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Friday, May 12, 2017

Flat Win Threat Notation in PTN

While making my last puzzle, I ran into a discrepancy in Portable Tak Notation (PTN). It seems that we have symbols to denote road threats ('Tak' and 'Tinue'), but nothing to show when a win via flat count is impending. This blog is about those flat count win threats and a possible way to incorporate them into PTN.

There are two conditions that cause a win to be determined via flat count:  Board Fill and Stone Exhaustion. During the game, if either player causes the board to have no spaces open (either with the placement of a stone, or the spreading of a stack), the game ends and the win goes to the player with the most flat stones showing (Board Fill). This same method of determining who wins is used if either player places their last piece (Stone Exhaustion).

I did some pondering on 'Tak' and 'Tinue' and came up with with what I feel is the main difference between them:  the percentage chance that the threat of a road will be converted to a win. 'Tak' is a road threat with a low to moderate chance of conversion. When playing the computer at any level above BeginnerBot, the chance of conversion is 0%. When playing a human opponent, the percentage chance of conversion is variable, depending on the sneakiness of the threat and the attentiveness of the opponent. 'Tinue', on the other hand, has a high to very high chance of conversion, though it is still not a guaranteed and automatic win. The player making a 'Tinue' threat may not be aware of it, may run out of time, resign, his opponent may resign, or the player making the threat may even choose not to complete the road on their next turn.

To mirror this 2-level, percent-conversion system with flat count win threats, I came up with this:

The level 1 threat is denoted by placing '#' after the move that initiates the threat. The number symbol seems to fit because the determination of the possible win relies on the number of flats showing. The level 2 threat is simply a doubling of the symbol, much like the PTN for 'Tinue' is a doubling of that for 'Tak' (' escalates to "). So, a high to very high percent chance of a win conversion is denoted by adding '##' after the initiating move.

In a game where 'Tak' must be called, it also seems fitting that flat win threats should be vocalized. I suggest 'Dev' for a low level flat win threat and 'Gaelet' for a high level flat win threat. 'Gaelet' was coined by u/Bismuthsnake on r/tak and refers to the ruthless moneylenders in the KKC. I went with 'Dev' as a shortened form of Devi. She is a subset of gaelets, just as 'Dev' is related to, but not encompassing of 'Gaelet'.

Following are some examples of when these notations would come into play:

In this example we see that Black is making a Dev threat via board fill. If White places a stone instead of moving one, Black can win by filling the board on the next turn.

31. 2e3-11 Se3#

And, in this example, we see Black making a Dev threat via stone exhaustion. If White places his last stone, the game goes to Black. So, the Dev threat is forcing White to move stones instead of place them.
29. Sa4 Sb5#

The last example here shows a Gaelet threat. White can win next turn by placing his last stone, regardless of what Black does.

41. 4a3+4## 2c3<2
42. b5 

We also need to explore how these symbols interact with one another during those rare board states, such as the one below, where we have both a Tinue and a Gaelet threat. Black has achieved 'Tinue', but White can place his last stone, causing a 'Gaelet' win.

31. b1+ 4c1<22##”   ?

 tl;dr (philosophy version)

Threats in any form should be notated (and vocalized in games requiring it).
Road Win threats already meet this requirement.
Flat Win threats do not.

Therefore, Flat Win threats need notation and vocalization options.

'Tak' and 'Tinue' are both road threats with 'Tak' denoting a low level threat and 'Tinue' an almost inescapable threat.

'Dev' and 'Gaelet' are both flat win threats with 'Dev' denoting a low level threat and 'Gaelet' an almost inescapable one. 

Or, said another way...

Tak : Tinue :: Dev : Gaelet

' : " :: # : ##


 Let me know what you think; I'm open to suggestions!

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