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Subject: The Gyges Stategy Guide, written by an idiot rss

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(ron lee)
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baton rouge
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An attempt to codify some of my thoughts on Gyges strategy. For all examples below, you are playing South.

Caveat: I'm a neophyte. My entire experience is playing at www.gyges.com against the AI, who I can now beat 80% of the time at the beginner level, and not at all at any higher levels. But as no English-language literature could be found for Gyges, I thought I'd share my small, minor thoughts and maybe start some discussion.

Like most abstract games, the endgame is easiest to comprehend, while the opening is the most mysterious. So let's work backwards.

ENDGAME

Your penultimate move will hopefully be the move that allows access to the goal on your final move--a move that creates at least one path that cannot be blocked by your opponent. We can do this by creating a single path that your opponent cannot touch in one move:


1..... 1..... (Example 1)
...... ...2..
...... ......
..32.. ---> ..32..
..1.2. ..1...
...... ......


Or by creating multiple paths to victory such that your opponent cannot completely block all routes in a single move:


.2.... .2.... (Example 2)
..33.3 ..33.3
.....1 ..1..1
.21.2. ---> .21.2.
.2..31 .2..31
.1.... ......


MOBILITY

In Example 1, it North is locked out of any meaningful plays after South moves. It may be that North had early on abandoned his 1-ring piece as unmovable, which led to problems later on when the 1-ring was the only piece available to move. So it seems important to keep all of your back pieces available for play as much as possible. If the board is developing such that pieces are lining up on the left side, you shouldn't completely abandon a piece on the far right side unless you have very good reason to do so.

PARITY

In Example 2, South goes from a situation where only 1 piece can be moved to a situation where 3 can be utilized. This increase in mobility is due to the fact that, once South has moved all the pieces of the back row, the pieces on the 2nd row can be put in play. My theory is that, in general, it is to your advantage to be ahead in the race to move pieces off the back row. Being the 1st one to clear your back row gives you that 'power-up' before your opponent, allowing you a chance to KO your opponent before she/he can counterattack.

12/2006 EDIT: The above paragraph may be very, very wrong! I got myself in trouble by moving all my back pieces off the back row quickly in one game. My opponent then managed to get a 1-ring piece into a lonely corner of my back row! It would have taken me 3 moves to just get the 1-ring piece to the next nearest piece! He finished me off well before that. Not sure how he did it--it seems dangerous to keep a lot of pieces on your back row, doesn't it? But that's what he did--kept everything on his side, and then stuck it to me at the end.

MIDGAME

ONE-WAY/TWO-WAY ROADS

In the example below, North has a nice pathway to go down, while South cannot follow the same path up:


..1... (Example 3)
..2...
...3..
......
..2...
.1....


The reason that this is a one-way road is that the "adjacent" pieces are different from each other. If you have a path where "adjacent" pieces are the same, you have a 2-way road:



...... (Example 4)
..2...
...2..
......
...2..
..2...


You want to create 1-way roads headed to your goal, block or repave wrong-way roads, and be extremely wary of 2-way roads.

DIAGONAL VS. STRAIGHT CONNECTIONS

Two "paths" are shown below. Both are one-way roads for South, but of the two, Example 6 is, I think, the preferred path.


...... (Example 5)
......
..3...
......
..2...
......




...... (Example 6)
......
..3...
...2..
......
......


The problem with Example 5 is that North can easily block the path by placing a piece directly between the two pieces. Moreover, if North places a 1-ring or 3-ring piece there, the one-way street suddenly reverses direction!

In contrast, North must place 2 pieces down to block the paths in Example 6, and by placing those extra pieces to block, North may open up new avenues for South.

OPENING

The opening game is a great mystery to me. I have no sense of what the initial ring placement strategies are. Currently, I am playing with


...... ...... (Example 7)
...... ......
...... --> ......
...... ......
...... ...3..
312123 31212.


Seems to open up a lot of possible future moves, both in terms of bumping and replacing.

As for the first moves, other than the mobility issues discussed above, I have little sense of what to do.

PATTERNS

In this section, I'll list some patterns that seem to pop up reasonably frequently.

THE BOX

Let's call any rectangular (sides ≥ 2) or almost-rectanglar cluster of rings a "box":


...... (Example 8)
.232..
.232..
......
......
......


If there are no 1-ring pieces in the box, it will be impossible to travel through it. If there are 2-ring pieces at the corners, travel around is difficult without some help from pieces outside the box.

THE 3-LEAF CLOVER

Let's call any piece (other than a 1-ring piece) surrounded on 3 sides (but with a 4th open side) a "3-leaf clover".


...... (Example 9)
..1...
..32..
..2...
.3....
......



If you're trying to move through the center of a 3-leaf clover through the empty side (in the example above, South moving the 3-ring piece through the 3-ring piece), you will find you can't procede any further since the remaining 3 sides are blocked. The only way you can utilize the center of the clover is if one of the leaves is a 1-ring piece--then you can go in through that 1-ring leaf and exit out the empty side. North can use the 1-piece in the example above to win.

This applies just as well to a "2-leaf" clover on the side of the board:


...... (Example 10)
1.....
3.....
2.....
......
......



--------------------------------------------

This is a work in progress--I'll update as I become smarter! In the meantime, please feel free to add your own thoughts.
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Quinn Swanger
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ronlee wrote:
...
Or by creating multiple paths to victory such that your opponent cannot completely block all routes in a single move:


.2.... .2.... (Example 2)
..33.3 ..33.3
.....1 ..1..1
.21.2. ---> .21.2.
.2..31 .2..31
.1.... ......



Ron, did you intend for this example to illustrate a move by South that would assure him a victory on his next turn? If so, did you perhaps not notice that North would be able to win *before* South's next turn?

Here is the sequence (please excuse, I'm not sure of the proper notation):
B6-C5(via B5)-D5(via C6,D6)-E3-F2-E2-goal!

Perhaps you thought that South bouncing the single B1 piece to C4 would prevent North from bouncing the C5 triple to D5, but he can actually still get there by utilizing the spaces behind him.

Great article. Thanks so much for writing this. It stinks that there has been no response or anything similar to this since. I just got the new Gigamic reprint. It's pretty sweet (see my general forum posting for initial impressions). I've also played on gyges.com and have to say that the bots are pretty tough ... though I did manage to win on Medium once. I'm enjoying getting my butt kicked and learning some tricks in the process.
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Pablo Schulman
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Caveat: This is the first post with some editing to it. Just trying to make it a little easier to read (graphicwise).

An attempt to codify some of my thoughts on Gyges strategy. For all examples below, you are playing South.

Caveat: I'm a neophyte. My entire experience is playing at www.gyges.com against the AI, who I can now beat 80% of the time at the beginner level, and not at all at any higher levels. But as no English-language literature could be found for Gyges, I thought I'd share my small, minor thoughts and maybe start some discussion.

Like most abstract games, the endgame is easiest to comprehend, while the opening is the most mysterious. So let's work backwards.

ENDGAME

Your penultimate move will hopefully be the move that allows access to the goal on your final move--a move that creates at least one path that cannot be blocked by your opponent. We can do this by creating a single path that your opponent cannot touch in one move:

. .
1 . . . . . 1 . . . . . (Example 1)
. . . . . . . . . 2 . .
. . . . . . . . . . . .
. . 3 2 . . ---> . . 3 2 . .
. . 1 . 2 . . . 1 . . .
. . . . . . . . . . . .
. .



Or by creating multiple paths to victory such that your opponent cannot completely block all routes in a single move:

. .
. 2 . . . . . 2 . . . . (Example 2)
. . 3 3 . 3 . . 3 3 . 3
. . . . . 1 . . 1 . . 1
. 2 1 . 2 . ---> . 2 1 . 2 .
. 2 . . 3 1 . 2 . . 3 1
. 1 . . . . . . . . . .
. .



MOBILITY

In Example 1, it North is locked out of any meaningful plays after South moves. It may be that North had early on abandoned his 1-ring piece as unmovable, which led to problems later on when the 1-ring was the only piece available to move. So it seems important to keep all of your back pieces available for play as much as possible. If the board is developing such that pieces are lining up on the left side, you shouldn't completely abandon a piece on the far right side unless you have very good reason to do so.

PARITY

In Example 2, South goes from a situation where only 1 piece can be moved to a situation where 3 can be utilized. This increase in mobility is due to the fact that, once South has moved all the pieces of the back row, the pieces on the 2nd row can be put in play. My theory is that, in general, it is to your advantage to be ahead in the race to move pieces off the back row. Being the 1st one to clear your back row gives you that 'power-up' before your opponent, allowing you a chance to KO your opponent before she/he can counterattack.

12/2006 EDIT: The above paragraph may be very, very wrong! I got myself in trouble by moving all my back pieces off the back row quickly in one game. My opponent then managed to get a 1-ring piece into a lonely corner of my back row! It would have taken me 3 moves to just get the 1-ring piece to the next nearest piece! He finished me off well before that. Not sure how he did it--it seems dangerous to keep a lot of pieces on your back row, doesn't it? But that's what he did--kept everything on his side, and then stuck it to me at the end.

MIDGAME

ONE-WAY/TWO-WAY ROADS

In the example below, North has a nice pathway to go down, while South cannot follow the same path up:

.
. . 1 . . . (Example 3)
. . 2 . . .
. . . 3 . .
. . . . . .
. . 2 . . .
. 1 . . . .
.



The reason that this is a one-way road is that the "adjacent" pieces are different from each other. If you have a path where "adjacent" pieces are the same, you have a 2-way road:

.
. . . . . . (Example 4)
. . 2 . . .
. . . 2 . .
. . . . . .
. . . 2 . .
. . 2 . . .
.



You want to create 1-way roads headed to your goal, block or repave wrong-way roads, and be extremely wary of 2-way roads.

DIAGONAL VS. STRAIGHT CONNECTIONS

Two "paths" are shown below. Both are one-way roads for South, but of the two, Example 6 is, I think, the preferred path.

.
. . . . . . (Example 5)
. . . . . .
. . 3 . . .
. . . . . .
. . 2 . . .
. . . . . .
.


.
. . . . . . (Example 6)
. . . . . .
. . 3 . . .
. . . 2 . .
. . . . . .
. . . . . .
.



The problem with Example 5 is that North can easily block the path by placing a piece directly between the two pieces. Moreover, if North places a 1-ring or 3-ring piece there, the one-way street suddenly reverses direction!

In contrast, North must place 2 pieces down to block the paths in Example 6, and by placing those extra pieces to block, North may open up new avenues for South.

OPENING

The opening game is a great mystery to me. I have no sense of what the initial ring placement strategies are. Currently, I am playing with

. .
. . . . . . . . . . . . (Example 7)
. . . . . . . . . . . .
. . . . . . ---> . . . . . .
. . . . . . . . . . . .
. . . . . . . . . 3 . .
3 1 2 1 2 3 3 1 2 1 2 .
. .



Seems to open up a lot of possible future moves, both in terms of bumping and replacing.

As for the first moves, other than the mobility issues discussed above, I have little sense of what to do.

PATTERNS

In this section, I'll list some patterns that seem to pop up reasonably frequently.

THE BOX

Let's call any rectangular (sides ≥ 2) or almost-rectanglar cluster of rings a "box":

.
. . . . . . (Example 8)
. 2 3 2 . .
. 2 3 2 . .
. . . . . .
. . . . . .
. . . . . .
.



If there are no 1-ring pieces in the box, it will be impossible to travel through it. If there are 2-ring pieces at the corners, travel around is difficult without some help from pieces outside the box.

THE 3-LEAF CLOVER

Let's call any piece (other than a 1-ring piece) surrounded on 3 sides (but with a 4th open side) a "3-leaf clover".

.
. . . . . . (Example 9)
. . 1 . . .
. . 3 2 . .
. . 2 . . .
. 3 . . . .
. . . . . .
.



If you're trying to move through the center of a 3-leaf clover through the empty side (in the example above, South moving the 3-ring piece through the 3-ring piece), you will find you can't procede any further since the remaining 3 sides are blocked. The only way you can utilize the center of the clover is if one of the leaves is a 1-ring piece--then you can go in through that 1-ring leaf and exit out the empty side. North can use the 1-piece in the example above to win.

This applies just as well to a "2-leaf" clover on the side of the board:

.
. . . . . . (Example 10)
1 . . . . .
3 . . . . .
2 . . . . .
. . . . . .
. . . . . .
.



--------------------------------------------

This is a work in progress--I'll update as I become smarter! In the meantime, please feel free to add your own thoughts. [/q]
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