how much is a stone worth?

[djhbrown]

i remember reading that Japanese pros had done some tests to figure out the value of handicap stones, by playing games against each other at various handicaps, and concluded that, on average, each handicap stone was worth about 10 points.

this does not quite gel with the other common pro wisdom that during the fuseki, sente is worth about 30 points. however, if one takes into account that the other player gets to play after, it might be reasonable to guess that a stone is worth about half that, ie 15 points. one would expect that lesser players would play less efficiently, making their average value of sente less than that.

the common practice about the value of komi has moved up from 5.5 to 7.5 points over the last 40 years. but i bet no-one has ever done a proper statistical survey of actual game results to determine what komi really should be. part of the difficulty of such a survey is that in actual play, the one behind will generally tend to make riskier plays, making the score difference an unreliable estimator.

so the most convincing evidence comes from the pro-pro handicap games, ie that a stone is worth about 10 points.

that suggests the notion that sente is worth 30 should maybe be changed to 20.

[Uberdude]

i remember reading that Japanese pros had done some tests to figure out the value of handicap stones, by playing games against each other at various handicaps, and concluded that, on average, each handicap stone was worth about 10 points.

About 10 is a reasonable start, and makes for easy arithmetic: e.g. if I want to estimate someone's rank and I play them on 9 stones and win by 100 points then I say I'm about 9+(100/10) = 19 ranks stronger than them so they are about 16 kyu. In my experience (dozens of such games) this gives a reasonable rank estimate (+/-3 or so), but in such games I'm probably not playing all-out. Between strong players I think a handicap stone will be worth more than 10 points (as double komi is more than 10), and quite possible not linear in the number of handicap stones (my guess is the 6th handicap stone (2 sides points) is more useful than the 5th at tengen). In this post Bill says he got 13.75 points per stone from pro-pro handicap games, and Robert Jasiek about 14 from reverse komi 9 stone games, which fit better with the double komi logic than 10.

this does not quite gel with the other common pro wisdom that during the fuseki, sente is worth about 30 points. however, if one takes into account that the other player gets to play after, it might be reasonable to guess that a stone is worth about half that, ie 15 points. one would expect that lesser players would play less efficiently, making their average value of sente less than that.

"Sente worth about 30 points in fuseki" is not something I've heard. If you are trading large gote moves and there are an even number of them, sente is not worth much. If there's an odd number then tedomari comes into play and it is. If there are double sente moves then sente is very valuable, etc etc.

the common practice about the value of komi has moved up from 5.5 to 7.5 points over the last 40 years. but i bet no-one has ever done a proper statistical survey of actual game results to determine what komi really should be. part of the difficulty of such a survey is that in actual play, the one behind will generally tend to make riskier plays, making the score difference an unreliable estimator.

From SL: "The Nihon Ki-in looked at about 15,000 tournament games [at 5.5 komi] from 1996 to 2001 and found that Black won 51.86 % of all games, a margin of nearly 4 percent over White. The directors voted to change to 6.5 komi and negotiate with the Kansai Ki-in and tournament sponsors." As you say you can't then take the 2% or whatever of games in that sample that were half point wins for black and say if komi had been 6.5 instead of 5.5 white would have won them, because players will change how them play (risky/safe etc) according to the komi in effect. But it does tell us 5.5 was too low (for those players, for kyu players or perfect play it could be different).

so the most convincing evidence comes from the pro-pro handicap games, ie that a stone is worth about 10 points.
that suggests the notion that sente is worth 30 should maybe be changed to 20.

Unclear reasoning, and I question the value of a proverb that tries to assign a numerical value to sente.

On a related note, you might like to peruse a thread on the value of moves: http://www.lifein19x19.com/forum/viewto ... e&start=10, note the link to Environmental Go I posted there.

[djhbrown]

thanks for that; in sum, one wouldn't be too far off the mark to say that on average a handicap stone is worth about 14 points.

i can't remember where i read the bit about the value of sente during fuseki, but it hardly matters... oh, wait, it would have been in an old Ishi Press book from the 1970s, as those are the only Go books i have ever read - and not since then the author was emphasising the need to look for sente instead of just going for oba. i don't think i'm confusing it with the oft-quoted proverb about the value of ponnuki, which i think is a more recent amateur colloquialism rather than expert opinion, since it depends hugely on what's around it.

i also remember reading that during late yose, when precise counting is possible, one heuristic way of estimating the relative value of a sente move vs a gote one is to double the sente gain; same for reverse sente. so does that make double sente worth double again? i believe there was one Japanese pro (Ishida?) they nicknamed "the computer" because he was so good at counting, but i don't know whether he used that heuristic - i rather suspect not, as it sounds like a bit of an oversimplification.

[Dragonstone]

Nice Link for Komi:
http://senseis.xmp.net/?Komi%2FStatistics

[Kirby]

Value of sente changes throughout the game.

[Bill Spight]

i remember reading that Japanese pros had done some tests to figure out the value of handicap stones, by playing games against each other at various handicaps, and concluded that, on average, each handicap stone was worth about 10 points.

Japanese pros (and top players before there were pros in the modern sense) used to give handicaps to other pros. The estimate of 10 pts. per handicap stone comes from those times. It was a rough and ready estimate. That is why Japanese komi started out at 4.5 pts. in the mid-20th century.

this does not quite gel with the other common pro wisdom that during the fuseki, sente is worth about 30 points.

You seem to be the only person who knows that pro wisdom. Even at the start of play, the value of sente is only around 7 pts. Or if you mean the value of one player having sente vs. the other player having sente, it is around 14 pts. Nobody thinks that it is even close to 30 pts.

one would expect that lesser players would play less efficiently, making their average value of sente less than that.

Good point. A good komi for DDKs might be 3.5.

the common practice about the value of komi has moved up from 5.5 to 7.5 points over the last 40 years.

I don't know exactly when Ing adopted a komi of 7.5 for his rules, which use area scoring, but it was by the early 1980s. 40 years ago some Japanese tournaments used a komi of 4.5, some used a komi of 5.5 (nominally 5 pts. with White winning jigo). It took them a long time to adopt a komi of 6.5.

but i bet no-one has ever done a proper statistical survey of actual game results to determine what komi really should be. part of the difficulty of such a survey is that in actual play, the one behind will generally tend to make riskier plays, making the score difference an unreliable estimator.

Ing was no dummy. I expect that he adopted the 7.5 komi on the basis of statistics.

Good point about the value of the komi affecting the play.

40 years ago someone (sorry, I don't recall his name) submitted an article to the American Go Journal based upon his statistical analysis of 2800 Japanese professional games. He concluded that the proper komi is 7. Terry Benson asked me to review the article before publication, and I made the same point you did about komi affecting the play. Terry included it in a footnote to the article. Terry also sent me the guy's data, which the Nihon Kiin had collected. There were 1400 games with a komi of 4.5 and 1400 games with a komi of 5.5. I analyzed the two sets of games separately. The median board result of the games with komi of 5.5 lay between 6 and 7, as expected from the article. To my surprise the same was true of the games with a 4.5 komi. Obviously, the komi difference had not affected the results very much.

so the most convincing evidence comes from the pro-pro handicap games, ie that a stone is worth about 10 points.

The 10 point value did not come from analyzing pro-pro handicap games, and when I looked at them, I got a value of 13.75 pts. The American Go Journal article buttressed my prediction that the Japanese would adopt a 6.5 komi by the year 2000. (It took them a little longer. )

i don't think i'm confusing it with the oft-quoted proverb about the value of ponnuki, which i think is a more recent amateur colloquialism rather than expert opinion, since it depends hugely on what's around it.

Sorry, the saying that ponnuki is worth 30 pts. comes from the same era as the estimate of 10 pts. per handicap stone. The 30 pt. value was adopted by pros, and everyone understood that it referred to the value on a relatively open region of the board. It seems to me that it holds up surprisingly well, as a rough estimate. Unlike the proverb about the tortoise shell shape being worth 60 pts. (It is the result of capturing 2 stones instead of 1 for the ponnuki.) That shape is worth only about 40 pts., roughly. (FWIW, the estimates of 30 pts. and 40 pts. are equal to 10 pts. times the difference between the number of stones played locally, 4 - 1 for the ponnuki, 6 - 2 for the tortoise shell. )

i also remember reading that during late yose, when precise counting is possible, one heuristic way of estimating the relative value of a sente move vs a gote one is to double the sente gain; same for reverse sente. so does that make double sente worth double again?

Good guess, but no. Ogawa and Davies pointed out back in the 1970s that the theoretical value of double sente involves division by 0. (I suppose that people multiply the value of sente by 2 rather than divide the value of gote by 2 because multiplication is easier than division. The division of gote by 2 is theoretically correct to get the average value per move, which means that for double sente you divide by 0.)

[djhbrown]

i got the answer i wanted - that a handicap stone, ie at the start of the fuseki, is worth about 14 points. The reason for my question was that Swim thinks a bare hoshi stone with nothing near it is worth 12, so i wanted to check. Since it's only a preliminary perception rough estimate, 12 is near enough to 14.

as to that magic number 30, it's either Alzheimer's or it's in a book, or someone high up at the Nihon Ki-in in 1985 told me. Or it might be in an old Go World magazine. the name James Davies rings bells, but for some reason i think the author i am vaguely remembering was Japanese, and male. The only thing i recall with any confidence is the surprise it was for me to see (or hear) it, much larger than i had thought at the time, which made me think about it.

the opposite holds for the article that talked about the pro-pro experiments, conducted expressly to figure out the value of handicaps, because that result was for me merely confirmatory.

.. anyway, who cares? As Henry Ford said, "History is Bunk" (particularly for those who don't study it - perhaps Henry was thinking of the historical record of his commerce with the Nazi Party before and during WWII when he said that)

... a sente move that gains 15 is worth two in the oba gote. 14 is quite close to 15. kakaris are bigger than obas.

perhaps, when the board is really empty, the value of sente is less, since komi is a kind of compensation for not having sente. but as soon as there are a few stones around, the value climbs, because there's more at stake than just empty space.

By the end of an average game lasting an average 250 moves, with an average territory of about 50 each, the retrospective average value of each stone is about 250/100 = 2.5

it all fits.

[Schachus]

one would expect that lesser players would play less efficiently, making their average value of sente less than that.

Good point. A good komi for DDKs might be 3.5.

I heard the theory of weaker players needing less komi before. I actually question it.
My experience from my very first games on KGS was that they(games between beginners) usually end with winning margins bigger than 50 points, because both players are solely trying to surround each others groups while making very bad shape, which eventually ends in one player capturing a large chunk of very badly shaped stones, thereby connecting all his stones.
In such a game, how would komi help white? One the other hand, being the first to have placed a stone really does help black, because these fights start very early and so that could potentially be the one stone you have more in the fight. At least, I prefered to play black until I more regularly started to have games that were decided by a reasonably close margin.

[Bill Spight]

one would expect that lesser players would play less efficiently, making their average value of sente less than that.

Good point. A good komi for DDKs might be 3.5.

I heard the theory of weaker players needing less komi before. I actually question it.
My experience from my very first games on KGS was that they(games between beginners) usually end with winning margins bigger than 50 points, because both players are solely trying to surround each others groups while making very bad shape, which eventually ends in one player capturing a large chunk of very badly shaped stones, thereby connecting all his stones.
In such a game, how would komi help white? One the other hand, being the first to have placed a stone really does help black, because these fights start very early and so that could potentially be the one stone you have more in the fight. At least, I prefered to play black until I more regularly started to have games that were decided by a reasonably close margin.

Well, if nearly all games between weak players have huge swings, komi hardly matters, does it? And who knows where the 50:50 point is? It could change drastically, depending upon specific pairings. And, in the case of rank beginners, it probably changes from game to game, because they learn something from every game.

Your assumption that a beginner can reliably profit from having played the first stone in a fight against another beginner is questionable. Both players will blunder.

In general, the closer the play approaches random play, the less komi becomes. This is fairly easy to see with simple games. Suppose, for instance, that we have a few simple gote where the player to take one can make a certain number of points. Let's say that the player to take the largest one gets 4 points, the player to take the next largest gets 3 points, and the player to take the next largest gets 2 points, and the player to take the smallest gets 1 point. Proper komi is 4 - 3 + 2 - 1 = 2 points. But if the players play randomly, because they do not know how large the plays are, for instance, you may verify that komi should be 0. 1 - 2 + 3 - 4 is just as likely as 4 - 3 + 2 - 1.

[Bill Spight]

kakaris are bigger than obas.

Not sure what you mean by oba. But that seems to be what top Japanese players thought 400 years ago. As a result, it was common for to be a kakari. In time, they learned better.

perhaps, when the board is really empty, the value of sente is less, since komi is a kind of compensation for not having sente. but as soon as there are a few stones around, the value climbs, because there's more at stake than just empty space.

The top players 400 years ago knew better. Usually, when was a kakari, was a pincer. Then, according to the theory that the value of the move climbed because there was more at stake in that corner than just empty space, White should have continued to play in that corner -- as a lot of amateurs would today, BTW. But White switched to a new corner. Over time, Black stopped pincering, and then White stopped playing kakari. In general, having a few stones around reduces the value of sente.

By the end of an average game lasting an average 250 moves, with an average territory of about 50 each, the retrospective average value of each stone is about 250/100 = 2.5

You mean, 100/250 = 0.4.

[Schachus]

reliably profit is clearly an overstatement. But I do think, that if both players tend to make plays that raise the local temperature, then the temperature is sonn going to be very high and as players are not really knowing the best moves, the stone that was there first has about as good a chance to be just in the right spot as the newly placed ones have, so it's like you were allowed to make your one extra move in a position with higher temperature than the starting position, but you were a bad player, so you didnt choose an optimal move(maybe not even close to). It's hard to say, which weighs more.

PS: In your randomness example, you did "cheat" a bit. Sente can be worth something also in random play of finitely many gote moves, because if there is an odd number of plays(here also 0 point plays count, if they are option for the randomly playing player), sente assures you to get one more random pick than your opponent, it might even be the case that "random sente" is worth more than normal sente(for example if 2,2 and 1 point are divided randomly, the player having sente gets at least 1+2(which he would also get with correct play) but he also has the chance to get 2+2 if he gets lucky).

[hyperpape]

In general, the closer the play approaches random play, the less komi becomes. This is fairly easy to see with simple games. Suppose, for instance, that we have a few simple gote where the player to take one can make a certain number of points. Let's say that the player to take the largest one gets 4 points, the player to take the next largest gets 3 points, and the player to take the next largest gets 2 points, and the player to take the smallest gets 1 point. Proper komi is 4 - 3 + 2 - 1 = 2 points. But if the players play randomly, because they do not know how large the plays are, for instance, you may verify that komi should be 0. 1 - 2 + 3 - 4 is just as likely as 4 - 3 + 2 - 1.

I too question whether komi is lower for weak players (let's say 20kyu). It's cetainly possible, but nothing I've read really seems to indicate the answer one way or another.

Random play is quite a bit below 30 kyu in AGA ratings, so showing the effect with random games doesn't tell us what the effect is for beginners.

[Bill Spight]

I too question whether komi is lower for weak players (let's say 20kyu). It's cetainly possible, but nothing I've read really seems to indicate the answer one way or another.

Random play is quite a bit below 30 kyu in AGA ratings, so showing the effect with random games doesn't tell us what the effect is for beginners.

Oh, but 30 kyu play is a lot closer to random than 10 kyu play, to pick a number. And don't EGF records show that the value of handicap stones is less for weak players than for strong players? That means that komi, which is approximately the value of 1/2 a handicap stone, should be less, as well.

[djhbrown]

i did mean 2.5 - but i should have meant 0.4

but, should i complain to the thought police, because the last few posts have all been off-topic, because the topic is how much a stone is worth and everyone is banging on about komi....?

oh, well, if you can't beat 'em, join 'em... i reckon komi should be 10, and that draws should be something to be cherished, rather than avoided.

continuing that line of thought, the rules of Go should be rewritten, so that players win only if they achieve a draw, otherwise they both lose (and if if they don't, their children certainly will).

Would that make the world a better place?

[Bill Spight]

i did mean 2.5 - but i should have meant 0.4

but, should i complain to the thought police, because the last few posts have all been off-topic, because the topic is how much a stone is worth and everyone is banging on about komi....?

Komi is worth approximately half a stone.