Toe-Tapping, Game-Winning Tempo

After my Flat Count writeup, I thought I would address another pillar of current Tak theory, tempo.


Tempo is another one of those words like "influence" that Tak has taken into it's folds and modified the meaning slightly.  In the non-Tak world, tempo is just the speed or pace of something. In Tak, tempo is similar; but is normally stated as:  the number of turns it will take to complete a road, assuming no interference.


Now, how is that similar to the speed or pace of something? Glad you asked. I have a convoluted analogy to help out:

But first, a couple definitions may be needed (Thanks to r/tak comment by Ikb879):


Tinue - Similar to checkmate in chess...where all play options for your opponent still result in your win next turn.

Road to Tinue - Usually refers to the sequence of moves prior to Tinue. Most of the time used when Tinue is inevitable, though sometimes only used as a general term to indicate a strong likelihood of Tinue.

Squirrel - a bushy-tailed rodent that lives in trees, chitters at you, may or may not throw acorns at your head, and ranges in size from "awwww" to "holy crap, is that a cat?"


Imagine tempo is a train and you are a person (I know that's a stretch, but just go with me here) who is trying to save a squirrel that has wandered onto the tracks. The squirrel getting killed is a metaphor for you losing your game of Tak. A low tempo is that train being far down the track, chuffing along without hurry. You have plenty of time to shoo the squirrel off the tracks. At this point, you might not even care about the squirrel. You figure that it will take care of itself (maybe the train isn't even coming this way?)...and you wander off to get a coffee at the station. As the tempo/train gets closer/faster, you begin to worry more and more about that squirrel. Sure, it was okay to ignore when the train was a cloud of steam 3/4 mile a way, but it is another thing when it is 100 yards out, barreling down on that poor, big-eyed, innocent squirrel, that is apparently deaf, (and oh, no...look, he only has 1 leg!). If you want the squirrel to live (please don't tell me if you don't), then you have to act. Now.


Does that clear things up? No? Well, read it again, and this time, try caring more about the squirrel. When a train hits a squirrel, it doesn't turn out quite as cool as those pennies you used to tape to the tracks.


Implied in this idea of tempo is that there is a tempo controller. In music, it's the conductor. In my metaphor above, it would be the train's engineer. In Tak, it is the player who is the fewest turns away from completing their road.


So, if I look at the board and it will take me 2 turns to complete my current road and my opponent will take 3 turns, then I have control of tempo. If the number is even ( 2 vs 2) then control goes to the player which gets to play next. You could be sitting on an awesome road to Tinue, but if your opponent controls the tempo, then you may never get to realize it because you are using your moves to thwart Tak threats instead of building your road to Tinue.


White player starts out with tempo control and a good player will keep that control for most of the game. Black player gets to chase squirrels and wait for the white player to run out of coal, switch to a dead end track, or some other such train metaphor.


I usually count tempo out in my head while playing a game. This is probably second nature for a lot of you reading this, as well. If not, I would urge you to make it part of your game.  It is part of assessing the board before your turn (and the only way to save those cuddly, deaf, 1-legged squirrels)
.

Tempo really becomes important as the number gets closer to 1...usually around 2 (or even 3, depending on whether or not you see a road to Tinue approaching). The player with the lower number can force the other to counteract his threats instead of forming ones of his own. At a tempo of 2 or 3, this is a soft force; meaning that the opponent can choose whether or not to respond to your threat. At a tempo of 1, it is a hard force...deal with the threat or the squirrel dies.



Take this basic example of soft force:


Black Player did not HAVE to place at e3; they chose to in order to detour white's edge crawl.

And hard force:




You can see that the black player has ignored white's edge crawl and now is FORCED into counteracting the threat or they will lose next turn.





So now that you know what tempo is, what can you do with this knowledge?  Get better! At least, that's what I'm trying to do (and help you do as well).  If tempo is a key to controlling the game, then let us see some things we can do to 1) keep tempo control, or 2) disrupt tempo control in your opponent's game.


1)

Tempo control can be kept by continuing to place flats in a directly threatening manner. This will force your opponent to deal with these threats. And, more often than not, dealing with these threats comes with a cost...usually in the form of Future Potential Flat Count Differential (FPFCD) or less contiguous/weaker board presence.

Black turns the tables


This is an excellent example of black gaining tempo control and not giving it back. He gains it on turn 4 with a single capture and then uses soft force to push white into a non-contiguous flat placement followed by a wall. Then, he continues to wallop white with threats, ending in a nice Tinue.

Just be sure to make threats that cause your opponent to act in deleterious ways and not threats that back you into a corner and gain you nothing. Take this botched game of mine as an example of what not to do when making threats:

The Great Wall



2)

If you do not have tempo control, or are looking to gain more:  think about what moves you can make that will not just delay your opponent's road by 1 turn, but by 2 or more. This usually involves a capture (this is one of the exceptions to the FPFCD guidelines).

Let's look at a basic example:






You can see that black has used a single flat capture to delay a road build by 2 turns, taking black from a tempo of 1 to a tempo of 3. This then gives some tempo control back to black.



Compare the above move choice to this one:





Here, black placed a stone instead of capturing. This only reduces the tempo by 1. It also allows white to fill another space on the board (thus keeping black from placing there), continues to build flat count, and goes right back to threatening with a tempo of 1.

A wall is a nice way to grind your opponent's tempo to a halt. But, just like the Highwaymen flats above, a Highwayman Wall must be in play before tempo reaches 1 to be able to be useful.

I am by no means saying that a single capture is the right move all the time. But, the liability of negative FPFCD should be weighed against the tempo change of a move.


Now that I have made you all aware of what is at stake...STOP LETTING ALL THOSE SQUIRRELS DIE!

Wild and Wonderful Walls

When I started playing Tak, I thought that walls were just something you used when you were out of options...a desperate attempt at delaying defeat. But, the more I play, the more uses I see for walls. Almost all games at higher levels employ at least a wall or 2 on either side. I would like to learn to use walls more effectively, but for that, I needed to find out some of the uses I see others applying.


Everyone knows that Tak has walls. But, these are not your Momma’s walls. These walls don’t just sit in the garden and look pretty. Tak walls are antsy and schizophrenic--they rarely sit still and you never know which personality is going to rise to the surface. Below, I have attempted to categorize the wall personalities that I have come across. I’m sure there are more, and I welcome your additions.

Detour Walls – placed at the end of a linear run of opponent’s road to force a detour or abandonment of his road. This wall can easily turn into a Hoarding Dragon Wall if the opponent tries to circumvent the wall. Or, another type of wall can be placed a turn later to hamper progression of opponent’s road.

Deputy Walls – placed with the intention or threat of flattening with your capstone to create a deputy.

Lurker Highwaymen Walls (thank you r/tak user humanalog) – placed beside a linear run of road with intention or threat of moving on top of the road. I’ve heard some people call these “assassin walls”. That name sounds cool, but there is nothing stealthy about them...I think of them more as potential muggers that just need the slightest prod to attack :)

Peeling Walls – placed beside a single capture stack with intention or threat of peeling opponent pieces off to free prisoner. I believe Asgardiator called them Lego Block Remover Walls. I just tried to shorten the name.

Dragon Walls – placed to take control of a stack and sit on top...like a dragon :) There are 2 kinds: Flying and Hoarding. Flying Dragon Walls have 1 or more of your own recruits underneath and have the intention or threat of flying across the board, raining down fire and destruction to your enemies…umm...I mean...leaving flats of your influence behind them. The second kind is the Hoarding Dragon Wall. This wall (sometimes called a Hoover Wall) gathers and sits on a stack of opponent’s pieces and contemplates how awesome gold is.

Bouncer Walls – placed in between opponent’s grouping of pieces and your own as a blocker. Especially effective against opponent’s Flying Dragon Walls.

Cap Trip Walls Hurdlestones (thank you r/tak user humanalog) – placed with intention or threat of tripping up opponent’s capstone. This only works if the capstone does not have a deputy. Opponent cannot flatten your wall without leaving a stack in your control behind it.

Notice the wording “intention or threat of” in the examples above. A wall does not have to perform the intended action to threaten it. It may never move from the spot that you put it. But, it can intimidate your opponent into shifting his focus elsewhere and give you some breathing room to contemplate your next moves.

 Always remember that there is a flat count cost for deploying a wall and a flat count cost each time you move it. So, make sure your walls are placed in relevant spaces and you would not be better served by placing a flat or capstone. Also, keep in mind, a wall cannot be built through by either side. So, be aware that what looks like a good move to stop your opponent can turn into a roadblock for your own road threats. Skilled opponents will use this to their advantage and build their own initiative while you figure out how to build around your own wall.

Flat Count Differential Chart with Lots of Acronyms!

After my post on Wild and Wonderful Walls, I got to thinking more about flat count. More specifically, I got to thinking about the cost versus potential benefit for each move (in flat count terms). I am not trying to reduce the game to flat count concerns only. But, since flats are what make roads and flats are also the determining factor when awarding a full board win or a material depletion win, it is important to realize that each move you make has a flat count cost and needs to pay for itself over the course of the game. For example: Your opponent decides to capture in order to contest a position on the board and you respond in kind, creating a stack. To create this stack, each of you paid flats, in hopes of a decent return on investment...or, at the very least, to keep the stored flat energy away from your opponent (For he who controls the stacks…). 
 

Below, I have attempted to chart the Immediate Flat Count Differential (IFCD) cost/benefit for each basic move in Tak, as well as a projected Future Potential Flat Count Differential (FPFCD). Italics are needed because many times immediate threats leave you unwilling or unable to utilize the stored power of your stacks. Potential can also be dampened by your opponent’s well placed walls or capstones.

If you are playing Takticianbot, you will notice how well it spends its flats. It tries to deplete its Reserve Pieces Remaining (RPR) as fast as humanly (computerly?) possible, only making moves that lessen the IFCD if they have great FPFCD or block or mitigate your FPFCD. You must spend your flats in the same Scrooge McDuck manner or you will lose...every time.

---Addendum---

Thanks to comments on r/tak by Bismuthsnake, I realized that I didn't really tell you how to use this chart (oops). And, also, I am changing the FPFCD to include the reasonable response of your opponent to place a flat (-1 to each FPFCD).

So, as to how to use this chart...If you were considering a move:  find that move on the chart below, weigh the cost vs potential benefit in flat count, compare that to the strategic value (I don't know how to put a numeric value on this (ask TakticianBot)), and then proceed with play.

If you see an easy response (other than flat placement which is now included in the chart below) by your opponent, let's say a recapture of the contested stack, look at the chart and find their potential move, reverse the sign of the differential, and compare it to your current proposed move.

Formula would look something like this:  Potential move (IFCD + FPFCD) - Opponent's potential response (IFCD + FPFCD) = net flat count gain/loss.

Also, keep in mind RPR and, in general, if you are ahead in flat count, lean towards moves that deplete your RPR.  **See sectenor/Turing's excellent blog on End Game for more on this.

	Immediate Flat Count Differential (IFCD)	Reserve Pieces Remaining (RPR)	Future Potential Flat Count Differential (FPFCD)
Flats
Placing	+1	-1	0
Moving (no capture)	0	0	-1 to 0
Single Capture	+1	0	0
Opponent-controlled stack capture (stack less than 5 pieces (5x5 board size)):
Prisoners = 1	+1	0	0, +1, +2, or +3
Prisoners = 2	+1	0	0 to +5*
Prisoners = 3	+1	0	0 to +7*
Prisoners = 4	+1	0	0 to +9*
Self-controlled stack capture:
Recruits = 1	-1	0	0 to +3
Recruits = 2	-1	0	0 to +5*
Recruits = 3	-1	0	0 to +7*
Recruits =4	-1	0	0 to +9*
Walls and Capstone
Placing	0	-1 (0 for Capstone)	-1 to 0
Moving	0	0	-1 to 0
Single Capture	+1	0	-1 to 0
Opponent-controlled stack capture (same caveats as for flats):
Prisoners = 1	+1	0	0 to +2
Prisoners = 2	+1	0	0 to +5*
Prisoners = 3	+1	0	0 to +7*
Prisoners = 4	+1	0	0 to +8*
Self-controlled stack capture:
Recruits = 1	-1	0	0 to +3
Recruits = 2	-1	0	0 to +5*
Recruits = 3	-1	0	0 to +7*
Recruits = 4	-1	0	0 to +8*

* Higher numbers are usually only seen when teaching or playing inexperienced Takkers (or some of Takticianbot’s ruthless finishing moves).

I calculated the highest possible FPFCD by using an edge-bound stack without obstacles and opponent’s flats covering the linear path of the stack run-out.

This chart seems to back up these currently held Tak theories:

1. The basis of your Tak strategies should rely on flatstone placement. Flats are the only piece that can be played that both adds to your flat count and also depletes your reserve. And, since both are desirable, the foundation of your game should be to place relevant flats as much as possible.

2. Single captures and simple movement (without capture) should be avoided unless there is a clear board advantage given to you by the move. Single captures only give you a +1 IFCD, do not offer any ROI (-1 to 0 FPFCD) and do not deplete any RPR.

3. Capturing your own pieces should be avoided unless there is a clear board advantage given to you by the move. Capturing your own stack (usually with a Wall or Capstone) should only be done to protect said stack from your opponent, make a robust Tak threat, or as part of a long, devious strategy.

4. Stacks are powerful; but, they are also a big liability. Stacks are inevitable in intermediate level play and above. Stacks have a the huge potential to swing the flat count for or against you. They also are the only entities in the game that can make threats more than 1 square away from themselves. But, they can be stolen away from you in the blink of an eye and leave you wondering how you ended up like Ozymandias. This is why you see most large, relevant stacks controlled by a wall or capstone...an attempt to keep control of them. And I’ll say it again for all you Frank Herbert fans... He who controls the stacks...

I realize that more advanced players have learned all (or most) of this through experience (or through coding bots). But, let me know what you think and what I might have missed.