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.