Being able to count is important - in the end, it's about the points. Does anyone have any tips to get used to counting during a game, little things that can speed it up or make it a little less tedious in the beginning?
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The advice I have heard most is to count in pairs. The human mind can easily count groups of around four objects, and so it may be beneficial to eventually move to counts of fours, but pairs tend to be easier in my experience. Count a dead stone as one pair, and if you see a lone empty spot, just mark that in your mind and continue, removing the mark and adding a pair once you see another lone empty spot.
Once you have your count for one colour, either subtract that number from 50 (or 100, if there's a lot of empty room), or start counting down. Otherwise, you are very likely to forget the score you counted, making you start all over again.
Another useful trick is to simply balance large pieces of territory against each other, and then count what's left; this is less accurate, but in the mid-game speed may be more important and you may be unable to give good estimates, anyway. Make sure to multiply the value of an area by the probability of the player keeping it; a good way to do this automatically is to count in threes or fours when looking at large areas that are very likely to be invaded.
A fairly obvious trick is to count in your opponent's time; however, be careful that you still count the effect of your move before you play it (if possible), and not afterwards. Especially in the yose, if you have time, try to count how many points a move will cost. In many cases, you may find that taking sente may be worth more than responding to the opponent's move.
Finally, if you happen to have trouble keeping track of the score, consider learning binary; it'll let you count to 1023 on your fingers, which should be enough for most games. :)
Also try an intuitive count as a way of training that intuition. Think about how you've come out in the exchanges you've had with your opponent. Did you get something and your opponent got something? That's roughly equal. Did you come out with a very poor result in one place and your opponent in another? That's also roughly equal at that point. If you've been robbed and your opponent has not then you're behind. This approach will also lead to you asking others for advice on how to assess positions and results of exchanges. In the long term this is very useful. Point by point counting is actually easier to learn.
You can make notes. Note what are your estimates of every territory avery 10 or 20 moves.
Not only it will allow you to track the score but also you will learn on your mistakes (in the end of game you will get accurate score). But also you will learn values of particular moves expanding territories. You also will get a grasp on value of thickness as territories will start to appear "out of thin air".
Also with time you will remember all you have written, as it will become a habit.
The way I was taught is to count groups of two points:
In my experience, this makes counting board score much easier.
Count the space, ignore the stones. I usually count space like Japanese rule.
I don't count very often, usually after most of the board are shaped.
After counting, remember the delta. For example, if I am 5 points behind, play like I am going to gain 6 points. Adjust the delta along the game. In such way, I don't have to count staring from zero every time.