[Note: see below for attached original MS Word file and excel charts.]
[Note: You can choose two options in the poll, and you can change your vote later on.]

ASR League 2010: The Math
By Usagi

I’ll go ahead and use my KGS handle for this paper.
The ASR league’s policies have been designed by hand with a best-intentions strategy. Now that the league has been active for over an entire year, there is enough data to analyze how the rules and what not of the league have affected it’s membership base. Normally this would not be a question; however at first glance it would appear there are certain serious problems with the ASR that demand immediate attention. This, of course, does depend on the people in charge to a certain extent – it is one thing to propose that something is a problem – it is quite another for others to agree on this and then to care enough to take positive action to solve the problem. So assuming that people are interested in making the ASR league a better place, I would like to make three strong statements about three key problem areas with the ASR as it now stands:
1. Activity rewards are imbalanced.
2. There are management issues or negligences which contribute to inactivity.
3. Member retention is low, what to do?

Activity Rewards
The biggest problem with the ASR right now is that it is focused on rewarding activity. This was done because a strong player is not necessarily an active player. Activity rewards are a good thing; however the way they are implemented into the league has unbalanced the basic idea of a room-based league; to promote stronger players, in general, and demote weaker players thus allowing players to play people close to their level and have a relatively smooth gradient of people to play against. The idea behind this is that it will help people learn to play Go.
The way the league rewards activity (currently) is to give essentially 1 point for a loss, and 2 points for a win. The danger with this system is easy to express mathematically. If there are two players X and Y in any room, where Y is X+1 (such as 2d and 3d) then we know by the ranking system that player Y’s chances of winning an even game against player X are greater than 2/3rds (~67%).
We can thus generalize that over a long period of time, player X will get 2(1/3) + 1(2/3) points for every game he plays, and that player Y will get 2(2/3) + 1(1/3) points for every game they play. With this generalization we may make some probabilistic statements about what is likely to happen during a period given any particular room structure.

Assume a 14 player room with 13 players of strength X and one player of strength Y, where Y is X+1. We now know that over 10 games, player Y will get ~16.5 (16.67) points, and over ten games, each player of strength X will be expected to get ~15 points.
In the long run this works as expected; stronger players promote. However, if just one of the players ranked X plays more games than the Y-strength player, they will end up with more points. One game with a win or two losses will tend to give the X-rated player 17 points, ½ point higher than what the Y-rated player is expected to get.
Therefore we arrive at the general principle that playing an extra two games is sufficient to cover a deficiency of one stone of strength.
This is an incredibly serious problem. This means if a 5 dan plays 15 games in a month, a 1 dan is statistically likely to beat him if he can just play 22 or 23 games. This is the reason why there are no 6 or 7 dans in the league; statistically they just can’t make it past the dozens and dozens of “active” 1 and 2 dans in their way.
The Math
For any player x, there are two variables; strength (winning percentage) and # of games. If we examine thousands of cases, we can chart the results as follows:

(SEE CHART #1: "POINTS BY STRENGTH" BELOW)

The above chart shows the distribution of points scored by the strength of the player in the league. The variation in the noise on the Y axis is due to players playing different numbers of games. This chart clearly shows the average points a player of strength X can expect to get has little to do with his playing strength – although the expected score does rise with strength it does not significantly reflect the that difference. For example, The difference between a 40% win ratio and a 60% win ratio (approximately two stones in strength) is only 4 points; i.e. between 2 and 4 games played, depending on if those games were won or lost. This is in line with the earlier analysis.

(SEE CHART #2: "POINTS BY ACTIVITY" BELOW)

This chart bears a striking difference to the one presented previously; it is a chart of expected point score by number of games played. It now becomes visually clear what has been said so many times; playing strength is not the deciding factor in who gets promoted in the ASR; it is not even close. The expected score falls in a very narrow range based on number of games played.
This is solid proof that the activity reward of 1 point for a lost game is horribly flawed and must be changed.
Reccomended Course of Action
Of course, no one is proposing that the reward system be eliminated, but it must be reduced if the league is to move closer to fulfilling it’s role of providing a structure whereby players can play competitively serious games (not just “serious” games). Using the same software I used to produce the above two charts I determined that a reward system of 5 to 1 (versus the current 2 to 1) will increase the number of games required to game the system from 2 to 8. Even this is somewhat disturbing but any improvement in this area will have a positive effect on the league. Because of this I recommend an immediate move to a 3 points-win, 1 point loss system, phasing in 4 to 1 after two months, and 5-1 two months after that.
There are other ways to cap the activity reward. The one with the most popular support appears to be limiting the number of lost games which count for points to the number of won games. Therefore a player with a 3/10 record will have 6 points for his wins, but only 3 of his losses (3 points) will count towards his score, for a total of 6+3 or 9 points (not 16!)
Now that this has been covered in detail we can move on to another pressing issue; management.
Management Issues
No, I don’t mean that management is incompetent; far from it, Stalkor, CGBSpender, Vortex and others have done an amazing job running the league. This isn’t about a lack of abilty or a lack of dedication. It is about what could be done, and done very easily to make the league a better place.
Communication Issues
As it stands, a large number of people drop out of the league and are not removed for that month. Some examples; in October 2010, at the end of the month, there were over two dozen completely absent players, for a total of 55 players with 3 games or less.
Alpha:1, Beta I: 3(+3 with less than 4 games), Beta II: 2 (+1 with less than 4 games), Gamma I: 2+2, Gamma II: 2+1, Gamma III: 5+2, Gamma IV: 4+3, Delta I: 4+2, Delta II: 3+3, Delta III: 0+3, Delta IV: 2+3, Delta V: 0+1, Delta VI, 0+3
The painful thing about this is that it would be extremely simple to make changes in how the league is organized to prevent this from ever happening again – in contrast to having it occur in almost every room, every single month.
Suggestion: Keep in Contact with Members
There are several ways this could be done. A mailing list is one good solution, but would require keeping player’s e-mail addresses when possible. Another option is sending messages on KGS. Either way, the general idea is to send a reminder sometime during the last week of the month that if a player is not planning to participate in the league, they should inform the admins.
A Better Suggestion: Early Removal Rule and Discounted Game Rule
Sending messages to members has it’s flaws, least of which, it’s admin intensive. A better solution is probably adding an early removal rule. This idea is both small and beautiful and can be expressed simply: “A player must play at least one game in the first two weeks of the month, or they will be removed from the league and replaced by the someone on the waiting list” (I am aware that this violates current policy).
Another Interesting Suggestion: reorganize by time zone.
No matter how you slice it, this makes sense. Organizing people by the time they are likely to be available (or by the time they are available) makes sense. In the past the counter to this suggestion was that some rooms would become imbalanced; it is so happened that the “European” time zone room was stronger than the “American” time zone room it may not be fair; however, this is not as relevant as it may seem at first. For one, there will be some bleed over as people join and leave the league. Secondly the I, II and so on of each class can begin with a random timezone each month, thereby mixing it up while still keeping people in the same room with others who are likely to be on at the same time.
Finally, the Alpha room question. This has zero effect on Alpha room; As the activity factor is reduced in the lower rooms, the strongest players from each timezone class will be promoted to alpha. If we assume that of Beta I and Beta II, beta I contains players who are on average stronger, then players from Beta I’s timezone-class will tend to dominate Alpha anyways. There is really no drawback to not organizing by timezone.
All it takes is a simple question whenever anyone joins the league; “what timezone are you in?”
Please do this.
Member Retention Problems
This month perhaps 55 people will be removed for inactivity and several others may announce their retirement. This is over 1/3rd of our player base and is a serious, recurring problem. Turnover is simply too high and long-term retention is ridiculously low. I’d ask the administrators to seriously consider the rationale behind the league in the first place. What is it for? Without any clear focus people will leave. Please listen to me, I’ve run the league in the past and in the meantime I’ve run two separate and successful top-end raiding guilds on World of Warcraft. I know something about motivating a team. And if you want to motivate people in this league to stay, you need to make them think they are getting something out of it.
Focus point: learning go
Put it in the rules, the FAQ, mention it everywhere: Winner is expected to review. You don’t have to, but….. //just talk about the game, share it//. Make this a part of the ASR culture. Just do it. This is a necessity. There is zero reason to play here if you don’t learn anything.
Seriously, playing serious games is not really enough…
Focus point: prizes
There’s been some debate about prizes and member rewards. You have to be careful about people who are only there to win the prizes and have no intention of reviewing games. I’ll say it again, mandate the reviewing of games. If you have to, do it like this, just state that you will not be eligible to win a prize if you don’t review at least half the games you win. You don’t have to check this all the time, but it is useful to have it in the rules if you need to step in and do something.
Focus point: being part of something, being part of the community
Involving the ASR in other things on KGS is extremely important. It is very important to tie the ASR league to KGS and to anything else which is familiar to KGS Go players. Having prizes of audiogolessons, having prizes related to atsumi school, insei league, etc. is EXTREMELY POSITIVE.
Strong suggestion; add rewards such as 1-month KGS Plus memberships (a $5 value per winner), get sponsorship from a pro and advertise his service (suggest to the pro of donating one or two SHORT game reviews per month in return for trumpeting the fact he is doing this and how great his reviews are.. yes, include testimonials if at all possible, and links.)

Focus Point: Letting them know you care
This sounds CHEESY but you would be surprised how WELL it works. On a regular basis, chat up members in the league. Just talk for a bit, offer to play a game, maybe a game outside the league structure. Offer to teach a weaker member. How often? Pfft, once a week. You don’t have to be their friend. You just have to show them that you are paying attention by paying attention to them, even for just 5 minutes a month. If somehow all of the 4 or 5 admins (and junior helpers, whomever) in the room manage to talk to every member for just five minutes every 2 or 3 months, believe me, everyone in the room will have a completely different picture of the ASR and the league.
Make regular news releases. Talk about your plans for the future. Create some project which members can focus on. The ASRScore software is something like that. Focus on that.
I’d even bring back the “usage edition” of goproblems.com, or even start a new collection for members, if you want, or perhaps a lecture series on memorizing shusaku games. But it must be institutionalized as a part of the room, for it to have the greatest effect. Meaning the information/material is somewhat separate and independently accessible without me. I can explain that in greater detail if need be.. I’m going to cut this short now because it’s late here.
This is pretty much everything I’d like to say which is easily implenentatable, NOW.
I really suggest that all this be taken seriously, and implemented swiftly.. the problems discussed are extremely easy to fix and don’t require any lasting investment of time…

I could explain why i don't agree with your post here, starting with the mistakes in the math (ignoring the fact 2nd and 3rd games with the same person count less, for example)

But why?

I did so before and obviously you didn't care...

I guess you want to make the league better, that's nice, but presenting the own oppinion as the only right way is not a good start.
You write about things that are wrong, that must be changed ... i'm not doing it the same way as you and say it's perfect as it is, but i think it's better this way.

Because you're nitpicking. Yes, 2nd and 3rd games cost less - for everyone. The point is it's a sliding scale. It's a statistical approximation. The point is, there are TWO variables; X and Y -- strength and games played -- and games played is mathematically more important than playing strength under the current system. There's lots of ways to fine tune what I did here.

But are you seriously suggesting the charts would look any different? They won't. The range of points scored will be less, but the charts will look exactly the same. Really.

If you want I could update the formulas to account for games being worth less as more are played with the same person. It's no big deal, but like I said it won't change the charts.



I believe I've shown that that was false. I've said it before -- The fact that the league is operational is not an excuse for leaving things the way they are.

At any rate, are you also commenting on the second and third ideas I mentioned? The ideas I had about organizing rooms by timezone, for example? Or of working harder to get the "ASR School" up and running? It sort of sounded like you were lumping everything I said together.

I know you and I don't always agree and that I have a somewhat confrontational style, but what I have said makes pretty good sense. Anyways there's a poll, not that it will count for anything, but I believe it will be interesting to see how people vote.

Good luck

Thanks for all the effort you've put into doing this usagi. You've put a lot of time in.

The poll appears to be swinging towards "everyone's happy", but that's not to say there aren't still improvements can be made.

Have you thought about volunteering to do all the data collection for the availability thing, including each month dealing with the turnover issues? If you can collect the data and actually orchestrate the group seeding in co-operation with stalkor for a couple of months, we can see if it has the positive effect on matches played that you think it will

Well, I really don't think it would take too much effort. It would involve speaking to everyone in the league at least once. I'd do it if stalkor let me.

And yes, it does seem that most people seem happy with the league, but statistics can easily be misleading and difficult to understand. Seven votes were cast that no changes were neccessary, but nine votes were cast towards various changes

It seems that what most people are pinning their hopes on right now is the supergroup idea. Stalkor and I and others had a long discussion about it the other night, I'm sure he's been discussing it with the admins. I think it's a great idea but I have no idea how they are going to pull it off. Anyways, we'll see how that works out, one step at a time

Be careful making your own argument based on statistics and then saying how misleading they can be

The votes to me sort of say "We're really happy, things are running really well, but if there were changes these are the things it would be nice to look at" - and of those, it's clear that the supergroup seems worth investing the priority effort into for the time being.

That said, there's hardly many votes placed anyway. Besides, you know my views on seeding by availability anyway

I will be very interested to see the trial results of your idea if it can be piloted for a couple of months.

I'm not yet a member of the league - I'm starting in November - so my opinion is not at all based on experience with the league, but after reading through usagi's text, I must say that most of his ideas make sense to me.

As far as I can tell, the main point of the league is for players to get a chance to improve by
1) playing even games with stronger players and
2) participating in reviews, either as the reviewer or the reviewee.

The question is: how to make this the most valuable experience for the most people. In order to satisfy the above two points, there must be a range of strength in each division, and those at the stronger and weaker edge of the scale should have the opportunity to change divisions, thus reversing their status in the new division, in other words, after switching, a player who had mostly been winning and giving reviews would get the chance to get his games reviewed, and the other way around for a player who had mostly been losing.

In light of this, usagi's criticism of the current situation seems valid, and I think his ideas have merit. If a stronger player can't move up, he will most probably get bored, and perhaps even quit the league. On the other hand, the chance for weaker players to move up a division and get their games reviewed by even stronger players is also nice, but it seems to me that the current system might be a bit unbalanced. I think the scale should be not quite so easy to tip simply by playing lots and lots of games.

Perhaps my opinion will change when I'm in the league, but until it does, I support the ideas of reweighting the win-loss points as well as creating timezone organized divisions.

_________________
Patience, grasshopper.

I don't say you (or usagi) are wrong, but it's only one side you see...



If you change the system like usagi demands the stronger ppl will play less and get the same result, there will be less games, less reviews, less improvement...

It's not a perfect system now, but imo it's better to have a slightly unfair system, that forces the ambitious ppl to play then a fair system that allows strong ppl to be lazy.


Anyway...comparing strength with activity is strange...
The strength is more or less fix, the activity not. And only strength doesn't give points but activity does (and strength influences the points one can get with a certain activity)

And simplifying to much lessens the meaning of statistics...
Its of great importance if you play games with different ppl or only with a few 3x each.
Also idealising the league to 13 ppl of same strength and one person 1 rank stronger makes nice statistics, but in reality you can't use the win-ratio anymore, there are ppl stronger and/or waeker then the 2 persons with 1 rank difference you want to compare and both will have the same win-ration against them (0 or 1).

usagi made statistics fitting to his opinion, leaving out things that don't fit. I don't deny there is some truth in them, but to much is missing to say they are "the truth".

I don't know about that. I see some aspects of what you are saying but it is just expectations about what might go wrong. We've already discussed that the only way to be perfectly fair is to have everyone play the same number of games. That isn't going to happen so we need to analyze what we have and work from there.



If you change the system the way I am suggesting (this thread is entitled ideas about the league), and we can assume that it will make the league a better place, then how will this cause people to play less?



I don't think lazy is the proper word to use here to describe a situation where participation would not be rewarded to the extent it is now. Please remember that the league already contains a natural participation filter -- the fact that you get points for wins, alone, is a form of rewarding participation. If wins were worth 1 point and losses were not worth anything, the league would be a fairer place. But, I like the idea of awarding points for a loss. Just not so much as is rewarded now.



I didn't make statistics fitting with my opinion -- what I said is simply "true". It is both true and obvious that participation has a much stronger weighting than it "should" have in this league.

Ask yourself a simple question. Do you deserve to stay in alpha?

your record is 4 wins and 23 losses. But because participation is rewarded so much you will be allowed to stay in alpha. Lebertran is 7-3 this month. That's 10 games. But vortex, with 9 games, will be staying in alpha.

Both lebertran and vortex are stronger than me, by about a stone and two-three stones. And you're ahead of them in points. No offense gabalon but you couldn't win one game against me if we were in the same room. What are you doing in alpha? You don't belong there.

That's really my beef with the league -- people who are essentially hyperactive are getting the top spots. I have 15 games this month. That's enough to compare. You have 27. So you are "ahead" of me. Simply put the league doesn't compare players of equal strength, it compares players of equal activity.

if that's what you want then you will like the ASR. Most strong players think the system is "unfair" in that it does not actually do what people think it will do. I dare say that I think this is why so many players just drop out of the league. It becomes obvious that it's a farce.

Seriously what's the point of playing in this league if someone with 4/23 is going to stay in alpha while players like lebertran get demoted, and players like me can't promote to alpha for months in a row?

Go ahead, say it Gabalon. You think the league would be a better place without players like me, right?

-

Because you may be wrong. For what it is worth, I also suspect your proposals will lower activity in the league.



Yes. The current system says so, so yes.



No offense, but he does belong there, and deserves to remain there. The fact he couldn't win against you, even if true, is irrelevant.



Which is only a bad thing if you don't like it. It's not "worse".



I don't know if I would consider myself a "strong" player, but it seems reasonable from the perspective of the members of the ASR, and I certainly don't consider it even slightly unfair. Unfair to me would be making adhoc judgements about rewarding people points on how much they are liked. Unfair to me would be doubling the points of everyone with a username beginning with "k". As it stands, everyone knows the rules and plays with the same reward for the same achievement, and knows where they stand all the way through. This is, in my opinion, a pretty good definition of a fair system. You may not like the rewards as they currently are, but that doesn't make it unfair, and in my opinion doesn't make it a farce either. "Real life" I suspect is the primary reason people drop out of the league.



In fairness, on strength alone, neither of us would, I suspect, be promoted to Alpha this month. So even in your system "players like you" doesn't cut it here. Romanwahoo and stalkor I think are fighting for 2nd strongest player in Beta II, with karnesun in the lead.



The league is a better place with you, with Gabalon, with me, and with anyone and everyone else that wants to join it and play Go.

Why so? Again, from the position of one who has not yet participated, my expectation is that I will be inserted in a low division and will play free games against both stronger and weaker players. If it turns out that I'm the strongest player in my division (doubtful, but just theoretically), I'll spend this month mostly in a helper role. I'm glad to do this, but I also want to be in the opposite role. To do this, I'll need to move up a division. Since I'm a working adult living in Europe, I probably won't be able move up just on the quantity of my games. So...I can't move up, and after a while of mostly just winning, giving reviews and not getting promoted, I get bored and drop out.

Preventing this is what makes sense to me about usagi's proposals.

On the other hand, I do see that if some such proposal were implemented which increased the value of a win making it easier to promote with a higher win/loss ratio, weaker players might be less inclined to play lots of games. But why? Because they would have less chance of promoting? Is that why people play in the league? To get to the top, irregardless of skill level? I guess that's ok, but I thought that people were in the league mostly in order to improve. That's what my plan is anyway. If it's a question of being able to get some recognition and earn prizes even if you aren't the strongest in your group, one could consider offering rewards (promotions, prizes, etc.) for both high win/loss ratio and high participation.

_________________
Patience, grasshopper.

My experience is most of the lower divisions have a good mix of players. There's a Delta division this month that has at least 3 dan players, of which one I suspect is around KGS 5-6 dan. It is rare that you don't get the opportunity to be both a helper and a helped. As a result, getting promoted isn't a necessity anyway, there'll be plenty of dan players around you for most of your time in the league _even if you stay in Delta_. So, the question is, why do you feel the need to promote?

So, why do I think it will encourage less activity? Well, let's say this month I really want to promote. With a win worth 1 point and a loss worth 0, I'll only play players I can beat, and prioritise players I know I will beat. I'll avoid playing stronger players. There's no incentive for a weaker player to play stronger players other than to learn, and a disincentive if you actually want to promote. This feels against the spirit of the league.

As it is, I can play 3 stronger people, lose each game, and still gain more points than any one of the three of them gained. So, for example, I had 3 thoroughly enjoyable games against karnesun this month, and even though he gets more points than I do, I still get a good amount of reward on top of the teaching aspect of playing a 5d. Next month, I intend on playing him 3 times as well, it's fun, I get points, and I learn - he's not going to turn me down either because it is useful to him. Take away that incentive, and I'll pick my opponents carefully as opposed to play anyone who happens to be on at the time in my division (which is what I do right now).

I find the biggest key to improving is playing more games (encouraged by the system) with sensible time controls (one of the rules of the system), and review them afterwards with my opponent (encouraged in the spirit of the system). The only reason to change the reward system is if you feel strongly that weaker players shouldn't be in the higher tiers or you feel that stronger players should have no problem getting up there. My responses to this, from my limited experience with the league, is twofold:

1) If a weaker player has played as many games as he can to get the privelege of lots of games in Alpha against strong players, then good luck to him, and I hope his dedication reaps him fair reward for his efforts.
2) If all the stronger players promoted easily and we ended up with a tiered system closely based on strength, we'd lose the strength mix we currently have in the tiers. Alpha would just be a bunch of dan players playing each other, and Delta a bunch of DDKs playing each other. There are plenty of competitive systems that do this already. One of the prime appeals of ASR to me is that I can expect such a breadth of skill in any division I'm participating in. If it was just me vs a bunch of other dans in some round robin system, I probably wouldn't still be playing in ASR.

All I know is that there is no way stalkor is going to read your whole post; even when you tell him simple things he says no (it's his league, he makes that clear), so with something like this, no way he'll even look at it closely .

More seriously, it is a league for active players. There is no "easy" way up the ranks, and even though it can be a bit boring sometimes when you are forced to play weaker players repeatedly (especially when they are very motivated and pushing you), I do like the idea everyone has to go down the same path, it is fair.

The league makes that clear, and whoever doesn't agree isn't forced to play.

There are many types of leagues, many systems we can come up with. ASR league implements just one of them. Is it a bad system? That depends on opinion alone, there is no system that will make everyone happy.

So yes, if you are not willing and not able (time-wise) to play 15+ games a month, no matter what your strength is don't expect to go up the ranks very quickly.

Also, I would like to say that players who don't play many games are a nuisance to the league. They don't fit in the system, it was made for active players but they let anyone in and I think this is a problem. Because of them we get so many classes and we are stuck with those inactive players (by inactive I don't just mean the 4 games requirement, I just mean players who don't play that many games) while if they just didn't join the league, there would be fewer classes with more active and moticated players in them. But the way it goes, it's all the opposite, the admins try to accommodate inactive players by limiting active and motivated players on purpose (talk to stalkor in private for a few minutes and you will understand what I mean). I think they miss the point, but whatever I say won't change anything.

As I told the admins and even wrote in this forum, the only real problem I see is how hard it can be to get a game and I did suggest a solution, but they don't like it (they pretend they thought it over already and so on), so I try to enjoy the league the way it is and I suggest that you do the same thing, those guys aren't going to do any major changes anytime soon.

Also, another small problem (in my opinion, always opinion here) is the way players are promoted. I think regardless of the total amount of points, the guy with the most wins (and with the same amount of wins, we look at points may be?) should always be promoted. And for the other(s), points based, to make it just a little fairer to stronger players.

And now that I got started, another thing I dislike: I understand they have issues with inactive players, but as a player, not knowing for sure how many players will get promoted (without having to calculate it yourself) is a bit annoying. I think players should always know.

@Topazg

I liked your post, and thanks for the explanation. If things are as you say, and there is a good skill mix in each division, then I'm sure for me, I'll be able to get what I want, and I'm certainly looking forward playing in the league.

I am however still unsure what's in it for the strongest player in a division, besides the opportunity to give as many free teaching games as he has time for... Well, I guess he can still win prizes, and who am I to criticize the altruism of others on my behalf.

You mentioned your games against karnesun as also being useful to him, and as of right now, karnesun leads your division having played and won all 16 games. However you, who have played 18 games, could still edge him out just by losing one more. Seems a little silly. But then again, maybe not. Everyone knows and understands the criteria for promotion, and karnesun could put up a fight to stay ahead...but I don't really see why he would want to do so.

_________________
Patience, grasshopper.

The supergroup will give a great incentive for the strong players. For my part, I'm just wanting to win Alpha if I can, and that's enough for me as a stronger player to aim for. To do that, I have to play a lot of games, and the process of simply playing this many serious games is helping my own strength. A stronger player can use games against weaker players as a chance to experiment with new ideas as well, there's plenty of scope for doing things along the way of getting your points for that month

Certainly my record is largely positive, but I enjoyed each and every one of the games (apart from my embarrassingly awful performance against xenofhonto) even against those over 6 stones weaker.