For those of you who are unaware, Tak is a game that I have been playing a lot of recently.

EDIT: After a short discussion on the Tak subreddit, it was decided that a better name would be influence, as opposed to concentration. BenWo then explained this idea in a video which describes the term and it’s implications better than this article does.

I’ve been thinking about how to teach Tak strategy, and I think I’ve come up with a metric that will help explain the way I play. If you’re familiar with Go, this will be the Tak equivalent of liberties. Concentration defines how I play Tak, and helps me develop large stacks under my control.

Your concentration on a point is the number of turns in a row that you can move one of your stones to a given point. Said another way, your concentration is the number of turns in a row that you can take over the same stack. It’s essentially who will win control of a stack. You can say “My concentration on b3 is 4.” Note that concentration only works with flatstones. Walls and Capstones change the game entirely. That being said, many fights where both sides want a specific area offensively don’t use walls, and many times the Capstones are somewhere else or being kept in reserve.

Motivation

The way I win at Tak is by controlling large piles, and then striking out with them. The way to control large piles is to concentrate on them.

My piles

If I have an equal or higher concentration than my opponent on a pile that I own, it can’t be taken from me without me immediately taking it back. This allows me to keep the pile handy, to strike in the direction that I want, when I see fit.

Opponents piles

If I have a greater concentration than my opponent on a pile he owns, he has to split up the pile, or I’ll take it from him. I find that large piles are often more of a threat than a specific line of pieces, due to the options that they have. By forcing my opponent to take one of the options immediately, he has to realize one potential option for the stack, instead of me having to defend against all potential options.

Calculation with Examples

To start, let’s take a pretty easy example of a game that demonstrates the concept pretty well:

The early game here hinges on the concentration on b3, by the way the early game developed. (I have no idea how to explain the early game. I would appreciate advice on that area of my game.) At the end of turn 4, both players’ concentration on b3 is 2. Since the tie goes to the owner of the spot, the first person to play on b3 will own it.

And Scott does take it, but is forced to move off the square by Tim’s early Tak. Scott ends up moving up to b4, where he has a concentration of 0, and Tim has a concentration of 1. Tim then takes a4.

At the end of turn 7, Tim has a concentration of 3 on b3, meaning that he can take the spot from Scott. Which he does, moving stones onto b3 for three consecutive turns. This gives Tim control of a pretty powerful stack. Scott then lays his Capstone, and Capstones break the whole concept of concentration, so I’ll stop commenting on the game there. Tim ends up winning, partially because of his good use of a powerful stack.

Now, a couple of more complicated examples, from a game that I had trouble finishing aginst ShikiBot:

At the end of turn 11, I’m trying to force my opponent into a bad situation, by leveraging my near-road. I would love to take e2, but I don’t have enough concentration there to hold it. I could play a flat at e4, but my opponent has the concentration there as well. (And moving onto my stone would gives him a Tak.) So I decide to drop an early Capstone, forcing him to play into my formation. My formation here is really tight, since, at all of the places where I have flats (other than c1 and a4) I have at least a concentration of 2. Everybody ends up piling onto d3, where I now have control.

Move forward to the end of turn 16, where the focus is on a4, b4 and b3. I’m trying to keep my offensive options open, in an area where we both have pretty low concentration. So I play at a3, giving a concentration of 1 at a4 (where it doesn’t help), and b3 (where it matters). Note that I maKe this move because it also caused a Tak. If I couldn’t have caused a Tak, I probably would have used my concentration at b4, by playing b3+, giving me that powerful stack. My opponent moves down to b3, where I get to control a stack with an extra one of my pieces, as opposed to if I had taken it at b4. I also like controlling big stacks closer to the center of the board.

I’m pretty sure I would have had a guaranteed win in 2 or so turns if I had played move 19 at c3. But I didn’t, and then my opponent drops a Capstone, and I run around for a few turns. I only claim to be good at concentration battles…

The coolest concentation battle occurs at c3, starting on turn 25. After I move 2c2+, it looks as though I’m going to lose the concentration fight 2-1. (If I was worried about that, I could have left an extra stone behind on c2). But my concentration at c3 is actually 3, because of the tall stack on e3, which I happily use to my advantage.

After that it’s just me splitting that big stack, due to the capstone looming, making the Capstone useless due to the carry limit, and eventually winning.

Conclusion

There are many more intricacies to this that I haven’t figured out yet, or at least can’t explain well. One that I have been trying to deal with is that two stacks next to each other can end up with a super weird concentration, especially if there are a bunch of flats around the two stacks. Since moving onto a stack from further away can capture intermediate stacks, it can be very dependent on the order of moving pieces. It’s pretty easy to calculate in the simple examples I’ve provided, but your mileage may vary.

I hope you all find concentration to be a useful mental guide when fighting over board position in Tak.

The Name

If anyone has better ideas for the name of this than concentration, I would be happy to hear them. I chose concentration for a few reasons. First, it is a measure of your ability to concentrate your pieces at one spot, in the physical sense. Second, it is what I focus on most when I play, so I concentrate on concentration. Finally, it seems to go well with Alar, where my concentration on holding a space is strong enough that I end up holding it. It works in the sense of a sympathy duel, since me and my opponent are both trying to concentrate hard enough to hold the space, working against each other.