It is currently Thu Oct 31, 2024 3:53 pm

All times are UTC - 8 hours [ DST ]




Post new topic Reply to topic  [ 13 posts ] 
Author Message
Offline
 Post subject: How AI study has helped me
Post #1 Posted: Sat May 07, 2022 7:23 am 
Oza
User avatar

Posts: 2420
Location: Ghent, Belgium
Liked others: 359
Was liked: 1020
Rank: KGS 2d OGS 1d Fox 4d
KGS: Artevelde
OGS: Knotwilg
Online playing schedule: UTC 18:00 - 22:00
Here I am playing an opponent who's probably also low dan. In this game he died in gote, which was a big mistake, but overall I found I played very well myself. I wanted to translate this feeling into a review, indicating where I may have improved by stuyding with AI and also where I made good choices due to a bit of extra reading. Questions, doubts, comments ... welcome.


Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #2 Posted: Sat May 07, 2022 10:09 am 
Oza

Posts: 3698
Liked others: 20
Was liked: 4660
Quote:
Questions, doubts, comments ... welcome


Quote:
where I may have improved by stuyding with AI and also where I made good choices due to a bit of extra reading


(1) I start with the assumption that to improve at go you have to change your brain - in the same way that to improve at table tennis you have to practise hitting the ball LOTS of time, or in music you actually have to wrestle with the instrument even till your fingers bleed. It is my experience (of myself and observing others) that the only way people improve consistently is by such hard work. Advice, lessons, books, videos or AI do not of themselves create improvement. All they can do is stimulate you into doing some hard work. Which "whip" you use depends on your own personality, tastes, preferences and opportunities.

If you accept, therefore, that you actually have improved after (NOT really by) choosing to study with AI, what was it about AI that suddenly make you want to work harder? And why did the other methods not make you work so hard?

(2) I make a further assumption, to see whether you agree with it. Namely, when we work hard, rather than improving we get a FEELING of improving. We believe we understand more. In fact, I'm pretty sure we do understand a lot more. But that doesn't necessarily translate into results on the board (or on the table or on the piano). I suspect the reason is that we are still not working hard enough, and as a result we haven't actually changed our brains. Such changes can happen easily at kyu level, but when you get to dandom the law of diminishing returns kicks in horribly. And when you move up the dans it becomes almost impossible for amateurs living a normal, varied family life to find the time to do that extra brain-changing work.

When I do my go books, I am concentrating intensely on understanding comments in pro sources and trying to render them in English. The result is that (I feel) my understanding of go is continuously improving and is at a high level. But I stop there. I make no effort into translating that into a brain change. Although I don't actually take part in the tournament scene any more, I have no doubt whatsoever that my extra understanding would not produce better results if I did play, and it would not even surprise me if I played like a kyu player.

I suspect Robert may have a similar problem. He focuses on go intently when he is studying theory, and I'm sure he feels he has a much better grasp of the game. But on the board he is not even near the level of his notorious lowly Japanese 9-dan. He still plays but, in grade terms, as I see it, is just treading water. Is that fair comment, Robert? We may all find these things unpalatable, but it's part and parcel of life and of being an amateur.

And do you, Dieter, sense the same problem?

Personally, I don't think it's a problem if that IS a problem. Just understanding more about one's favourite game brings more than enough joy to most fans.

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #3 Posted: Sat May 07, 2022 12:19 pm 
Judan

Posts: 6230
Liked others: 0
Was liked: 793
Improvement does not always require hard work. It is sometimes sufficient to acquire precisely the right knowledge, such as to learn from one's mistakes at all if one overlooked this basic insight. Such is possible more easily as kyu than as high dan, of course.

As to why I do not become 9p quickly, ugh, who ever became 9p quickly? :) I have already described why my level is where it is. Let me reformulate your question: Why do I study much that does not (or only hardly) make me stronger instead of much that immediately makes me stronger? This, however, is not quite right. Rather I use my too little time available for study with a long-term plan. Currently, I focus on what I can spend time: accelerating endgame value calculation. Creating and correctly solving many such problems as part of my work has this side effect. When I will have done that enough, I can attack my next major weakness.

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #4 Posted: Sat May 07, 2022 2:51 pm 
Lives in sente

Posts: 967
Liked others: 24
Was liked: 173
Rank: panda 5 dan
IGS: kvasir
Knotwilg wrote:
[...]Questions, doubts, comments ... welcome.


Some doubts, actually just comments.

:w24: looks slow but solid to me and maybe :b25: is an example of take care of yourself when the opponent is strong but maybe black could also play on the left side instead. It bothers me that both players play like the opponent has a strong shape, I don't think that is the AI way of playing, maybe black should tenuki to the lower right at :b22: because blocking on the second line could be too slow. My feeling is that white is the one that has strong shape but there is no danger for black and therefore I doubt black's solid play more than white's.

I think :w26: R16 is the widest open area. The AI programs do prefer the widest area in my experience but it is an old lesson.

I doubt white's approach to reducing the upper right corner, not because it doesn't work, but because it is very complicated. I think white should play Q17 before letting black get R12 and R13 and this is just to make it manageable. Also I suspect R16 is an overplay compared to the normal clamp S17. Black can just capture the stone and poke at white's shape until it is a fairly weak group and because black keeps most of the territory and there is a long game remaining it could be a big mistake by white. Anyway, stronger players will not be fazed easily and the real benefit needs to be weighted against ones own chances at delivering a complicated technique. I am not sure AI is helping here, it just doesn't seem to have a good sense of what is normal and what is too difficult.

Edit: typo


Last edited by kvasir on Sat May 07, 2022 3:18 pm, edited 1 time in total.
Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #5 Posted: Sat May 07, 2022 3:16 pm 
Lives with ko

Posts: 148
Liked others: 134
Was liked: 23
24 and 96 in particular are nice moves that I'd guess may reflect AI influences.

The game doesn't strike me as very AI-like overall though. In this game White takes an early lead after Black plays out a position to confirm a loss of points, and Black goes on to play very slow moves - and that's the main narrative. It doesn't have the qualities that I personally associate with AI, such as: tenukis from 'unfinished' positions, groups of unsettled status, indirect connections and threats, sudden 'unexpected' trades.... So it's bit difficult to tell the influence of AI.

I think it may take more than one game to display the influence of AI.

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #6 Posted: Sat May 07, 2022 4:26 pm 
Oza
User avatar

Posts: 2420
Location: Ghent, Belgium
Liked others: 359
Was liked: 1020
Rank: KGS 2d OGS 1d Fox 4d
KGS: Artevelde
OGS: Knotwilg
Online playing schedule: UTC 18:00 - 22:00
John Fairbairn wrote:

(1) I start with the assumption that to improve at go you have to change your brain - in the same way that to improve at table tennis you have to practise hitting the ball LOTS of time, or in music you actually have to wrestle with the instrument even till your fingers bleed.



In my multi-quest for improvement, I've read and thought at least as much about how to improve at the guitar, or why I didn't, and table tennis. A recurring theme is that not only you have to practice a lot but also have to practice well. In particular when muscle memory is involved practicing a lot with bad form can hurt you more than it does good. While the brain is arguably less of a muscle, it definitely applies here too that bad habits are not easy to get rid of.

Of these three activities, I've had by far the better tutoring in table tennis. My fundamentals are strong there and therefore I think quantity of practice will have the bigger effect.

Quote:

If you accept, therefore, that you actually have improved after (NOT really by) choosing to study with AI, what was it about AI that suddenly make you want to work harder? And why did the other methods not make you work so hard?



I accept that AI has stimulated me to work harder and that hard work has paid off. But as pointed out above I also think I worked more effectively under constant expert surveillance.

As to your key question, if I can modify it a little: why did AI stimulate me to pick up studying Go again this late in my journey and why did it give me back the hope I had lost to still significantly improve?

I've allowed myself the modification because I HAVE worked hard in the past too: reviewing my games before AI were available, studying with Guo Juan for a brief spell, memorizing and trying to mimick Otake Hideo, doing lots of tsumego, working on Sensei's libary, playing live tournaments, reading books ...

Of all these methods, reviewing my games (in particular while pushing myself in a kind of friendly rivalry) has been the most beneficial, bringing me from 2k to 2d in a few years.

AI's challenging existing heuristics and patterns was nothing short of a thrilling episode. I like revolutions in any area of society. In terms of ideas I'm a progressive not a traditionalist. There's no judgment here, just a preference, my nature.

Combining the advent of such a revolutionary power with the practice of reviewing, having the expert constantly available at zero cost ... well, how could I not be rejuvenated :)


Quote:
when we work hard, rather than improving we get a FEELING of improving. We believe we understand more. In fact, I'm pretty sure we do understand a lot more. But that doesn't necessarily translate into results on the board (or on the table or on the piano).


Oh I agree. And I'm still only 2d on both OGS and KGS. But I'm sensing the leap to 3d is closer than before now, from matches I play against that level, the relative ease with which I'm winning against 1k and 1d these days, and a recent game against a 5d, which I lost but did not make many big mistakes - he just made even less and smaller mistakes.

Quote:
I suspect the reason is that we are still not working hard enough, and as a result we haven't actually changed our brains.


The posted game is an attempt to show where and how my go-brain has changed, after two years of rather hard work. It took those years because I'm not spending too many hours a day, rather a few hours per week.

Quote:
And do you, Dieter, sense the same problem?

Personally, I don't think it's a problem if that IS a problem. Just understanding more about one's favourite game brings more than enough joy to most fans.


I felt that way a lot more when reading books or other study methods. Reviewing my games consistently with AI and deliberately applying lessons learnt to subsequent games, has been the most effective method so far. But the proof will be in a consistent 3d rank.

Thanks for your thoughts and comments.


This post by Knotwilg was liked by 2 people: CDavis7M, schrody
Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #7 Posted: Sat May 07, 2022 4:39 pm 
Oza
User avatar

Posts: 2420
Location: Ghent, Belgium
Liked others: 359
Was liked: 1020
Rank: KGS 2d OGS 1d Fox 4d
KGS: Artevelde
OGS: Knotwilg
Online playing schedule: UTC 18:00 - 22:00
dust wrote:
The game doesn't strike me as very AI-like overall though.


No but that was not the point. It was a fairly easy victory over an opponent to whom I have lost before, due to some bad plays on his behalf but also because of some choices I would not have made pre AI study. I felt my game had improved and I tried to express where and how.

There were still many moves unlike AI, even consciously so. 96 for example was a sector line reduction, courtesy of Bruce Wilcox. 94, securing the corner with a slow 3-3, is a move that AI doesn't even consider, very unefficient, but also converting a large advantage into a more certain victory, almost a declaration of it.

Quote:
It doesn't have the qualities that I personally associate with AI, such as: tenukis from 'unfinished' positions, groups of unsettled status, indirect connections and threats, sudden 'unexpected' trades.... So it's bit difficult to tell the influence of AI.


Sure enough I'm not trying to imitate AI but learn from it. The emphasis in this review was more on the improvement than on the AI-likeness.

Thanks for your comments!

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #8 Posted: Sun May 08, 2022 5:58 am 
Lives in gote

Posts: 389
Liked others: 81
Was liked: 128
KGS: lepore
Interesting thread.

Personally I've found improving with AI to be very challenging:

- I enjoy making moyos, and AI seems to hate grandiose plans. It is coldly efficient, and wants me to divert from many of opening tendencies. :-|

- My tactics are not sharp, and AI can show me the correct local tactic. But so can a stronger player (and with some helpful accompanying intuition/explanation).

That said, I'm glad you've benefitted from it Dieter.

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #9 Posted: Sun May 08, 2022 6:43 am 
Gosei
User avatar

Posts: 1769
Liked others: 180
Was liked: 492
AI is like a strong pro who is always available, but who only speaks a foreign language. Not as good as a someone who can explain with words but most of us don't have the opportunity to get every game reviewed by a stronger human player.


This post by jlt was liked by: Akura
Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #10 Posted: Fri May 13, 2022 9:16 am 
Lives in gote

Posts: 646
Liked others: 62
Was liked: 116
Why the diagonal for :w24: instead of a jump? Has it anything to do with your shape or is it to be able to attack the black group more severely later on (potentially)? Or something else?

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #11 Posted: Fri May 13, 2022 12:14 pm 
Oza
User avatar

Posts: 2420
Location: Ghent, Belgium
Liked others: 359
Was liked: 1020
Rank: KGS 2d OGS 1d Fox 4d
KGS: Artevelde
OGS: Knotwilg
Online playing schedule: UTC 18:00 - 22:00
Ian Butler wrote:
Why the diagonal for :w24: instead of a jump? Has it anything to do with your shape or is it to be able to attack the black group more severely later on (potentially)? Or something else?


AI thinks the jump is at least as good as the diagonal. In my thinking the diagonal had more of a "miai" aspect, threatening the cut at the top against which Black defended, and the attack at the angle point on the left.

A jump would more likely prompt Black to defend on the left, which is where I really wanted to attack.

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #12 Posted: Fri May 13, 2022 12:32 pm 
Honinbo

Posts: 9550
Liked others: 1602
Was liked: 1712
KGS: Kirby
Tygem: 커비라고해
Knotwilg wrote:
Ian Butler wrote:
Why the diagonal for :w24: instead of a jump? Has it anything to do with your shape or is it to be able to attack the black group more severely later on (potentially)? Or something else?


AI thinks the jump is at least as good as the diagonal. In my thinking the diagonal had more of a "miai" aspect, threatening the cut at the top against which Black defended, and the attack at the angle point on the left.

A jump would more likely prompt Black to defend on the left, which is where I really wanted to attack.


In this scenario, you have the diagonal move, which you understand and have a reason for. Yet the AI seems to suggest a jump is "at least as good". Do you try further to understand the reason that the AI likes the jump? Or is the evaluation close enough such that you keep your own move? Based on the point that Black may defend on the left, it would seem to me, in terms of reasoning for the moves, the diagonal is superior. Maybe there's a hidden value to the jump that I don't understand, though. Perhaps the evaluation is close enough that it's not beneficial to overanalyze it...?

_________________
be immersed

Top
 Profile  
 
Offline
 Post subject: Re: How AI study has helped me
Post #13 Posted: Tue May 17, 2022 9:19 am 
Lives with ko

Posts: 131
Liked others: 151
Was liked: 30
Rank: British 3 kyu
KGS: thirdfogie
This is a report from a weak player about learning from AI. Apologies for the
length and for mainly talking to myself. I have White in all the examples.

KataGo Cannot Cure Cognitive Collapse
I recently won 5 club games in a row, and thought that study with AI was
finally bearing fruit. Pride goeth before a fall, so I lost the next 3. The
first was a loss on time when 50 points ahead. The second was lost due to
overlooking a large atari when ahead by 20 points. The third happened in a
game where the opponent took 9 stones and 179 points komi. I had equalised by
killing half the board, then stupidly lost some important cutting stones. All
these happened near the end of the game when the board was visually busy and I
was short of time.

Another recent club game unveiled a fresh horror, which was playing the illegal
move at 'a' below. I'd worked out that if White plays 'b', Black should not
connect at 'a' and then somehow mentally switched the two points and placed a
stone at 'a'.

Click Here To Show Diagram Code
[go]$$
$$ -------------+
$$ . . . X X a |
$$ . . . X O X |
$$ . . X O O X |
$$ . . X O . b |
$$ . . X . O . |
$$ . . . X X O |
$$ . . . X O . |
$$ . . . X O . |
$$ . . X O . . |
$$ . . X O . . |[/go]


AI cannot help one avoid such ridiculous blunders. Perhaps the remyelinisation
mentioned by Joaz Banbeck would help. Absent that, maybe public
self-criticism.

I have learnt and applied a few things and failed to apply many more.
Examples follow.

Learnt and Always Applied
In the simplified diagram below, assume that White needs to prevent Black
connecting on the first line. I used to play 'a', 'b' or 'c' pretty much at
random. Now I always think about the fact that 'a' or 'c' gives Black a
forcing move on one side, whereas 'b' does not. On the other hand, 'a' or 'c'
may remove a crucial liberty or create a false eye in a useful way.

Click Here To Show Diagram Code
[go]$$
$$ -------------+
$$ . . a b c . |
$$ . . X O X . |
$$ . . X O X . |
$$ . . . O . . |
$$ . . . . . . |
$$ . . . . . . |[/go]


Mostly Learnt and Applied
I now rarely miss obvious moves that force the opponent into bad shape. I am
less good at forestalling such moves by the opponent, but there is some
progress there too.

Sometimes Learnt and Applied
One bad habit is playing nakade before the opponent's group has been securely
cut off. If that group then escapes and lives, I have given him an extra
point. In such a case, it would be better to complete the enclosure so the
opponent has to play inside, he loses a point and I get sente. The diagram
shows a failure: I was so keen to play 'a' to demonstrate my recognition of a
variant of the flower-six shape that I did not stop to think whether it was
wise. It can also be useful to "Keep your secrets" (credit: Matthew Macfadyen).

Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . O . X X O . |
$$ | . . . . . . . . . . . . O X X X O . . |
$$ | . . . O . . . . . . O O O O . X O . . |
$$ | . . . . . . . O . . X X O X . X X O . |
$$ | . . . . . . . . . X . . X X X O X O . |
$$ | . . . . . . . . . . . a . X O O X O . |
$$ | . . . . . . . . O X X . . X X O O X . |
$$ | . . . . . . . . O O O X X X O O X X . |
$$ | . . . . . . . . . . O O X O O . O X . |
$$ | . . . . . . . . . . X X O . . . O O X |
$$ | . . . . . . . . b . X O . O O . O X . |
$$ | . . . . . . . . . . X O O O X . . X . |
$$ | . . . . . . . . . X O X X X . . X . . |
$$ | . . . . . . . . . X O . . . . . . . . |
$$ | . . . O . . . . . X O . . X . . . . . |
$$ | . . . . . . . . . X O . . O . X . . . |
$$ | . . . . . . . . X O . O . . O X . . . |
$$ | . . . . . . . . . X . . . . . . . . . |
$$ +---------------------------------------+[/go]

KataGo actually recommends White 'b' here.

Occasionally Applied
Katago is often ready to sacrifice stones on a large scale. I am beginning to
ape her. It requires accurate reading, but has shock value against kyu-level
opponents. The example is hidden.

I played 'a' in the position shown below. With 5000 visits, KataGo
never considered 'a', but once she saw it, she preferred it to her own ideas.
I had been aiming at 'a' for some time, so that was nice. The plan was to
sacrifice the squared white stones in order to kill the bigger black group to
the left. If Black resists that plan, he loses his two crossed stones at the
bottom and White rescues the squared stones.

Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . O . X . . X O O O O X O . |
$$ | . . . O . . . . . . . X O X . X O O . |
$$ | . . O . . . . . . . . . X X . X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . X X O . . . . |
$$ | . O O O . . . . . . . . O O X X . . . |
$$ | . X X . . . . . . . . . O X O X X X . |
$$ | . . . X . . . . . X . . . . O O X O . |
$$ | . . . . . . . . @ X . . . . . O O . . |
$$ | . X . . . . . . @ X . . O . . . . . . |
$$ | . O X X X a . . @ X . . . . . O O . . |
$$ | . O O X O X X . @ @ X . . . . . X X . |
$$ | . . . O . O X @ . . X . . X . X . . . |
$$ | . . O . O O O Z Z . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]


Never Applied
Lots of lessons fall into this category. This section mentions some that
happen a lot and are easy to understand but never used by me.

I am too attached to the stones most recently played. KataGo tells me this
again and again, but I never learn.

Near the end of the game, KataGo often spots chances to gain points by
semedori. I never spot them. Similarly, KataGo often spots chances to
falsify an opponent's eye in a way that forces him to lose another 1 or 2
points connecting back across other false eyes. I never do.

Games occasionally end with unresolved situations. Fixing this requires
reading everything, everywhere, all at once - yes, I have just seen the film.
In reality, one is happy to fall over the line at the end of a game without
obviously blundering or losing on time. An example is hidden below.
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . O . X X O . . . . . . . |
$$ | . . . . . . X O . X O . . O O O . . . |
$$ | . 5 6 . O X O O X X O . . O X X O O O |
$$ | 9 . . O O O O X X O O O O X . X X X O |
$$ | . 1 X O X X X X X X . O X X . . X O O |
$$ | 7 2 O X X X O X X O O O O X X O . X O |
$$ | 8 . O O X X O O O X X X O X . X X . X |
$$ | . 3 4 O X X X O O O X O O O X . X . . |
$$ | . . O X X . X O . O X X X O O X X X X |
$$ | O O O O X X O O O X X X X X O O X O X |
$$ | X O X X X X X O O O X O X X X O O O O |
$$ | X X X X O O X O O X X O . . X O . . . |
$$ | O O O . . X O . O O X O . . X O . . . |
$$ | X X X X X X O O O X O O . . X O X O . |
$$ | X O O O O O X X X X X O . X . X O O O |
$$ | O O . O . O O X . . . X . X . . X X O |
$$ | . . . . O . . O X . X . . . X X O X X |
$$ | . . . . . O O O X X . . . . . . . . . |
$$ | . . . . . . . O O X . . . . . . . . . |
$$ +---------------------------------------+[/go]

The above game was scored as a 4-point win for White, with no komi. The moves
starting at :b1: were not played. (I read as far as :w4:, but did not consider
:b5:.) KataGo sees that the sequence from :b1: to :b9: results in a picnic ko
for Black and a win by 16 points. Black only needs small ko threats because
White's previous 'lead' was small.

Let us end with a little bit of magic from KataGo. The game was against a
regular opponent who is especially found of cuts, wedges and double peeps. In
other words, he keeps me honest. In the diagram, Black has played a double
peep with :bx: and I connected at :ws:. Black later peeped underneath with :bs:
and it looked like White will lose some corner territory. However, KataGo
sees that White can play 'a' and hold on to everything. The details are left
as an exercise for the reader. Maybe I will remember this move next time.

Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O O X . X . . X O O O . . . . |
$$ | . . . . O X . X . . . X X X X O O O . |
$$ | . . . O . X . X O X . . . . . X X X . |
$$ | . a # O Z . . O X X O . . . . . . . . |
$$ | . O X O @ O . O . O . . . . . X . . . |
$$ | . . . . . . . . . . O . . . X . X . . |
$$ | . . X . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . X O X X X O . . |
$$ | . . . . . . . . . . . X X O X X O . . |
$$ | . . . X . . . . X . O O O O O O . . . |
$$ | . . . . . . . . . X O X . . . . O . . |
$$ | . . . . . . . . X O O X O O X . . O . |
$$ | . . X . . . . X X O X O . . . . X X . |
$$ | . X . . . . . X O X . O . . . . . . . |
$$ | . O O O . . . O O X . O X . . . . . . |
$$ | . . . . . O . O . X . O X . . X . . . |
$$ | . . . . . . . . . . . O X . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]


Also, this.
Quote:
Just understanding more about one's favourite game brings
more than enough joy to most fans.

Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 13 posts ] 

All times are UTC - 8 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group