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Topic: Formalization of Pente Opening Theory
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karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Formalization of Pente Opening Theory
Posted: May 16, 2006, 7:47 PM

This thread represents my attempt to break new ground in the seemingly bone-dry pente theory universe by organizing a complete opening theory for pro-pente, focusing primarily on black's first move and white's best answer to said move. Recognizing that I do not know nearly all there is to know regarding pente openings, I humbly ask all pente masters out there (richardiii especially; he seems to be the de facto pente guru in these parts) to aid me in this daunting endeavor. These are my goals:

a) Create a pente jargon which will make it easier to describe complex positions and patterns.

b) Define which of black's first moves are "strong," i.e. can hold up against all of white's attacks.

c) In the same vein as (b), define all of white's second moves which are "strong," i.e. have the potential to form various patterns which sustain enough initiative to win the game if not blocked by black.

After this comes the fun part: Using the language established in (a), I will attempt to categorically analyze the relative strengths and weaknesses of each of black's first moves, as expounded in (b), against the various winning positions white can come up with, as expounded in (c).

Here goes nothing!

It's no use going back to yesterday, because I was a different person then.

karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 18, 2006, 12:33 AM

THE DEFINITIONS

So as not to waste time analyzing lines that are clearly inferior and result in certain defeat for black, I will set some restrictions on black’s first move, and to make things easier for me, I will only focus on second moves for white that I deem significant—more on that later.
Regarding black’s first move, I officially and infallibly define as “acceptable” only those moves that have the potential to divert white’s keystone. This narrows it down to nine possible moves: L10, M10, L9, M9, N9, O9, N8, O8, and O7. If there is a move not on this list that any one can prove to be equally strong as those that are, I will gladly add it to the list, but I stand convinced that these are the only moves that give black a chance for survival.
Now for white: Among all of white’s second move choices I define as “acceptable” only those which create potential for several “winning positions,” or those positions which will lead inevitably to victory if not answered by black early on. “Several” is a subjective description, but to me three moves stand out as being the only ones worth taking into consideration. These are the 2-point jump (o - - o), the 3-point jump (o - - - o), and what I will call the broken wing jump, which involves a 2-point jump followed by a perpendicular 1-point jump (K13 and N12 are both examples). I do NOT include diagonal 2- and 3-point jumps. I will abbreviate these 3 moves by 2J, 3J, and BJ (yuk yuk). This leads to sixteen strong second moves for white, but symmetry will occasionally pare it down to eight. Once again, if there are any moves that are equally strong, let me know and I will take them into consideration.
With these restrictions in mind, I will now compare black’s nine opening moves by analyzing how they fare against white’s sixteen “strong moves,” determining black’s best answer(s) to said moves, and making an educated guess as to what black’s chances are in the resulting position. It is my uninformed opinion that three of these openings are stronger than the other six (I won’t say which); let’s see if I’m proved right.

It's no use going back to yesterday, because I was a different person then.
dweebo

Posts: 1,032
Registered: Dec 16, 2001
From: Powell, OH
Age: 37
Home page
Re: Formalization of Pente Opening Theory
Posted: May 18, 2006, 3:27 PM

You are undertaking a big project!

Good luck to you, have you looked at Mark Mammel's opening book of over 300 openings? http://users.erols.com/msmammel/marksfiv.html

I haven't ever really looked at it that closely, not sure how up to date it is with current Pente openings but you should definitely check it out.

-dweebo

Pente Rocks!
up2ng

Posts: 542
Registered: May 9, 2002
From: Northeast USA
Re: Formalization of Pente Opening Theory
Posted: May 20, 2006, 3:41 AM

Dweebo beat me to the punch. That opening book is a great resource for your project. It is similar (although not identical) to what you are trying to do. His book if I remember correctly is actually a compilation of well known matches that actually happened between decent players, and those openings were analyzed and categorized afterwards (slightly good for white, neutral, slightly good for black). A lot of experts will see many flaws with the openings themselves and also with the corresponding analysis of their strength, but it is a great start.

This project of yours is actually something I've always meant to try but never found the time. In fact, studying and mastering opening theory IS pente for the best players. It becomes more like solitaire, the quest to "solve" the game, and matches with other players simply aid in testing and "proof-reading" their knowledge of the game.

Opening Theory could actually be an entire published book, no joke...

karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 20, 2006, 9:34 AM

Yes, my ultimate goal in this undertaking is to discover the holy grail of gaming, "perfect play." I was talking with a friend the other day about a hypothetical supercomputer that has every single imaginable chess position stored in its memory, and the power to analyze any given position and play a move that leads to victory for the computer no matter how white plays, which is the definition of perfect play. I told him that due to the complexity of chess it is very unlikely that perfect play exists, i.e. that as either white or black there exists a branch from the first move to the end that leads to inevitable victory, but, pente being a simpler game, it is very possible that perfect play exists for white. Since white doesn't need the help, though, I am devoting my search to perfect play for black, or the closest approximation.

It's no use going back to yesterday, because I was a different person then.
karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 22, 2006, 3:27 AM

Alright, I have finished analyzing L9. Remember that I've chosen only to follow the lines with white's 2nd move being either a 2J, 3J, or BJ. If there is an alternate and equally powerful 2nd move for white against L9, let me know and I will look into it.

Also, I have designated black's position after his best 2nd move as either Weak, Medium, or Strong. A weak position is one in which either black has failed to prevent white from forming a strong offense, or has failed to form his own offense while blocking white's. In a weak position, black will be behind for much of the game, and will only have a chance at victory if white makes a huge mistake.

A medium position is NOT one in which black's odds for victory are 50-50, but one in which black has managed to prevent white from forming a winning position as well as created some initiative for himself.

A strong position is one in which black has stolen the initiative from white and has a good chance of winning the game if he makes no serious mistakes.

Regarding my nine acceptable openings, i will deem those which contain no weak positions "strong" openings, and those which contain at least one weak position "weak" openings. The number of strong positions does not matter nearly as much as the number of weak positions because the smart white player will avoid the weak positions in favor of the strong ones.

Without further ado: L9

Key: (White's 2nd move): (Black's best answer(s)); (Black's position)

White: K10; Black: L9;

N10: N9, J10; Medium
G10: L11, N9; Medium
F10: L11, N9; Medium/Strong
O10: J10, L7; Medium

N12: J9, N9, L11; Medium/Strong
M13: L11, L7, N9; Medium
H13: L11, N9, L7; Medium/Strong
N8: J9, N9; Strong

(Continued)


Message was edited by: karlw at May 21, 2006 9:39 PM


It's no use going back to yesterday, because I was a different person then.
karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 22, 2006, 3:36 AM

Analysis

L9 is the safest, most popular, and possibly the strongest of black's defenses. It can handle anything white can throw at it with ease, and the smart L9 player will be able to hold off white's attacks and build an offense at the same time. In all 8 openings, black is able to maintain a medium to strong position. Even better, with symmetry black has much less to worry about, as white's potential replies are cut in half. However, there are some drawbacks.

First, While black has a safe and sound answer to every move in white's repertoire, in none of these resulting positions does he really have a chance at pulling ahead of white very soon. This is easily the safest opening for black, but he will have to work very hard just to eliminate white's advantage. Second, being the most popular opening, an experienced white player will have a ready answer for everything black can throw at him, and this is bad news for black, because one of the best ways to overcome white's advantage is to make things so complicated that white is forced to make a move he's not sure about, and this isn't going to happen very often in the L9 line.

Overall rating: 8.5/10

It's no use going back to yesterday, because I was a different person then.
samwise

Posts: 65
Registered: Jul 19, 2002
From: British Columbia, Canada
Age: 19
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 5:52 AM

First I am having trouble understanding your move Sequence
Is the correct sequence for your first two examples?

[N10: N9, J10.]
White: K10; Black: L9; White: N10; Black: N9; White: J10.

[G10: L11, N9.]
White: K10; Black: L9; White: G10; Black: L11; White: N9.

If so I see all eight of these moves a weak rather then medium to strong, and the moves I would consider the best for a K10, K9 opening are missing.

You might be better off mapping opening moves to the fourth stone.
I.e.) K10, K9, N10, J10, rather then to the fifth.

As for the statement “L9 is the safest, most popular, and possibly the strongest of black's defenses.” I think it is one of the weakest of black’s defenses.

Good luck with this undertaking, scary to think that with only four stones on the board and one being a fixed move with the third having and opening restriction there have already been 4.3 million move combinations.

Peter-

gnoza

Posts: 42
Registered: Feb 15, 2005
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 12:03 PM

but after black second move on L9 there is easy or rather easy sure win for white

btw white always have sure win in pente, i don't know it now for all openings (in fact I knew it for most but it was boring to play), but it can be found

karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 7:11 PM

To samwise:

Key: (White's 2nd move): (Black's best answer(s)); (Black's position)

In other words, [N10: N9, J10.] means after white K10, black L9, White N10, black's two best answers are N9 and J10 for his 2nd move. After that white has a number of choices, all of which lead to a win if white plays correctly, but in which black has a good shot at taking over if white makes even a minor mistake.

And L9 is not one of black's weakest defenses. Against all but the strongest opponents it leads to a good position for black.

To gnoza: yes, white has a sure win, but he has to play perfectly to have a sure win, and this is practically impossible given all the opportunities black has to muddy up the waters. If white has an easy sure win, then why has black won 48.3% of all games on this and other sites?

It's no use going back to yesterday, because I was a different person then.
karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 7:31 PM

There is a two-player game called "Nim," in which you lay out rows of toothpicks (or any other object), usually in the pattern of 3,5,7. You play the game by taking turns removing any number of toothpicks, but only from one row. The object of the game is to force your opponent to pick up the last toothpick.

This game is simple enough that so-called "perfect play" has been calculated for player 1, meaning there is a way that player 1 can play such that no matter how player 2 plays, he can win.

In the game, there are certain "winning positions" which lead inevitably to victory if p1 plays correctly. The most obvious is [1,0,0] (1 toothpick in 1 row): p2 has to pick up this toothpick, therefore losing. Other winning positions are [1,1,1], [2,2] and [1,2,3]. The reason these are winning positions is that no matter how black plays them, white can then take them down to [1,0,0] no matter how black plays.

Here's where things get interesting: beginning with [3,5,7], if p1 removes one toothpick from any of the rows, no matter how p2 responds, p1 will be able to progress from winning position to winning position, and black will be able to do nothing to stop him. However, if at any point in the game p1 does not play a winning position, black can then take over, play a winning position, and have a sure win.

This is because of two things: 1) Every conceivable position is either a winning position or can be brought to a winning position in 1 move, and 2) You cannot go from a winning position to another winning position in 1 move. This means that one player is always winning, but if he makes even 1 mistake, the other player can take over and have guaranteed victory, but only if he plays perfectly. The way to win as p2 is to make things so complicated for p1 that he cannot find a winning position, and is forced to play a weaker move, giving black the opportunity to take over.

If you haven't guessed already, I believe that "Nim" is an exact parallel of the game of pente: white has a sure win if he plays perfectly, but black has countless opportunities to make things so messsy that white cannot tell the best way to play, and black gets his chance. Then it's white's turn to mess things up for black, etc. etc. I highly doubt that even the strongest pente players out there are capable of anything near "perfect play." This is because instead of things getting progressively simpler (less toothpicks), things are getting more complex (more stones). The capture rule also makes things much, much more complicated. End result: black has a chance to win every game.

It's no use going back to yesterday, because I was a different person then.
gnoza

Posts: 42
Registered: Feb 15, 2005
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 7:43 PM

To karlw: to say the truth I don't know why people don't win when they play white and black plays L9, but it's really strange that sb who plays hundreds or more games doesn't know sure win in the most popular open, where in database you can find almost every move

and in general if you are really good player it's enough to know sure win to lets say 5th move and then you can find continuation (especially here because most games are played on 20 min)

karlw

Posts: 970
Registered: Mar 7, 2006
From: Eugene, Oregon
Age: 36
Re: Formalization of Pente Opening Theory
Posted: May 24, 2006, 9:51 PM

you make a good point--notice how i mention that the fact that L9 is the most popular opening is one of its main weaknesses. All I'm saying is that against all but the strongest opponents, L9 gives a smart p2 plenty of opportunities for defense and counterattack, no matter how white plays. This was my major reason for giving L9 an 8.5--it, unlike several of black's other defenses, has a good response to all of white's good openings.

There are some openings (M9 being an example) that are stronger than L9 in many of the main openings, but unforgivably weak in one particular opening, and that of course will be exploited by white. L9 is, to me, the safest (if not the best) defense for black.


Message was edited by: karlw at May 24, 2006 3:51 PM


It's no use going back to yesterday, because I was a different person then.
ryan11

Posts: 13
Registered: Mar 11, 2005
From: Huntsville
Age: 13
Re: Formalization of Pente Opening Theory
Posted: May 26, 2006, 7:46 AM

interesting

richardiii

Posts: 382
Registered: Dec 8, 2002
From: Huntsville, Alabama
Age: 66
Re: Formalization of Pente Opening Theory
Posted: May 26, 2006, 7:50 AM

I have much more to say about openings, but in an address to:

a) Create a pente jargon which will make it easier to describe complex positions and patterns

Here’s some pente jargon that I use, some are old and some are mine.

Cap : to capture, ie to take a pair

Atari : (a Japanese Go term)to lay a stone that threatens to cap.

Extend : to lay a stone on the end of one’s own existing line of connected stones.

Sente : a Japanese Go term meaning ‘initiative’ or the ability to lay a stone that demands a continuing defensive posture from one's opponent.

Tres : 3 stones in a line.

Split 3 : a tres formed with a pair, a space, and then one more stone.

Posted or Divided 3 : a stone, a space, a stone, a space, and one more stone all of the same color.

Open 4 : 4 stones in a row with no defending stones at either end

Extended 4 : a 4 formed by 3 stones, a space, and one more stone.

Split 4 : a 4 formed by a pair, a space, and a second pair.

Trap : to lay a stone that forces one’s opponent to play into atari against himself.

Soft block : to block one space beyond the end of a tres or pair in such a way that denies one’s opponent an extension into sente on one end.

Draw : to make a pair that temps ones’ opponent to play an atari move. An opening tactic favored by many players such as up2ng.

Winding the Clock : laying consecutive split 3’s in such a manner that as one’s opponent keeps playing into the split, and the split 3’s keep forming. The overall pattern evolves in a circular pattern of split 3’s. this pattern must be set up right for proper execution or it fails, but when it is set up right, it is a beauty to behold.


more terms forthcoming.

R3

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