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Value Of A Monkey Jump
Difficulty: Advanced
Keywords: EndGame
In Monkey Jump, unkx80 wonders what the value of this sequence is. I will try to answer this question.
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.
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 White 3 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 White 3 is not sente, White 3 (now giving a value of -5) and Black 5 (giving a value of -3) must be regarded equally likely, so the outcome is the average of the two, being -4.
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 1 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.
More complicated is the situation when White captures at 1. 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: White 1 is sente in either case. So assume White 1 - Black a. 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 White 1 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! I think that I followed Andre's answer and agree. The one thing that I found unusual was the zero-diagram. I have not seen this approach before. I am more used to something like the one below. Is there something about Andre's choice that aids in the analysis or does it come down to personal preference?
Starting point black territory versus white territory.
The real question that I always have is whether Black should play 1 here rather than the monkey jump in cases like this? Is this better or worse and why? Please allow me to answer DaveSigaty using a similar way to whatAndre Engels did, except that I shall be using DaveSigaty's notation. I'll agree that it's my own personal preference, but I guess everybody will agree that we could simplify life and do away with negative numbers! :)
White plays first at 1. Case I: If the hane at 3 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 3 and 5 respectively and Black has 8 points and White has 10 points.
Black plays first, and the sequence ends at 4. 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 Black 1? 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: Black 1 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
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.) Real positions will be different, anyway. Who is komaster makes a difference, of course. I will assume neither player has ko threats, to give a neutral result.
White 2 tenuki. To evaluate the position after Black 3, we play out the subsequent sente sequences, White 4 - Black 5 and Black 7 - White 10. (Black 7 is the four-point play that we can treat as sente.) The net score is +3 (for Black.)
B 4 tenuki. White 1 threatens White at 2. Afterwards, White 5 - Black 6 is sente. The local count is -5 1/3. A play at a has a miai value of 2/3.
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.
After White 1, 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.
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.
White's response is different, however. If White 5 instead of White 1, White does not threaten White 4 right away, because there is no sizable follow-up threat. The 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:
The kosumi is worth about the same as the small monkey jump. It is very solid, and Black 1 - White 2 is later sente. The crawl:
The crawl of Black 3 gains three points. It takes away two points from White and adds one to Black. This is a copy of the living page "Value Of A Monkey Jump" at Sensei's Library. ![]() |