Close games

[Uberdude]

I've always found it remarkable that after playing ~250 moves games can still often end up as half point games, even when there have been huge exchanges, big territories etc. When pros do this it is sometimes explained away as "Oh they wouldn't have made those big exchanges/territories if it weren't for them counting accurately and judging it to be fairly even". But I get close games too and I can't claim to count accurately like that, it seems more like a fluke that some benevolent Go God is watching over the game and ensures the result is balanced.

What made me think of this recently is I just beat nrx, a 5d on OGS, by 1.5 points again. That was our fifth game and I won a previous one by 1.5 too. I also won another by 4.5 but really it should have been 1.5 again but he went silly at the end as it didn't matter. Another I won by resign, and another I lost on time (I was probably behind a little but often catch up in yose). Normally if I said I was 1.5 points stronger than someone it would seem absurd to specify that precision, but it seems it could be the case! Anyone else have a similar situation of an opponent who they often beat by the same small margin?

I included the games in the hidden below. In order the results are loss on time then win by 1.5, resign, 4.5 (but really 1.5), 1.5. As you can see in game 2 he made some huge territory on the right which I in no way counted when making my territory, yet magically it was very close. Similar thing in game 4 with big trades and territories. And then game 5 I think I got a good result on the lower side but then he made a big centre out of almost nowhere so I had to invade the top right and then again it came out as a 1.5 game. It seems like fate...

Edit: Hmmm, I just realised I am always white, is 6.5 komi correct? . I wonder if I would win by 1.5 as black too.

[SmoothOper]

I agree it is remarkable, how often a game is decided within a few points. I think of it kind of like an abstract mirror, where instead of mirroring each others exact moves, the players are mirroring their intentions on different parts of the board. IE, they take territory of 20 points over there, I take 20 points here. In theory if you were mirroring each others moves you shouldn't do worse than komi, without some specific tricks to break the mirror. I think it speaks of the high miai nature of the game.

[Joaz Banbeck]

We all suffer from apophenia now and then.

[Uberdude]

We all suffer from apophenia now and then.

Yeah, I didn't mention all the other opponents I beat with widely varying margins; as I didn't declare my hypothesis before testing it's not statistically rigourous. But still it seems I'm just an eensy bit stronger than him. I remember the coach of the kids from Chinese Taipei at the WMSG said they were komi weaker than pros which suggests a similar fairly consistent small margin.

[Uberdude]

I think of it kind of like an abstract mirror, where instead of mirroring each others exact moves, the players are mirroring their intentions on different parts of the board. IE, they take territory of 20 points over there, I take 20 points here.

Yes, that kind of thing can be true, and I remember one of my games (below) was a rather amusing strategic mirror like this (he makes big lower left, I make big upper left, he approaches lower right, I pincer, big jumpy fight, I approach upper right, he pincers, big jumpy fight, he lives in my right side, I live in his right side) but for example my 2nd game with nrx, he made a huge 60 points territory on the right but I never made anything that size in return. Instead it just so happened, almost by magic, that the sum of our territories at the end ended up so close.

[Polama]

Part of it is that we do tend to play towards a close score if we want to win a lot. A lead in the early to mid game gets redeemed in the later parts of the game by not having to make a tight invasion or by being able to simplify the board conceding a few points to the opponent.

Some games are won by 2 points, but without victory being in doubt, and some are won by 50 points but were very tightly contested.

[golem7]

Probably like many others I used to think that something like a 15 point difference was a close game in my lower kyu days. But my perspective changed as I got stronger. More and more you start to fight for small advantages that give you an extra point/ko threat/sente and you realize how important these are.

I also like the mirror analogy. After all, it is a two player game and for every move you make your opponent is getting one himself. So if two players are equally strong it is only natural that their moves should have the same mean and overall value. This is just getting more and more obvious at higher ranks because there is less variance in move quality (misreads,judgement etc.) which results in fairly balanced games.

Simple example: If you rate the moves of a game from 1 (dies in gote) to 10 (pro level), a, say, 10 kyu game might produce moves of each quality with a mean of 4, whereas a high dan game might consist mostly of moves with a 10-7 value and a mean inbetween. Of course we know even pros do self-atari but it's just much less likely. Two equally strong players should have the same expected overall value of moves, that's why close games happen on every level. It's just more probable on a higher playing level because of a higher consistency in play.

[Joaz Banbeck]

I was shipping the Amazon orders for my bookstore today. The first two customers ( different first names, different addresses ) were named 'Stone'. Seeing that as an omen, as soon as the mailman picked them up, I resumed analyzing my Malkovich game against MW - during which I demonstrated conclusively to myself that he would win by two stones. So I'm blaming my loss on Amazon.

EDIT: The third customer was a Mr Wood.