Do inferior plays have values

    Keywords: EndGame, Theory

Charles Matthews and I began this discussion in a footnote to Miai Values List / 2.00 and more. I think it has been fruitful, and that we both have gained from it. :-)

I now think that Charles was right and that inferior plays do have values. An inferior gote is worth whatever it gains. The question remains, how much is an inferior sente worth? I think that the most important number is how much it loses. The reason being that you take your loss and then continue to play. -- Bill Spight

B1 in the following diagram had been presented as a 3 point play:

Crawl on second line  

(Assumes infinite White territory to the right.)

Charles Bill, you edited this out - a problem ...?

Bill: The problem is that it is not correct play, given the conditions. The monkey jump is. Yes, if you play it, you pick up 3 points. But values are based upon correct play. You assume that your opponent's play is correct to obtain a value. Yours should be, too.

Charles OK - I think it would be useful either to have 'starred' status for something as conceptually basic as this one; or to include it in a footnote or other area. And to decide whether, for example, the comparison with the small monkey jump should be done on-list or off-list.

Bill: Conceptually basic, maybe. (It does depend upon infinity.) Miai value, no.

Look, if the miai value of B1 is 3, that means that the miai value of W1 below is also 3.

Prevent crawl on second line  

(Assumes infinite White territory to the right.)

But the miai value of W1 is 4.42. (See monkey jump).

Miai values are superior arithmetically, and less confusing when comparing sente with gote, than deiri values. But with deiri values it is clear that you are comparing correct plays by either side. The same applies to miai values.

Charles I feel I'm getting confused again...

Try this. If this list is only for best play, that's fine. Then plays do come in pairs what Black does/what White does. We then have to include enough data in the diagram to know unambiguously what best play is - that is also fine, and should in most cases come out in the wash of evaluation.

If I take Bill's point correctly the crawl in question is attributed 3.71 miai. I'll concede that this is a silly number because it (for example) says that Black having played the inferior crawl once might (next turn) see the error of his ways and correctly play the monkey jump.

Bill: Well, I do not attribute any miai value to the crawl. But if I did, how's this?

Losing sente  

After B1 - W2, Black has lost 1.42 points on average. B1 gained 3 points, W2 took back 4.42 points. So maybe B1 is a 3 point losing sente. ;-)

Gee, that doesn't make much sense, either. <shrug> How do you measure a losing sente? I don't know. You are 3 points better off than if White played at 1. So maybe 3 point losing sente makes sense.

(Later): Actually, Charles, the more I think about it, the more it makes sense. B1 prevents a 3 point loss by comparison with White's gote. It is made with sente, locally, because W2 is hotter. And it loses points. So the monkey jump is a 4.42 point gote, while the crawl is a 3 point losing sente. B1 is assigned a miai value in a manner consistent with other miai values. Even without saying that it is a losing play, you can tell that from the value of the monkey jump.

Note: Something I did not say, of which Charles is well aware, is that sometimes a losing sente is correct play, given the rest of the board. Conceivably, there are whole board positions where the exchange of B1 and W2 is correct.
Later discussion with evand on Combinatorial Game Theory / Discussion makes me wonder if the way to measure a losing sente is by how much it loses. Then this would be a 1.42 point losing sente. I don't know which way is better.

Iago: correct me if i got it wrong, but to be accurate you have to take into account the value of sente right ?

here is my reasoning : gote monkey jump : 4.42 / this sente move : 3 + the value of sente.

so the sente move is better iff sente is worth more than 1.42 which is the value conceided to keep it... correct ?

Bill: Theoretical values do not necessarily tell you what to play. It may depend on the situation. To a first approximation using the value of sente (s), we make this comparison:

 s - 1.42 <?> 4.42 - s

The left side corresponds to losing 1.42 points but retaining sente, and the right side corresponds to gaing 4.42 points and losing sente. This reduces to

 s <?> 2.92

So the losing sente is better when the value of sente is greater than 2.92. Then it gains better than 1.5 points.

However, tenuki is even better, gaining 2.92 points. Therefore, for the crawl to be better we require special circumstances with other specific plays.

You may be wondering, if the value of sente is less than 4.42, why tenuki is better than playing the monkey jump? Here is that comparison:

 s <?> 4.42 - s

which reduces to

 s <?> 2.21

We compare the value of sente with half the miai value of a play.

Iago: by the way... why not compare it with a sente monkey jump (the one where black make a one point jump instead of connecting)


Monkey jump  

We never get there, because White plays tenuki.

Iago: well thanks :)

I think i got it now... took me a moment to figure out where the 2.92 came from, since substracting felt so nice...

however I now think I wont be able to make a better yose ^^ how do you decide what to do in the yose ? i mean isnt there something between "this seems sente" and "lets calculate all the miai value, and estimate sente". basically, how do you play your yose ?

Bill: How do I play yose myself? Pretty intuitively. But my intuition is informed by having figured out many positions. Also, it was good even before I learned how to calculate the value of plays. :-)

But in the yose, I have nearly always been there before. When I started playing go I did not know joseki. I couldn't say, well, the joseki is over, time to play somewhere else. I had to decide that a play here was too small, while a play there was bigger. Every time I play tenuki, even from the start of the game, I already have an idea how large local plays are and what are good sequences of play. Because of this preparation, I can usually play the endgame quite rapidly.

Sometimes I bother to work out the value of a play precisely. Usually this is while my opponent is thinking.

Do inferior plays have values last edited by BillSpight on May 5, 2005 - 21:54
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