Value Of A Monkey Jump

Monkey jump.  

In Monkey Jump, unkx80 wonders what the value of this sequence is. I will try to answer this question.

Zero-diagram  

To know the value of the moves, we will have to look at the difference in outcome between various results. To make that easier, we will define some absolute values for the outcome. To do so, I have taken the result to the left arbitrarily as my zero-point - any result better than this for Black is given a positive value, and result worse is given a negative value.

White plays first.  

We will have to compare the result with the result we would get if White played first. For this result, it is important to know whether the hane of is sente. If it is, we may assume that White plays it at some time in the future, and the outcome is -6 (White has the four marked points more than in the zero diagram, while Black has played two moves in what is there considered his territory). If is not sente, (now giving a value of -5) and Black at 5 (giving a value of -3) must be regarded equally likely, so the outcome is the average of the two, being -4.

Black plays after the monkey jump  

Likewise, after the monkey jump, we have to look at the results when Black plays next and when White plays next. If Black plays next, he will connect at here. White's territory is 1 smaller than in the 'zero diagram', while Black's 0.5 larger (depending on who gets to play at a), so this is worth +1.5.

White plays after the monkey jump  

More complicated is the situation when White captures at . If Black answers at a, Black gets one point for the marked point, one for the marked white stone, -1 for the captured black stone, -0.5 for White's possibility to get a point of territory there, and +1/6 for Black's possibility to capture a stone in ko. Adding all up, the score is +2/3.

If White next plays at a, we can regard this as sente if the hane at 3 in the 'White plays first' diagram was sente (Black will lose quite a bit if he allows White to capture once more), leading to a result of -2. If it is not sente, the value is again the average between the result if Black plays next (-2) and the result if White plays next (-2 2/3), being -2 1/3.

So what is now the result after White's capture? If the hane were not sente, it is simply the average between Black moving next and White moving next, which is -5/6. If it is sente, we will assume that the value is -2, that is, we assume that White's original capture is gote.

Comment: is sente in either case. So assume - Black a.

(Suppose that the value after is -5/6. Then Black a is worth 1 1/2, moving from -5/6 to + 2/3. But if is gote, the value before is the average of 1 1/2 and -5/6, or 1/3, and is worth 1 1/6, less than Black a. Impossible if is gote, so is sente.) -- Bill Spight

Adding up everything, the value after the monkey jump is +1/3 if the hane is not sente, and -1/4 if the hane is sente. As the values after a white move are -4 and -6 respectively, the outcome is that the monkey jump is worth a bit over 4 points if the hane is not sente, and slightly under 6 if it is. In both cases in sente.

Andre Engels waiting for people to correct his calculation errors...

Bernhard Herwig? As Bill pointed out, White's capture is sente. So it becomes White's "right" to play that move. Andre already calculated the score of the position after and Black a: +2/3. This is now the expected position after White's monkey jump. So the score after the monkey jump is 2/3. Compare this to the value -4 or -6 if White plays the reverse sente. You get: The value of the monkey jump is 4 2/3 or 6 2/3 (depending if White's HaneTsugi is sente).

Bill: All of that assumes that the monkey jump is sente in the first place. Given the diagram, that is an unlikely assumption. Further discussion below.

unkx80: Thank You!

Alternative Zero-diagram  

Starting point black territory versus white territory.

But now the Big Question :-)  

The real question that I always have is whether Black should play the small monkey jump at here rather than the monkey jump in cases like this? Is this better or worse and why?

--DaveSigaty

zephi? The small monkey jump is chosen for the sake of sente in situations where the large jump is gote, but the small jump is sente. In situations of a solid wall on the 3rd line of 4 stones or more, either monkey is going to be gote unless b sacrifices his original stone (and since that is the case there is no reason to take the smaller monkey jump). Anyway, a monkey jump in this situation is easy for w to handle and not worth as many points as a monkey jump under 4th line (or higher) stones

White plays first.  

White plays first at .

Case I: If the hane at is sente, then Black is left with 6 points and White has 10 points of territory.

Case II: Otherwise, we assume that Black and White played at and respectively and Black has 8 points and White has 10 points.

Black plays first.  

Black plays first, and the sequence ends at . I shall assume that White gets the atari at a in sente, so Black will have to connect at b. So Black has 8 points and White has 7 points.

So what is the value of ?

Case I: Black's territory gained by 8 - 6 = 2 points and White's territory is reduced by 10 - 7 = 3 points. Thus the value is 2 + 3 = 5 points.

Case II: Black's territory is unchanged at 8 points, but White's territory is reduced by 10 - 7 = 3 points. The value is 3 points.

Conclusion: is worth 5 points if the hane is sente, 3 points otherwise. Comparing it with the monkey jump I proposed (<6 points or >4 points depending on whether the hane is sente), the monkey jump is definitely better.

Any objections? ...

--unkx80

Value of the monkey jump  

The values of the monkey jump, and of the alternatives, a, b, and c, depend on surrounding conditions. Let us suppose that if White c, White's hanetsugi is sente, and that the white wall on the third line extends indefinitely. (In that case we know that eventually the one-space jump on the first line is worth 4 points, and can be treated as sente.)

The calculations are complicated, and I will just summarize my findings here. (No guarantee that I haven't made a mistake! In fact, since my original posting, Prof. Teigo Nakamura, 6-dan, has showed me some of my mistakes. I have revised accordingly. -- And since then, both he and I have found other mistakes. This is the second revision. {Later. WTD's suggestion, a throw-in, seems to be generally better than the book play. See below.}) Real positions will be different, anyway. Who is komaster makes a difference, of course. I will assume that neither player has ko threats, to give a neutral result.

Monkey jump (one tenuki play)  

, tenuki.

To evaluate the position after , we play out the subsequent sente sequences, - and - . ( is the four-point play that we can treat as sente.) The net score is +3 (for Black.)

Monkey jump (White replies)  

tenuki.

threatens White at 2. Afterwards, - is sente. The local count is -5 1/3. A play at a has a miai value of 2/3.

Monkey jump (What is the count?)  

If Black plays the net count is +3; if White plays it is -5 1/3. The count now is the average, -1 1/6, and the miai value of a play is 4 1/6.

Monkey jump (White plays first)  

After , the hanetsugi is three points sente for White. The count is -12.

The original count is the average of -12 and -1 1/6, or -6 7/12, and this monkey jump has a miai value of 5 5/12.

Value of the monkey jump(2)  

In this case if White plays first, there is no sente follow-up. That means that White a originally garners two points less, and that reduces the miai value of the monkey jump by one point, to 4 5/12.

Monkey jump(2) White's response  

White's response is different, however. If instead of , White does not threaten White at 4 right away, because there is no sizable follow-up threat.
- is sente later, however, and it comes to the same thing in the end.

Small monkey jump  

Without going into any detail, the small monkey jump is worse than the large monkey jump in this situation. I reckon the count at slightly more than -3, while the count after the large monkey jump is a little less than -1. The difference is almost two points.

Two points can be accounted for as the difference in white territory from intruding one point less. The actual difference is less than two points because the small monkey jump is better connected than the large monkey jump.

I was surprised to find that the difference was so large. But it seems that Black's follow-ups to the small monkey jump are worth less than those to the large monkey jump. The reason seem to be that when Black intrudes further, the weakness at a becomes more critical. Of course, the large monkey jump has a corresponding weakness, but it is already very weak, and Black's extensions do not make it much weaker.

The kosumi:

Kosumi  

The kosumi is worth about the same as the small monkey jump. It is very solid, and - is later sente.

Crawl  

The crawl of gains three points. It takes away two points from White and adds one to Black.
gains four points, however, since a white play there takes away the two marked black points in addition when White plays hanetsugi with sente.

 

WTD Having set out to compose a problem for goproblems.com which demonstrated the superiority over it’s alternatives, of the large monkey jump to followed by a 1 space jump back to , when the defender has 4 stones on the 3rd line, and sente is required; I found it difficult because White can reply to at x, rather than the book play of y.

 

Here, Black has five 1st move options: s = small monkey jump, k = kosumi, c = crawl, m = large monkey jump, and g = gote move.

There are 4 branches of m that affect the outcome:

      m1 - bF9, wF8, bE9, etc.          ¦
      m2 - bF9, wF8, bD9, wG9, etc.     ¦Note that White decides
      m3 - bF9, wF8, bD9, wE9, etc.     ¦between m2 and m3.
      m4 - bF9, wF1, bH9, etc.          ¦

Let V = value of the gote move (g). If V is varied from 1 to 11, and the above sequences played out with best moves from both, the following results are obtained (X represents a solution):

White never picks m3:           ¦ White picks the better of m2 & m3:    ¦
                                ¦                                       ¦
 V   s  m1  m2  m4   k   g      ¦      V   s  m1  m2  m3  m4   k   g    ¦
                                ¦                                       ¦
 1   -   X   X   -   -   -      ¦      1   -   X   X   -   -   -   -    ¦
 2   -   X   X   -   -   -      ¦      2   -   X   X   -   -   -   -    ¦There were no solutions
 3   -   -   X   -   -   -      ¦      3   -   -   X   X   -   -   -    ¦from c in either table.
 4   -   -   X   -   -   -      ¦      4   X   -   -   X   -   X   -    ¦Whilst   k   did   give
 5   -   -   X   -   -   -      ¦      5   X   -   -   -   -   -   -    ¦solutions, it was never
 6   -   -   X   -   -   -      ¦      6   X   -   -   -   -   -   -    ¦the sole best 1st move.
 7   -   -   X   X   -   -      ¦      7   X   -   -   -   -   -   -    ¦
 8   -   -   -   X   -   -      ¦      8   X   X   -   X   -   X   -    ¦
 9   X   -   -   X   X   -      ¦      9   X   X   -   X   X   X   -    ¦
10   X   -   -   X   X   X      ¦     10   X   -   -   -   X   X   X    ¦
11   -   -   -   -   -   X      ¦     11   -   -   -   -   -   -   X    ¦

The first table shows that m is generally better than s, and never inferior (as is often indicated for such a formation) – but this conclusion depends on White not choosing m3.

In the second table, when V = 4, m3 is 1 point worse for Black than m2. When V > 4, m3 is 2 points worse for Black than m2. This has the effect of promoting s (when V > 3), so that it becomes a solution, until V = 11 when g becomes the sole best 1st move. For V = 5, 6, or 7, s is the sole best 1st move. Clearly, for V > 3, s is generally better than m. The only case where Black needs the monkey jump to , and jump bck to , (ie m2/3) is when V = 3 (here, m2 and m3 give the same result). For V = 1 and 2, whilst m2 is a solution, Black can also play m1 (ie the basic monkey jump sequence). See problem 5633 on goproblems.com for relevant sequences in full when V = 5.

To summarise: When the defender has 4 stones on the 3rd line, and sente is required to make a gote move worth 4 – 10 points, the small monkey jump is the best encroachment.

Bigger  

After - , is bigger than .

Even though it is not the book play, the throw-in for a ko is often better than the outside hane. Thanks for an example. :-)

Question

tapir: What is the value of the monkey jump + follow-up, if the opponent has fourth or fifth line territory there?