Tinue Terminology and Classification

There are many win conditions in Tak. There are times in a game when I will cross my fingers and hope the opposing player misses a sneaky threat of mine. There are other times that a stupid mistake leads to a win, like missing an obvious threat or letting the board fill up. Then, there are flat wins, which can be very elegant and make for a tense end game. Finally, there is Tinue.

Those of you that have been following The Fox Prances To The Barn, Smelling Turkey before each turn, have probably noticed a decrease in unnecessary losses (time, sneaky threats, obvious threats, and board fill) and an increase in the two remaining win situations: Tinue wins and flat wins.

If you want a good article on End Game play, with a focus on flats, read this by Turing/sectenor.  Supplement with my article on Future Potential Flat Count Differential (especially if you have trouble getting to sleep).

The remaining concept, Tinue, is one I thought I would focus on in this week's episode. Attain this board state and you really have your opponent by the short and curlies. Below, I would like to define Tinue and explore a few different types, in order to help us better understand this unstoppable win.


Tinue - the board state where no matter what move is made by player x, the win goes to player y on the next turn. Analogous to checkmate in chess, though, in Tak, it is customary to play through to the end (we like to twist the knife).

Road to Tinue - the board state where no matter what moves are made by player x the win will go to player y within 2-5* ** ^ turns. The countermeasures made by player x have ready retorts by player y and are considered only to be delaying the inevitable. These countermeasures are usually capture/immediate recapture scenarios.

* The best players can see 3-5 moves ahead with enough degree of accuracy to see a true Road to Tinue (vs a Potential Road to Tinue as explained below). Some bots may be able to spot it further out...we'll see. If that's the case, I can always update the blog.

** I'm excluding repetitive wall hopping and similar moves (wall captures flat, opposing player places flat in wall's former spot, wall captures new flat, rinse, repeat).

^ there are special cases where one player will have 2 ranks or files almost completely under their control and the Road to Tinue can be spotted further out. u/timerot on r/tak gives this example: Snowball's Chance 

Potential Road to Tinue - the board state where if player x does not play 1 or 2 certain countermeasures, then player y will attain Road to Tinue in the next turn or two.


Okay, so we have a straightforward definition of Tinue and the road to it. But that doesn't really do justice to the concept. So, I would like to flesh out the definition with discussion of 2 main categories of Tinue: Single Road Tinue and Multiple Road Tinue. After that, I will classify some subgroups of each and give some examples.

A philosophical note before we start:  Some may argue that all Tinue board states are multiple road threats. They would say that a forked road Tinue is really 2 roads that share almost every stone in common. Player x can block the potential road 1, but you simply place the missing piece to complete and actualize road 2.

I would reply to this by saying, yes, that is technically correct, but does little to help us classify (and thus comprehend) different Tinue patterns. So, I have labeled forked roads, bypass roads, and bi-cardinal roads as Single Road Tinues because the 2 potential roads overlap in almost their entirety. I feel that this makes intuitive sense -- but I welcome views to the contrary!

Single Road Tinue

To attain Single Road Tinue, your road must be:

1.  Untouchable by movement of your opponent's pieces. (We have seen that a road can be delayed and tempo diminished with a single opponent flatstone lying adjacent to a road (a highwayman), not to mention what a wall or capstone can do...).

How to reach untouchability:

a. Your road is more than 1 space away from your opponent's flatstones

b.Your road is further away than the reach of your opponent's stacks

c.Your road is blocked from stack capture by any combination of walls or capstones (not necessarily your own walls or capstone)

d. If part of your road is threatened by a highwayman capture, then you have an adjacent partner (or spreadable stack) ready to immediately recapture.

e. Or, you have a spreadable stack and no opponent's pieces able to stop it (i.e. the space between the stack and the end of the road is filled with flats.-icing the cake



AND


2. Unable to be stopped by placement of any opponent piece (flat, wall, or capstone (if not already played)).

This is usually done by 1 or more of the following (a through c are unbroken roads; d is a broken road):

a. Building a forked road. -forked road

b. Building a bypass road. -bypass road

c. Building a road from a corner (possessing the option of completion via north/south or east/west).- bi-cardinal road

d. If there is a hole in your road and your opponent has already played his/her capstone, then placement of a wall in your road must be able to be answered immediately by crushing with your capstone. -crush-mate

* the immediately part is important. If your tempo drops below 1, then you do not have Tinue.

Multiple Road Tinue - building the road less traveled

To attain this board state, you must have 2 road threats that do not share a weakness.  The method of completing each road can be different (ex: placement for 1; movement for the other), and the roads don't have to be untouchable; your opponent can stop 1, but not all of your concurrent threats.

It is harder to describe how to attain this board state. Each instance will probably be different from the last. But, below are a couple examples to get you in the right frame of mind for spotting these marvels.



Examples:

Single Road Tinues:





A Forked Road Tinue - this particular example has 3 forks, but 2 are sufficient. Placement to block 1 fork does not block other fork(s). Remember that for a Single Road Tinue, your road must be untouchable by opponent pieces.




A Bypass Road Tinue - placement at c2 results in a road via placement at b3 and vice versa. I named it Bypass because the 2 roads look like they will bypass one another and also because the completed road simply bypasses the placed countermeasure attempt.





Another Bypass Road Tinue. As you can see, it does not matter where in the road the bypass occurs.


*image needed


A Bi-Cardinal Road Tinue - As the name implies, it can be completed either North/South or East/West.





This is an example of a Road to Tinue. Note that white's only move it to capture e2 by e3-, and black has an immediate response with e1+. After this exchange, the board state will move to Tinue proper.







This is another Road to Tinue. Black just placed Sc4 in a belated attempt to stop Tinue. White's response is an immediate crush-mate with 2c2+11. This leaves black with a tempo of 2 vs white's tempo of 1. White's Single Road Tinue is untouchable by any of black's pieces and in the bypass pattern.








The above is an example of icing the cake. White has nothing to stop it's d2 stack from running north. Even a capture with 2c4> would not stop the cap stack.








One last example of Single Road Tinue. This is what I call the voila Tinue pattern. It is named such because whenever I see it done, I imagine a master chef pulling the silver cover (standing stone)  from his best dish, revealing it to you, while smiling and saying "Voila!"


Okay, on to Multiple Road Tinues:






Here we have a simple Multiple Road Tinue. Black can place or move whatever he wants, but it will only block 1 of the two road threats. You can see how this differs from the untouchability required in a Single Road Tinue.



Above is a very sneaky Multiple Road Tinue. White has just captured the stack at c4 and now black's response will only be able to stop one of the road threats. White has 3 road threats here, I believe. He can ice the cake in either direction using his stack at c4, or use a leaping voila (moving 3f2<12 to reveal his road).




Potential Road to Tinue:

Lastly, I thought it important to go over a potential road to Tinue. The below example hinges on 1 move by black. If black chooses poorly, white gains Road to Tinue. If black chooses wisely, he can stave off death for at least a while longer.

It is black's move. Placement cannot help him; so he must capture. Let's see what happens if he captures poorly.


 --pictures were taken on a phone, and the orientation changes halfway through. Sorry, I'll fix it sometime.--

 

And, bypass Tinue.




I haven't played out the other tree, but here is black's other option for a capture (you can see that it does not lead to an immediate Road to Tinue):

And just for fun, here is a game with FriendlyBot where he gets a nice dual road Tinue. On the last few moves, you can see the difference between two roads that share a weakness and two that do not.

Friendly? Or Fiend-ly?