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Doug's Go Blog
   

Welcome to my Go blog! Want to comment? Go ahead!

May 17: The business card rules of Go

Go is a complex game with simple rules, or so the sales pitch goes. Most statements of the rules don't come off as simple, however, so lots of people have tried writing simpler versions, of which the Tromp-Taylor rules are probably best known. It's probably a purely intellectual exercise, as there aren't any disconnected desert islands of would be go players out there, just waiting to be introduced to the game by a leaflet in a bottle. Still, it's a fun exercise. I'd like a simple ruleset which fits on a business card, along with a small but playable go set. Here's an attempt, based on no-pass go with prisoner return.

Equipment. A rectangular grid, initially empty, and enough black and white stones to fill the grid. Play. Two players take turns placing stones of their color on intersections of the grid. Black begins. Groups. All stones of the same color connected by lines are part of the same group. Empty intersections adjacent to a group along the grid lines are the liberties of the group. Capture. After placing a stone, a player collects all stones in opponent groups with no liberties remaining as prisoners. Prisoners are removed from the board and kept by the capturing player. No suicide. It is illegal to play a stone which would have no liberties, after removal of any captured prisoners. Ko. It is illegal to make a play which repeats a previously occuring position. End of game. During their turn, a player must place a stone on the board or pass by returning a previously captured prisoner. A player with no legal moves on the board and no opponent prisoners to return loses. Their opponent wins.

WillerZ: Not sure of the etiquette here, but below is my take on business-card sized rules for what that's worth. They are basically Japanese rules as close as I can get it. I think the Japanese ko rule is simpler, even if it is more lengthy to describe:

Equipment: A square grid; enough stones to cover each intersection on the grid, 1/2 of the stones should be black and 1/2 should be white. Turns: Players take it in turn to place a stone on any empty intersection of the grid; black plays first; In lieu of playing a stone, a player may pass. Groups: Any stone on an intersection horizontally- or vertically-adjacent to a stone of the same colour is in the same group as that stone. Liberties: Any intersection with no stone placed on it which is horizontally- or vertically-adjacent to a group is a liberty of that group. Territory: Any empty intersection which can be connected to one of your groups by following the lines is a point in your territory. Capture: If you play on the only liberty of one of your opponent's groups, you capture that group and take the stones in that group as prisoners. Suicide: You may not play a stone which reduces the number of liberties of your own group to zero, unless the stone so played captures some of your opponent's stones. Ko: You may not capture a stone if the stone you captured was the last move played and it captured a single stone. End of the game: If both players pass in succession or either player runs out of stones, the game is over. Score: Your score is the sum of the number of points of territory you have, and the number of stones you have captured. Result: The winner is the player with the highest score.

Hmmm, a little longer than I was hoping for. I think my rules are less ambiguous than those you give, and will not require that every possible point be played in order to give a fair result.

As far as etiquette, I love comments, and I'm also fond of the basic ko rule. Japanese style rules normally say what happens to capturable stones left on the board after both players pass, since having to remove them costs points. Defining capturable is what usually takes up all the airtime in Japanese rules. Your territory definition seems to include dame and points in seki, but I don't have a problem with that. You also might want to clarify that you can't follow lines through stones.

May 10: A 6x6 problem

[Diagram]
White to play, no komi, no prisoners.

From [ext] http://www.mathpuzzle.com/go. If W a, then the result is B+4 (area scoring). There's supposed to be a better move, attributed to Bill Spight, but I can't seem to find it. Help?



[Diagram]
Attempt (10 at 5)

It seems to me that W9 is key. If W9 at a, the result is B+4.


[Diagram]
Attempt (6 pass, 7 connects)

Black cannot win the ko on the upper right, so the game is a draw. --unkx80


[Diagram]
Better for Black? 7 at 1, 6 retakes ko, 9 at 4

Instead of B connecting at a, how about a hane and starting the ko in the upper right? Black can't win it, but White doesn't have enough liberties to stop Black from creeping around the edge. The final result is B+1 with White alive and Black in seki. White could atari at b to win the ko in the upper left, but this costs three points for a gain of two, so the result would be B+2.

unkx80: I think you are right. Guess I overlooked this.



8 May: Three two-eyed groups

[Diagram]
Three groups with two eyes each

What's the smallest board that can support three groups with two full eyes? Of square boards, 6x6 can do it (it can hold four groups of two eyes, actually), but 5x5 can't. Of rectangular nonsquare boards, 2x10 has the smallest area, and 5x6 has the smallest long dimension. The arrangement on 5x6 has essentially no wasted space (none at all if you ask that both sides play the same number of stones) and looks difficult to improve on.

On boards which can't support three two-eyed groups, stone scoring and area scoring are equivalent. The next question would be what size is required before three groups happen with reasonable play. It happens often enough on 9x9.


6 May: Happy anniversary!

I missed my blog's anniversary, which happened on May Day. Oops. Hopefully it will forgive me -- there are worse anniversaries to forget.

I've now been at this for a year, which is longer than I'd expected. I'd assumed that I'd run dry, get bored, or get busy, long before now. Fortunately or unfortunately, that hasn't happened yet. I haven't even finished the topics that first drove me to blog: capturing race theory, ko. I haven't even started on ko. As far as I know, I was the first go blogger, (or perhaps the first go blogger to call it a blog), but there are now a small crowd of us, some here on SL, some elsewhere, tracking our thoughts and progress, writing about go. I don't know if blogging is making me stronger, probably the opposite, but at least I'm having fun.

Arno: you are an unsung hero :-) Congrats.

27 Apr: Miscellany

Went to a talk on monte carlo go, but still don't understand it. Finished KPA level 3, and reread Davies' Tesuji. Haven't quite given up on Segoe-Seigen level C, but having to lay out stones to understand the given answers seems like a bad sign. Discovered during a game (to my surprise and dismay) that bent four in the corner is not necessarily dead. And found a nice piece in [ext] Salon on the trials and travails of Wikipedia, which faces similar issues as SL, but more intensely.

April 23: A metaproverb

For every proverb of the form, "X is dead", there is a corollary, "X has a whole bunch of liberties".

Not always true, perhaps, but still.

For every proverb of the form, "X is alive", there is a corollary, "X has a whole bunch of ko threats".

April 19: How strong are you?

To distract myself from a disastrous series of games on DGS (motto: play slow, lose slow), I've been thinking about ratings. A rating, as distinct from a rank, is supposed to say how strong you are, i.e. to predict the outcomes of new games. There has been a lot of work on rating systems over the years. The most famous system is undoubtedly ELO, developed by Arpad Elo in the 1950's and 1960's. Originally applied to chess, it has been used all over the place. In the go world, the EGF [ext] uses an ELO system. Other systems include [ext] Glicko, (developed by Mark Glickman, stats prof and chair of USCF ratings committee, also see the [ext] technical paper), which seems to be an ELO variant, [ext] ChessMetrics, another ELO variant, HoligorSRatingOfGoPlayers, which I don't understand at all, maximum likelihood methods such as [ext] mlrate (used by NNGS and DGS) and [ext] AccelRat (used by the AGA and maybe IGS), and I'm sure others as well.

All of these systems are in some sense statistical, and rely on an assumed probability for a win given the strength difference between the two players. You can think of this as the definition of a certain amount of strength difference. Several formulas are in use. KGS uses p = 1/(1+exp(k x)), where k is an arbitrary constant and x is the strength difference, which is called the Bradley-Terry model. MLrate uses p = 0.5 s^x for x positive, where s is a constant. This has the same large x behavior (single exponential), and is continuous but not smooth at x=0. AGA uses a normal distribution, just like Arpad started with, p = 0.5 exp(-x^2/2 sigma^2) for x positive, sigma a constant, which decays faster at large x, but is again not smooth.

Any reasonable formula is a monotonic mapping of a probability (range 0 to 1) onto some other number. Since any such mapping is (just about) invertible, one might think that the actual formula chosen is entirely irrelevant. It's not, however: these formulas implicitly encode some kind of transitivity relation, because the formulas talk about ratings differences: if A beats B x% of the time, and B beats C y% of the time, corresponding to ratings differences delta AB and delta BC, the chosen function predicts how often A will beat C from delta AB + delta BC. Different functional forms will predict different values from pAC. There remains an arbitrary scale factor. In games without

handicap, such as chess, a scale is picked purely esthetically: 200 points means 75% winning. For go, we can use the strength difference from handicap stones to set the scale.

function plot To see what these functions look like, I plotted the KGS, MLRate, and AGA functions as solid, dashed, and dotted lines, using their default parameters (k = 0.8, s = 4/19, px_sigma = 1.04).

euro One question is whether these probabilities are a function of absolute strength. One dataset is the [ext] European tournament results. This plot shows those results, with 95% CI error bars, plotted vs. the average strength of the two players, with 1, 2, 3, and 4 stone strength difference games shown in blue, green, red, and teal. The predictions of the rating functions with default parameters are shown in the same

colors, with KGS solid, MLRate dashed, and AGA dotted. All do okay for dan players, except maybe AGA is a little too pessimistic about the chances of a player weaker by three or more stones. None are correct for kyu players, where the weaker player wins much more often than predicted. This could be due to more variable play, more misrated players due to improvement or fewer games, or even weaker use of handicap stones making ranks closer together. Whatever the reason, the effect seems to be substantial.

Once you have a probability function you are happy with, you face the problem of fitting rankings to the results. This is a nontrivial problem, with issues like dealing with rating improvement. The ML methods typically try to fit a single current rating from the entire history of results available, with improvement dealt with by deweighting old results. This will track improvement, but slowly, and thus the usual advice to start a new account in these systems if you want a quick look at how much you've improved. It's also possible to include variations in time in the rating, but (according to Glickman) this becomes computationally expensive. I'd also worry about having sufficient data to model the time dependent function. ELO methods take a step towards the minimum based on each new result. This may not take full advantage of the data available (in particular, my opponent's future results can't change my rating), but it does track rating changes in a natural manner, and it is highly predictable, which players seem to like.

harry wang - I like the graph, I wonder what tools you used to plot it. I want to get some go game result histograms into this format.

I used matlab "plot" and "errorbar", with CI's computed with binofit from the statistics package. You might also try octave (which uses gnuplot for figures) or scilab, or even a spreadsheet. Email me directly if you want more specifics.

Apr 18: KPA 3:108

[Diagram]
Black to play

From the "almost errata" file. The given answer is a. I think b works too, but is a point or two worse.


[Diagram]
Ko

ethanb: b makes a ko for life - definitely not what black wants... Actually, I take it back. B3 at W6 would live, but now black can never push and cut white at W4 regardless of the board situation.


[Diagram]
no ko, and sente

rubilia: (B1 was played where W6 is now.) Maybe I am wrong, but I don't see why b should have to result in a ko. After B3 white can't cut at 5 because of shortage of liberties. The main difference between a and b is gote vs. sente, so b seems to be the better move. Do I miss anything?

You're right that there's no ko, but White need not answer B3 (at a cost of a couple of points maybe), so Black still doesn't get sente, and can't push and cut without making an extra move.

rubilia: If there's no additional hook, that still means b is the preferable move here.

It's not clear to me which is better: remember that it costs black a move to pick up those two stones, plus she loses the push in sente, so I think b gives a three point gote followup, or 1.5 pts better. a however leaves a defect in White's wall, which could be worth a lot more than a couple of points.



Apr 11: The Easter Egg hunt tesuji

[Diagram]
Does this work?

So, I'm working on tesuji. Here's a tesuji from a game. White could capture two stones, but wants more. B2 is a double hane, and after W3, has a beautiful squeeze...


[Diagram]
No.

[Diagram]
| 7 5 2 X O X . |

...and can capture all the white stones, and save his two threatened stones, ten moves deep from the W3 cut in the original diagram. A very nice tesuji to find during a game. Too bad I was White, and missed it. Black isn't reading any tesuji books, but knows how to fill liberties and found it.


Apr 2: Diagnosis: bibliophilia

The Segoe Tesuji Dictionary arrived a couple days ago, three volumes, ordered from Amazon.jp in a fit of insanity when owning more books seemed like a good idea. And a new copy of Tesuji came too. Too many years since I've seen my old copy. The Segoe dictionary is beautiful, lovely Japanese printing with not one but two ribbons in the binding, one to mark your place in the problems, the other in the answers. I find the level C problems hard, and rare: most of the problems are A or B, and way beyond me.

They say learning tesuji is the first step to getting better. I still feel like I don't know any tesuji, but that can't be blamed on my library. And if I have to know everything in these books, I'll never get to step two (whatever that is), but maybe I won't need to.

TesujiFreak?: Congratulations on getting the Segoe Tesuji-Jiten. I got it some time ago, and I think it is the best go book purchase I have ever made. Some of these problems are simply beautiful with so many subtleties it blows my mind. They also have a "natural" feel to them - as if they could actually appears in real games. Great books.


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(OC) 2004 the Authors, published under the OpenContent License V1.0.