There is a recent chess book for chess grandmaster preparation called “Calculations” by Jacob Aagaard in which he talks about calculation theory in a very broad sense. I believe that such an approach is a worthwhile study so I have paraphrased and adapted his thoughts for the game of go as follows.
Why do we need to focus on calculation ability? It’s because when you don’t know where to play next, analyzing the position is the tool which will give you the greatest success.
So how should we practice calculations? The best way is probably to concentrate on training material which is just above your own skill level because improvement starts where your comfort zone ends. And you need to have the determination to do your training regularly because all improvements are incremental. No one starts naturally as a 9d, they build up their skills one step at a time. To reach a goal you set, the amount of work needed to reach a goal is almost always underestimated by 25-50%. You really need to do the necessary work for your goal to see significant improvement. Remember that concentration and determination are the most important aspects of calculation.
So what are the eight core calculation techniques we should focus on?
1. Candidate moves
There is an art in seeing before thinking. Right away, we may see two or three ideas in any position we meet, but there is no guarantee that they are the best moves. We should therefore train ourselves to look for additional ideas and end up with a list of interesting items to check out. As we go through the list, ideas from one line may prove very useful in another line or perhaps help in calculating the right order of sequence.
2. Combinational Vision
There is rarely any really new ideas under the sun. Most every combination is mainly a rehash of well-known patterns. Therefore you need to spend significant amounts of time training and solving tsumego and tesuji to build up your own combinational vision.
Putting yourself in your opponent’s shoes, you must be aware of their ideas and how they might counter your ideas. You must figure out whether your opponent intends to attack or to defend and include their ideas in your thinking.
You must be able to compare similar decisions and work out the differences between them. This can range from obvious advantages to subtle ideas which make all the difference in the game.
Sometimes it is useful to look for defects in ideas and eliminate them from our thinking. This pruning is especially useful in defense.
6. Intermediate Moves
Tenuki, tenuki, tenuki. Many opponents think long and hard and make assumptions about how they think you will move. You should always be on the lookout for ways to think outside their box and how to throw a spanner into the gears of their thinking.
Imagination is the discovery of surprisingly strong moves which reveal the true nature of a position rather than just the obvious moves. Many people think that imagination is a natural ability and cannot be trained. Wrong, imagination is acquired just like any other skill. And it can be accomplished with proper training in developing tactical and strategical abilities together with solving hard go problems.
Setting traps is usually a poor way to play. As you end up only hoping for a mistake by your opponent. But nevertheless, it is a useful skill to turn to if all else fails.
Besides the above techniques, some other useful thought processes to consider:
— What is important in the current position? Do things still go according to the plans you formulated two moves ago?
— Define your aim and what you are planning to achieve.
— How much time do you want to invest on a move? Since most go games are played with a time limit, you must think about how to ration the time you use to calculate moves which are difficult to decide.
— Calculate forcing moves before other moves
— Common sense dictates what you should analyze
— Think about the drawback of your opponent’s last move
— Only analyze the necessary variations to make efficient calculations
— Focus on the now and leave decisions about the future for when it comes. You end up saving time which you might have used for doing much needless calculations which bear no fruit.
— Quality calculation over quantity calculation. Calculate a bit slower but make sure it’s only on variations which are needed.
— Ask yourself if it is really necessary to calculate a variation deeply before doing so. New ideas at the start are worth much more than refinements at the end of variations.
— Structure your thinking to be effective. Don’t let your brain rove round and round different lines several times over. Master your mind and emotions rather than letting them master you.
— Don’t assume. Assumptions play nasty tricks on you from time to time.
— Check the order of sequence. The wrong order of sequence can be just as deadly as playing the wrong moves.
— Make up your mind and just do it. Often times, what you decide on first after your calculation is superior to moves which you change your mind for. And you don’t want to end up with time trouble either.
— Have a firm evaluation of each variation to make easier decisions.
— Calculate only until you come to a definite conclusion and stop going deeper thereafter.
— Calculate half a move longer. Don’t jump to conclusions on what looks natural. Calculate a brief moment longer and look for candidates which might help avoid nasty surprises.
— Step back and try to see what you might have missed. At times, you may go so far down a track that you miss something important. Don’t be afraid to backtrack when needed but don’t run round and round in circles.
— Recheck your analysis as ideas from one line may prove useful in another line.
— When winning, keep things simple; When losing, make things complicated.
— Focus on what you can change and control on the board and try to make the next move you play a good one. During a review you may find many things you may have missed, but before you have finished the game, you need to focus on the now.