The event we (or at least I) have been waiting years for will finally happen, a Nongshim cup style win-and-continue tournament between the EGF and AGA pros!

http://www.usgo.org/news/2019/02/u-s-an ... mpionship/
https://www.facebook.com/transatlanticteamgo/

Place your bets. A few years ago I would have been fairly sure of a AGA victory, but the EGF pros have been more active and improved quite a bit recently...

The EGF pros are:
- Ilya Shikshin 3p (Russia). The top native European player for last decade, famous for his aggressive style. 5-time European champion.
- Pavol Lisy 2p (Slovakia). The first EGF pro in 2014, beat Ilya in the 2018 European Championship final.
- Artem Kachanovskyi 2p (Ukraine). A KGS fan favourite with a solid style.
- Mateusz Surma 2p (Poland). Won several games in the Chinese C league a while back.
- Ali Jabarin 2p (Israel). Won world group of 2016 Samsung cup to play in main tournament (but didn't beat Lee Sedol).
- Andrii Kravets 1p (Ukraine). The most recent pro and not as active.

The EGF has nice pictures and biographies at https://www.eurogofed.org/pros/

The AGA pros are (all 1p as they don't have a promotion system):
- Andy Liu (USA), the first and likely strongest, beat all the Asian pros living in the US when he was a kid, won US Open.
- Gangsheng Shi (Canada)
- Calvin Sun (USA)
- Ryan Li (Canada). Beat Chen Yaoye 9p in the 2017 MLily cup in a spectacular upset.
- Eric Lui (USA).

What is the typical strategy for ordering players on each team? Best players first or last?

In the Nongshim cup it's usual to have the best last, though recently China put Fan Tingyu (who was probably a middling strength player for them) first as he'd previously won many games in a row in that event, and he did so again. And before that in the Japan-China supergo Nie Weiping was famous as the Chinese "Iron Goalkeeper", their last player beating all the remaining Japanese team.

Best player last is standard.

For fun I just worked out the best strategy if both teams have only two players, a strong player and a weak player; the strong players are equally matched, as are the weak players, and the probability of a strong player beating a weak player is p, 0 < p < 1/2. Which way should you order your team? Does it depend on what order the other team chooses? Does it depend on p? I will hide the answer in case you want to work it out yourself; it's kind of fun.


I wonder if and how this generalizes to bigger teams.

Consider a team A with n players and a team B with m players. Suppose (as in Elo's theory) that there exist positive numbers a(i) and b(j) such that the probability that player A_i wins against player B_j is a(i)/(a(i)+b(j)). One may wonder what is the effect of changing the order of players.



By the way, is it possible to find reliable ratings of all EGF and AGA professionals?

On goratings I found 2937, 2930, 2888, 2862, 2876, 2851 for the EGF players, but only 3062, 2827 for the last two AGA players.

Andy Liu does have a gorating, but fell off the current list due to inactivity. Not sure they are particularly reliable with so few games, but they do actually seem fairly well aligned with my expectations...
Gansheng too

I have a feeling that AGA pros will put up a hellacious fight. Andy Liu and Ryan Li are quite strong, with Liu and Li having previously beaten Ahn Dalhoon 9p and Chen Yaoye 9p respectively. The European pros may have their work cut out for them.

Or am I being uninformed? Has any European pro won against strong Korean or Chinese pros?

Ryan's victory against Chen Yaoye was by far the most impressive scalp of a Western pro vs an Eastern pro. Here are a selection of such wins, sorted by gorating of the Eastern pro at the time.

3529: Ryan vs Chen Yaoye 9p, 2017 Mlily cup, only one vs current world champion callibre pro, Chen has been in world top 10 for most of last decade.

<big gap>

3227: Ilya vs Wang Yuanjun 6p, 2013 SportAccord WMG. Wang is one of top Taiwanese players, around world #200 at time.
3203: Ryan vs Cheng Honghao 2p, 2017 Mlily.
~3180 Andy vs An Dalhoon 9p. 2018 US Open. An was top 100 in 2000s, but no recent games so unsure of current strength.
~3150: Artem vs Yamashiro Hiroshi 9p. Informal game at some European tournament a few years ago. Yamashiro was top 20 in 90s and challenged for big titles but didn't win any.
3117: Mateusz vs Yang Qian 3p. 2017 Chinese C league.
3100: Pavol vs Li Xiang 4p. 2017 Chinese C league.
3085: Ilya vs Shi Yulai 1p. 2017 Chinese C league. wolfking reports 5 year old Shi is a well known child prodigy and new pro from last year. It was said that he finished Hatsuyoron at age of 7 and was 9D on Tygem at 8. Many believed he would make pro as early as 2014.
3032: Artem vs Sonoda Yuichi 9p. 2016 Sankei cup prelims. Sonoda is famous for his centre style, was a top 20 pro in 1980s, challenging for big titles but didn't win any.
3019: Gansheng vs Hei Jiajia aka Joanne Missingham, famous female player. 2014 Globis cup.
3017: Mateusz vs Zheng Hong 9p. 2015 Zhugang cup. Zheng was a top 100 pro in 1990s, has a go school in Beijing I visited.
2900: Ali vs Xu Jiawei 2p. 2017 Chinese C league.
2651: Ali vs Saito Tadashi 8p. 2014 Sankei prelims.

Ilya got a nice bunch of wins against young low dan Chinese pros in Chinese C league last year (https://www.eurogofed.org/index.html?id=223), and Mateusz did too before that (https://www.eurogofed.org/index.html?id=135). Quite a few also have wins vs young Japanese pros below 3000 rating from prelims or friendship matches.

In case someone is searching for it, here is the goratings page of Ahn Dalhoon (=An Dalhun):

https://www.goratings.org/en/players/143.html

What about Calvin Sun? Are there some game records against professionals?

The AGA pros seem to reserve their international outings for the major events. The European pros seem to spend more time in the crucible of China. Apart from the C League, they play in the Silk Road Cup, which is not a knockout, so they get quite a lot of games in against a few Chinese pros and a lot of Chinese and occasional Korean amateurs. They see to hold their own, without excelling, but that matchplay experience may give them an edge.

On a more general tack, I'm curious how the western pros are expected to improve. They no longer have teachers, presumably, so more matchplay is maybe what they need. Perhaps they should try crowdfunding from go fans to support a match with pros from the oriental organisations (the Kansai Ki-in would be up for it, I'm sure). It's different enough to interest oriental sponsors (the Chinese have already been very generous, so the will is obviously there). I'm also wondering if the T M Hall Fund could be used. There's a clause that offers funding for serious, long-term study in the Far East. It's aimed at British players, but if a benefit to British go could be woven in (e.g. pros give lessons here) there may be a way forward.

The European pros have online access to Golaxy, a strong bot (which gives point lead as well as winrate). Artem made a review of the Pavol vs Ilya 2018 European Championship final with it at https://www.eurogofed.org/index.html?id=232. With LeelaZero so strong too now and available to all maybe that's not such an advantage, unless you don't have a fast computer. These days, there are plenty of top pros they can practice against online (timezone troubles aside) on Fox or other servers, which I saw given as the main method how Ke Jie got so strong.

Others in this thread have provided evidence that under certain conditions, order doesn't matter. I ran this by a guy who researches combinatorics and he came up with a counterexample where order does matter:

Consider two two-player teams {A1,A2} and {B1,B2}:

Probability that A1 beats B1 = 1
Probability that A1 beats B2 = 0.5
Probability that A2 beats B1 = 0.5
Probability that A2 beats B2 = 0.5

Suppose Team B sends B1 out first, then B2.
- If Team A sends A1 out first, then their expectation of winning is 75%.
- If Team A sends A2 out first, then their expectation of winning is only 62.5%.
(you can build out the game tree and do the math yourself, but if you need help ping me)

It turns out the probability of team A winning will be independent of the order if the following condition is satisfied:

P(A1 beats B2) + P(A2 beats B1) = P(A2 beats B2) + P(A1 beats B1).

So in my extreme example, A1 really has B1's number. What is interesting is that making optimal use of this knowledge entails putting your ringer up front, and not saving her for the end. The only reason you might save this especially strong player for the end is to have the excitement build - otherwise it is a bad strategy.

The last three probabilities imply that all players have the same Elo rating. This not consistent with the first probability.

Elo ratings are not consistent with reality

Skill at go involves a number of different subskills. If we assign a number to represent the level of each subskill, then we get a vector which represents overall skill at go. Reducing this vector to a single number (rating) loses information. That means that any calculation of probability between two players based upon their ratings will have some degree of error. Furthermore, transitivity will not hold. Even using dan/kyu ranks, which cover a much broader range of skill than Elo ratings, is not enough to guarantee transitivity. Skill at go is only partially ordered.

The example given is extreme to illustrate the point. Real cases where, say, Player A1 can beat Player B1 with probability 60% while the other probabilities remain 50% certainly seem possible.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Yes the presumption is that transitivity does not always hold, and that causes ordering to matter. I've heard Yoda Norimoto had quite good results against Lee Changho when Lee was dominating in the 90's. Others can think of other examples.

By the way, to the extent that this is an actual issue, a mixed strategy seems to be the correct one where some randomizing goes on. (Japan would want to align Yoda so that he faces Lee Changho, and Korea would want to prevent that from happening. So it would be like hide and seek)

Your assumptions doesn't seem to match (p=1).

My attempt with my model proposed earlier, which may be closer to practical reality: we represent each player as a normally distributed random variable with known ev and deviation (his distribution of point drops in each game (compared to perfect play), independent of opposition for simplicity - a doubtful assumption OC). The player whose number/performance sample turns out to be above the opponent's wins the game in question.

I took a quick look at a random example (two teams two players each), and in this model order seems to matter slightly (even without rps-like dependencies, each player showing the same strength against each opponent).

This seems to be related to that each player can have different deviation (at least in this example order matters only if deviations are not the same).

Yes, of course I am aware that representing go skill with a single number (Elo rating) is not enough, but in the absence of other information, we have no other way to estimate winning probabilities than using Elo's theory. A better way to estimate the probability that A wins against B would be to use a formula which uses both Elo ratings and past game records of A against B.

First game in a week: Mateusz Surma vs Andy Liu. AGA putting out their big gun first.