Basic Tak Strategy
This piece assumes that the reader already know the rules of Tak. Tactical issues are not covered, no written word will replace experience in this area.
The single most important metric when playing Tak is the flatstone count. Not only does the flatstone count decide the game in case of no road, flatstones are also the main component of roads, having more generally means more opportunities for building roads.
Capturing single pieces is not advantageous. Placing a new flatstone increases your flatstone count by 1, whereas capturing an opposing piece decreases your opponent's flatstone count by 1, without advancing your own. Thus there is no flatstone advantage to simple capture moves. The disadvantage of a simple capture move is that it creates a stack containing an opposing piece, if your opponent capture such a stack they will have a stack containing multiple of their own pieces. This stack can, in the right circumstances, be used for making multiple captures in a single move, while also increasing ones own flatstone count.
Pieces and stacks should in general never be moved without capturing opposing pieces and/or splitting stacks. Placing a new piece is almost always a superior move. Possible exceptions include situations where a stack of mostly opposing pieces needs to run from an opposing capstone or wall, your capstone is needed elsewhere, or your own wall is in the way of a road. None of these situations however remove the undesirable properties of such a move, so look for alternatives.
Force your opponent to capture, and to play walls. Playing walls does not advance ones flatstone count, and making simple captures run a risk of giving your opponent an advantage, but these moves may be necessary to prevent your opponent from building a road. Ideally you should be the one forcing your opponent to make these moves, you do so by threatening to build a road. Throughout the game you should try to make as many threats as possible. Even though most of them may be easily defeated, the moves required to do so often come with disadvantages. Do however take care not to take make too many compromises just to produce threats.
When you play your capstone, it should make a big difference. It may be used to advance your own threats, stop your opponent's threats, or secure a big stack of pieces. Preferably, it should do at least two of those things.
You should rarely knock down a wall. When you opponent plays a wall it shifts the flatstone count in your favor, knocking down a wall essentially undoes this advantage. There are however situations where the increased threat potential makes up for this.
Take a flatstone win when you got one. If you have played well, and have a reasonable flatstone lead, including potential gains from stacks, you should focus on ending the game with your lead intact. Play for simple positions where neither player can gain much. If you can afford it, play a few walls to lock down the game completely. Making threats is still a good way of distracting your opponent's game, but it is not mandatory in this phase.