, I'm talking about a series of moves that leads to the same result but give the opponent a bigger chance to go wrong. In the end, you are not there to help your opponent, are you?

**Comment**: You do not say how large the threat is for C. Let's say that it is larger than A. Again, I assume that you are using deiri values. Normal play for White: White plays C and Black replies (0), White plays A (- 4 1/2), Black plays B (+ 3 1/2), White plays D (- 2 1/2), Black plays E (+ 2), and White plays F (- 1 1/2). Result: -3. Or White plays A (-4 1/2), Black plays C (+ 4), White plays B( -3 1/2), Black plays D (+ 2 1/2), White plays E (- 2), and Black plays F (+ 1 1/2). Result: -2. Starting with C is 1 point better for White. -- BillSpight

Feel free to clear my text after you make the information part of your text as I thing our discussion got a bit out of hand :).

Let's add G, 3 points sente for Black, in there. White to play 1.A(9),C(4 reverse), B(7), G(3 sente)-D(5), E(4), F(3) gives White 20 Black 15, White to play - but in case of absolute sente the correct sequence is 2. C-A(13),G-B(10),D(5),E(4),F(3) gives White 21, Black 14, Black to play. White lost sente but gained two points! The point to see in this, is that in the second run Black got to play B but White got to play C, and White C was bigger than Black B. In real games, after F there are still some points left which are smaller or equal to 3 points so sente/gote at the end of the above sequence may be evaluated differently. In order to play perfect yose you need to know (disregarding kos): 1. The value of every move 2. How many moves are left 3. Value of a sente follow-up if opponent doesn't respond - meaning that the attribute sente/gote of a move may change during the endgame so you must play it at the time it becomes sente to play it. If the move is absolute sente it doesn't matter when it is played, OK?

I remembered another thing! If I'm boring you please let me know as I do tend to talk people to death :)...
Playing a two-point sente move at any stage of the game is OK as long as it is absolute sente (and naturally if it doesn't lose points by making your opponent thick or safe etc...): it's money in the bank! *Dieter disagrees : if the value of the follow-up move is N points, you throw away a valuable threat for any ko worth less than N points. So, the higher the threat, the higher the cost for a profit of only 2 points.*In the A-G example the mistake White makes (when C is absolute sente remember?) is that he plays a gote move leaving a 4 point sente and 7 point gote move as the next largest moves on board. In this case Black will naturally take the 4 point reverse (8 point) move rather than the 7 point gote move. If there was another 8 point move on the board it wouldn't matter; and if there was a 9 point move (all gote) on the board Black could make the mistake of taking a 4 point reverse sente (8 points) instead of the 9 point gote move. Hence White's correct play is to leave the option for Black. That's why I said the proverb is aimed at the opponent's move not your own - you have to look at the situation on the board after you played.

By the way, if you seriously believe that hoping for a mistake by your opponent is wrong then your first move should be resignation :)

- No, I wouldn't go that far, but it's an interesting point. See Go and ethics.

(Original by MortenPahle, comments/corrections by Goran, Dieter, and Bill)

Tokumoto: This subject had been nagging in my mind for a long time until I heard "The difference in the value of the biggest move and the next is the value of Sente" stated by Myungwan Kim. Created Value Of Sente article with it.