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Discussion Of The Value Of Sente And Gote Plays
Difficulty: Beginner
Keywords: EndGame
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 loose 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 loosing 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 3 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. 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 7pts more then black and in the second black made 1pt more then white. The difference of points is 8pts for black due to white incorrect play! (GS)- What the proverb states in my opinion is this if black defends against white sente play (4pts) and there are twice larger gote plays he made an incorrect play therefore for the sake of ko's 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. (Ofcourse, 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) - :-)
(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 11pts to black 4pts.
or even white B, white A, black C.
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 (7pts), black B (4pts reverse sente), white C (4pts) and black to play - is worse then
2. White B (4pts sente), white A (7pts), black C (4pts) and white gets to play.
(GS)- The thing is sente plays are judged by their follow-up so in a way if a 1pt sente play is absolute sente (kills a group of 20stones in endgame if black doesn't respond and black has no bigger move) then it doesn't matter when white plays it if he (she?) doesn't care about the correct order of play (see before) and of 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 - Lets make an example then. A=9pt gote, B=7pt gote, C=4pt sente for w (only w!), D=5pt gote, E=4pt gote, F=3pts gote. White to play. 1. A,C,B,D,E,F gives w20 b12 white to play 2. A,B,CD,E,F gives w21 b11 black to play So white gained 2 pts but lost sente that is why the proverb states you should play sente moves at 1/2 value of gote moves. If there are further sente plays below the value of F then the optimal sequence for white changes - is this helpfull? To prove the other point... 3. C-A,B,D,E,F gives w21 b17 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 bigger chance of making a mistake in the 2nd sequence then in 3rd. Hoping for your opponents 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 lead to the same result but give the opponent a bigger chance to go wrong. At last 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 :). Lets add G 3pt sente for black in there. White to play 1.A(9),C(4reverse),B(7),G(3sente)-D(5),E(4),F(3) gives w20 b15 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 w21, b14 black to play White lost sente but gained two points! The point to see in there is that in the 2nd run black got to play B but white got to play C and white C was bigger the black B. In real games after F there are still some points left which are smaller or equal 3pts so sente/gote at the end of the above sequence may be evaluated differently. In order to play perfect jose you need to know (disregarding ko's): 1. Value of every move 2. How many moves are left 3. Value of a sente followup if opponent doesn't respond - meaning that the attribute sente/gote of a move may change during 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 o.k.? I remmebered another thing! If I'm booring you pls. let me know as I do tend to talk people to death :)... Playing a 2pt sente move at any stage of the game is o.k. 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 remmember?) is that he plays a gote move leaving 4pt sente and 7pt gote move as the next largest moves on board. In this case black will naturally take the 4pt reverse (8pt) move rather then 7pt gote move. If there was another 8pt move on the board it wouldn't matter and if there was a 9pt move (all gote) on board black could make the mistake of taking 4pt reverse (8pt) instead of 9pt gote move hence white correct play is to leave the option for black. That's why I said the proverb is aimed at the opponents move not yourown - you have to look at the situation on the board after you played. Btw. if you seriously belive that hoping for a mistake by your opponent is wrong then your first move should be resign :)
(Original by MortenPahle, comments/corrections by Goran and Dieter) BillSpight: Why you divide the deiri value of a gote by 2. Here is a simple 3 point gote (deiri).
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 divide the deiri value of sente. Here is a simple 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, so no conversion is necessary.
This is a copy of the living page "Discussion Of The Value Of Sente And Gote Plays" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |