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        Arimaa >> Off Topic Discussion >> Rekushu
        
(Message started by: The_Jeh on Jul 24^th, 2007, 7:09pm)

Title: Rekushu
Post by The_Jeh on Jul 24^th, 2007, 7:09pm

For a long time now, I have been fascinated by board game mechanics. I also have found pleasure in being an extremely amateur programmer. These two interests are what led me to Arimaa in the first place.

Before I started participating in the Arimaa community, I had invented a board game I named Rekushu. The game bears a few similarities to Go, but it is legitimately distinct. At this time, I believe that the rules, in their simplicity, are transcendental and beautiful.

It is not remotely close to Arimaa in quality. Although the game tree is astronomical, I can see how computers might easily master it. Although it depends on your taste, I think most would find Arimaa much more interesting to play. Nevertheless, I still find a certain mystery in it.

I spent a great amount of time perfecting an application to play my game. It has a pathetic AI, but it is still a notable accomplishment for someone of my age and minuscule programming ability. The game and application, in their current state, are the product of many years of intermittent revisions.

I hope it is not rude to advertise on Arimaa's site, but you are the only people I know who might be interested. As it is, the game just rests indefinitely in my hard drive.

Title: Re: Rekushu
Post by 99of9 on Jul 25^th, 2007, 3:41am

:o I hope it is at least backed up!!

I for one am always interested in learning about a new game.

Title: Re: Rekushu
Post by chessandgo on Jul 25^th, 2007, 5:25am

yeah, tell us more about this game ! :)

Title: Re: Rekushu
Post by The_Jeh on Jul 25^th, 2007, 1:08pm

The rules are embarrassingly simple, but here they are (verbatim from my application). I'd like to upload a screenshot. Can anyone tell me how? And yes, I've got many backups, which is good since my old hard drive just crashed a few weeks ago.

How to Play:

To win:
A. Have the higher score at the conclusion of the game.
or
B. Attain a score of over 180.

To play:
The game of Rekushu is played on a 20x20 board. The crossings are called "points" and the squares that the lines make are called "tiles."

On a player's turn, he must first place a piece on an unoccupied point on the board. The point must have at least one unclaimed tile beside it. This move is mandatory. If there is nowhere for the player to move, the game ends and the player with the higher score wins.

After the move described above is made, the player may, if he wishes, and if possible, identify a rectangle for scoring. To do this, he must first identify four of his pieces that form the vertices of an unblemished rectangle.
An unblemished rectangle...

A. has four pieces as vertices that match each other to form a rectangle. (The rectangle may not have diagonal edges.)

B. has no pieces, of either side, occupying points on its edges or interior.

C. has no claimed tiles, of either side, in its interior.

If the three conditions above are met, then the rectangle is eligible to be claimed by the player. To claim the rectangle:

1. All the interior tiles of the rectangle are claimed and marked for the claiming player.

2. The four pieces used to make the rectangle are removed from the board.

3. The claiming player's score is increased by the area of the rectangle in tiles.

The game ends when a player cannot make his initial move or a player's score exceeds 180 points, and is won by the player with the higher score.

Mirror Moves:
There is one special rule that eliminates an obvious forced draw by the second player. A player is not allowed to make the same type of mirror move consecutively. There are three types of mirror moves: playing horizontally opposite your opponent (h), playing vertically opposite your opponent (v), and playing at a 180 degree rotation from where your opponent just played (r). Thus, every point has three other points that are considered "mirror" points. For example, the mirror points of B3 would be B18, S3, and S18. You are allowed to make more than one mirror move in a row, but you cannot make the same type of mirror move twice in a row. If you cannot make your initial move because playing on the last point would be a mirror violation, then the game immediately ends as prescribed above.

Title: Re: Rekushu
Post by chessandgo on Jul 25^th, 2007, 1:47pm

interesting ! Have you already played this game live ?

Title: Re: Rekushu
Post by nbarriga on Jul 25^th, 2007, 3:23pm

Souds fun, I will try it one of this days, even though i will be using a 19x19 board, which for obviuos reasons iseasier to come across :)

I'll tell you how it goes.

Title: Re: Rekushu
Post by The_Jeh on Jul 25^th, 2007, 4:14pm

on 07/25/07 at 13:47:33, chessandgo wrote:

Have you already played this game live ?

What do you mean "live"? I've played it against my computer opponent and myself. My program allows for direct internet play, although I've only been able to test a connection between two apps running on the same computer. I haven't played it with physical material.

It may be hard to simulate the game on any board, because you have to mark both the tiles and the crossings. It's a large assignment. That's why I prefer my program, which is more aesthetic. Yes, as a physically playable game it leaves something to be desired.

I also prefer 20x20 because it creates an even number of crossings and an odd number of tiles.

Title: Re: Rekushu
Post by nbarriga on Jul 26^th, 2007, 3:07am

on 07/25/07 at 16:14:38, The_Jeh wrote:

I also prefer 20x20 because it creates an even number of crossings and an odd number of tiles.

It really would be nice if it would be 19x19 to be able to play it on a Go board. Like arimaa was chosen to be in 8x8 to be able to play it on a chess board.

Title: Re: Rekushu
Post by chessandgo on Jul 26^th, 2007, 4:59am

on 07/26/07 at 03:07:42, nbarriga wrote:

It really would be nice if it would be 19x19 to be able to play it on a Go board. Like arimaa was chosen to be in 8x8 to be able to play it on a chess board.

yeah, and for the problem of the "tiles", you could just use go stones placed on squares ... even though they really don't look like tiles :)

And how strong is your program, The_Jeh ?

Title: Re: Rekushu
Post by 99of9 on Jul 26^th, 2007, 8:28am

Thanks for letting us know about your game. I'm looking forward to trying it out.

I have only thought about it for 20sec, but I am worried that there might be more mirror moves you haven't considered. A square has more symmetries than you have identified:

* horizontal mirror plane
* vertical mirror plane
* 2 diagonal mirror planes
* 90 degree rotation right
* 90 degree rotation left
* 180 degree rotation

Title: Re: Rekushu
Post by UruramTururam on Jul 26^th, 2007, 9:27am

Since a turn is occupying only a single point than any 90 degree rotation is equivalent to either horizontal or vertical mirror and 180 degree rotation is equal to diagonal mirror. That makes only 3 distinguishable point/point symmetries.

Title: Re: Rekushu
Post by The_Jeh on Jul 26^th, 2007, 11:33am

Assuming I use a 20x20 board, there are only 3 types of mirrors I need worry about.

If the second player starts copying by playing diagonally opposite, the first player can foil this by playing on a point lying on the diagonal itself. Then the second player is forced to abandon the symmetry.

As for your 90 degree rotations...
Let's say that the second player starts copying by always playing on the point 90 degrees clockwise. All the first player needs to do to foil this is to play on a point 90 degrees counterclockwise from an occupied point. Again, the symmetry is forcibly abandoned.

However, the first player cannot foil an attempt by the second player to continuously play vertically or horizontally opposite, or at a 180 degree rotation. This is because the points involved in these mirrors only come in mutual pairs - B is the mirror/rotation of A, and A is the mirror/rotation of B. In the 90 degree rotations, B is the rotation of A, but A is not the rotation of B.

That is why these special rules are needed. However, these rules are rarely important in a real game, and they never forbid more than one point on the board at a time.

If you must use a Go board, I would request that you use an 18x18 point area, to keep my game principles and rules intact. You would also have to change the 180-win rule to a 144-win rule. Since I have the program, I can keep the 20x20 board, without having to bow my head to the game of Go.

And how strong is my AI? Let's just say it can identify obvious defensive moves and very obvious offensive moves. Other than that, it's pretty pathetic.

Title: Re: Rekushu
Post by The_Jeh on Nov 17^th, 2008, 7:36pm

Update:

Arty Sandler has recently added my game, Rekushu, to his website www.iggamecenter.com. This is the same website that was improved this year by the addition of Arimaa.

So far, only Arty himself has provided a decent challenge to me. If any of you would like to show up sometime and teach me a lesson in humility, I would be most grateful. :)

Title: Re: Rekushu
Post by RonWeasley on Nov 18^th, 2008, 5:24am

Wow. Somehow, I never saw this thread until today. The_Jeh has caused a game to exist where there was no game before. That's a hard spell to master. I'm guessing The_Jeh is a Ravenclaw?

Title: Re: Rekushu
Post by Adanac on Nov 18^th, 2008, 6:21am

Interesting, thanks for bumping this thread. I took half-days off work today & tomorrow for appliance deliveries. If anyone wants to try this out 4 hours from now, I’ll be at www.iggamecenter.com beginning at 13:30 North American Eastern Time Zone both today and tomorrow (4 hours from the time of this posting).

Title: Re: Rekushu
Post by omar on Nov 22^nd, 2008, 9:02am

I've been meaning to play this against you (The_Jeh; cause I think it's neat to be able to play the game against it's inventor), but we never seem to be in the gamecenter at the same time.

Can you tell us a little about the history of how you came to invent this, your motivation, etc.

Title: Re: Rekushu
Post by The_Jeh on Nov 22^nd, 2008, 10:23am

I don't know that I can remember. It must have been 2004 that I came up with the idea. (2006 is the last time I edited my computer program, so that is the year Arty listed on his site.) Basically, I was just interested in board games and wanted to create one that had rules the transcendent nature of which make them seem like they were discovered rather than invented. This is the game that came to me, although I cannot remember exactly how I was inspired. Obviously, Go was an influence, although anyone who has played the game will tell you that it is not related, or very distantly related at best.

Title: Re: Rekushu
Post by The_Jeh on Nov 22^nd, 2008, 3:55pm

on 11/22/08 at 09:02:21, omar wrote:

I've been meaning to play this against you (The_Jeh; cause I think it's neat to be able to play the game against it's inventor), but we never seem to be in the gamecenter at the same time.

When do you check in, usually? Randomly or predictably?

Title: Re: Rekushu
Post by clauchau on Nov 26^th, 2008, 4:25am

It looks fun from reading the rules. I keep a fond memory of an old video game where your moving point would claim unblemished rectangles.

Is the 180 threshold needed ? How would it translate to other board sizes ?

The mirror rule is embarrassing. Would the game be interesting on a triangular board with a triangular mesh ? There wouldn't be any draw by symmetry.

Is there a way to make the available space continuous instead of discrete ?

Title: Re: Rekushu
Post by Adanac on Nov 26^th, 2008, 5:43am

on 11/26/08 at 04:25:45, clauchau wrote:

The mirror rule is embarrassing. Would the game be interesting on a triangular board with a triangular mesh ? There wouldn't be any draw by symmetry.

I had a chance to play twice last week, including once against the creator ;) It was definitely fun to play, but also very tough to score points against a good defensive player. The idea of a triangular board also occurred to me, not only to eliminate the mirror rule but also to make it easier to score (3 corners rather than 4).

The most interesting aspect about Rekushu that I hadn't expected after reading the rules is that scoring points can clear the board for your opponent. If your opponent has stones at b1, d1 and d4 then you can block a 3x2 rectangle by playing stones at b2 and b3, for example. But if you later make a box with a2, a3, b2, b3 then your opponent can now play at b4 because your blockers have disappeared. Obviously it's not worthwhile to take the 1x1 square in this case, but in general this tactic adds an extra layer to the strategy.

Overall, the game is fun and you definitely need to think several steps ahead to avoid being forked. The biggest downside I noticed was that it's difficult to come from behind. Once I fell behind in the score, the board got cluttered up quickly and it was difficult to find any scoring chances to catch up. I'd be interested to see what a game is like between two highly-skilled players, though, as it would likely be a completely different style of play from the ones I experienced.

Title: Re: Rekushu
Post by Fritzlein on Nov 26^th, 2008, 7:34am

on 11/26/08 at 05:43:26, Adanac wrote:

It was definitely fun to play, but also very tough to score points against a good defensive player.

But it is possible to force a score against a player who plays only defensively?

Title: Re: Rekushu
Post by The_Jeh on Nov 26^th, 2008, 9:34am

on 11/26/08 at 07:34:27, Fritzlein wrote:

But it is possible to force a score against a player who plays only defensively?

Hopefully, that is too deep a question to know for sure. Usually, many moves are played before one player finds a way to score. In other words, a player cannot force a score in an obvious way from the beginning. You have to set up a strategic structure first - threaten to make threats. If anyone thinks he can prevent me from scoring by playing purely defensively, I would love to receive a challenge from him sometime.

on 11/26/08 at 04:25:45, clauchau wrote:

I admit the mirror rules are "embarrassing," but in a real game, they are rarely invoked, and the few times that they are invoked, the likelihood that they would block a point that a player wished to play on is extremely slim. If they are embarrassing, I think they're embarrassing in the same way the ko rule in Go is embarrassing or the 50-moves rule in chess.

The triangular version you proposed interests me. However, you may notice that a player can obviously force a score on such a grid, unless one-cell claims are disallowed. And if one-cell claims are disallowed, then my hunch is that defense would be very obvious. I want any forced scoring to be deep enough so as to not be trivially solvable.

And what video game was that?

Title: Re: Rekushu
Post by aaaa on Nov 26^th, 2008, 9:48am

on 11/26/08 at 04:25:45, clauchau wrote:

I keep a fond memory of an old video game where your moving point would claim unblemished rectangles.

on 11/26/08 at 09:34:53, The_Jeh wrote:

And what video game was that?

That would be Qix (http://en.wikipedia.org/wiki/Qix) (or one of its many clones).

Title: Re: Rekushu
Post by The_Jeh on Nov 26^th, 2008, 3:30pm

on 11/26/08 at 09:34:53, The_Jeh wrote:

And if one-cell claims are disallowed, then my hunch is that defense would be very obvious.

I take it back; the opposite is true. Offense on a triangular grid would be trivial regardless of cell size restrictions.

Title: Re: Rekushu
Post by gatsby on Jan 9^th, 2009, 3:13am

on 07/26/07 at 11:33:39, The_Jeh wrote:

However, the first player cannot foil an attempt by the second player to continuously play vertically or horizontally opposite, or at a 180 degree rotation. This is because the points involved in these mirrors only come in mutual pairs - B is the mirror/rotation of A, and A is the mirror/rotation of B. In the 90 degree rotations, B is the rotation of A, but A is not the rotation of B.

That is why these special rules are needed.

If you used a 19x19 Go board, you wouldn't need any special rules. With an odd number of crossings (361, in this case), there is always one crossing which has no symmetries at all - the central one. In fact, the reason why Go uses a board with an odd number of playable intersections is precisely to avoid a very known playing strategy for the second player called -will you guess it?- Mirror Go.

It is true that using a Go board would open the door to the possibility of draws, for there would be an even number of tiles, but this problem could easily be avoided by giving the second player the win in case of a tie, which would help to reduce the first player's advantage. You could even randomly choose one tile to be invalidated at the start of every game, which would make ties impossible and incidentally schew stereotyped openings when your game becomes a matter of endless study for an ever-growing number of Rekushu Grand Masters... ;)

By the way, would it be any possibility for you to share your Rekushu playing program with us? It'd be very nice in order to test your game extensively, which I would do with pleasure.

Title: Re: Rekushu
Post by The_Jeh on May 29^th, 2009, 6:34pm

Megamau treated me to a game the other day, so I thought it was high time I annotated a game to try to create a spark. Of course, I do not pretend to know what either of us were thinking during the game. I know my analysis is at this point underdeveloped and inaccurate.

Black: megamau (unrated)
White: The_Jeh (1294)
Board: 14x14
Time: 20 min + 10 sec/move
URL: http://gc1.iggamecenter.com/gm.phpgid=63&sid=76170&place=0&lang=en

1. J12 G07
2. H07v G12
3. E07 C03
4. E04 G05
This move creates the threat of a fork at F07.
5. E11
Black ignores the threat, because this move creates more potent counterplay.
5 ... E08
White disrupts the line of black stones.
6. H04
This is a strong move as the E04, H04, H07, and J12 stones are starting to create an offensive structure. Also, Black seeks to allow White's stones as little breathing room as possible.
6 ... I05
White defends against the aforementioned structure and also has ideas of threats in conjunction with the G05 and G07 stones.
7. J09
Keeping up the offensive pressure.
7. ... I09
A move that partially defends against Black's threats while at the same time creating offense in conjunction with G12, G07, and E08.
8. M09
Creates the threat of 9. M12xJ09-M12(9).
8. ... K09
White has no choice but to block black's threat to gain points.
9. M04
Black continues to build up a plan of attack. The E04, H04, M04, and M09 stones are well-aligned.
9. ... K04
White disrupts Black's structure in a way that also starts to align White's own stones.
10. G04
Those four white stones were looking suspicious, and now F07 doesn't work.
10. ... G06
White threatens to take two points with I06, and at the same time White threatens a fork at F06.
11. F04
Black defends by creating a larger counter-threat at F07.
11. ... E03
This move defends against F07, because if 12. F07xE04-F07(3), then 12. ... C08xB03-E08(10). This move is a better defense than to block Black's threat directly, because it also disrupts the threat of a fork at F03.
12. F07xE04-F07(3)
Black fails to see white's threat. Throughout the rest of the game, the first-time player takes pains not to allow such a trick to catch him twice.
12. ... C08xC03-E08(10)
13. H06 K07
This is better than the empty F06.
14. K06 B02
15. H11 G10
16. J11
A clever tactical find by Black.
16 ... I12
White defends, but...
17. M11
Recreates the dual threats of scoring at M12 or forking at N09.
17. ... K11
The correct defense in the situation, creating the most opportunity for counteraction.
18. L09
Black chooses to both block L09 and create a fork at the same time. Seems logical.
18. ... L07
An attempt to block both threats at the same time. First, it blocks the larger threat of L04. Second, if Black plays L11xL09-M11(2), white simply cancels the points by scoring at L09. Or does he?
19. L11xL09-M11(2)
Black ignores White's counterthreat, and rightfully so, for if White counters at L09, then Black scores three points at K07. Then after White continues by scoring two points at I06, Black will have gained a net total of one point.
19. ... L04h
An inaccuracy. Black has just gained a net two points. Why not follow the line mentioned above, where Black will only gain one point?
20. L06 J07
21. K08 K05
22. J04 K04
Scoring at L05 would be a mistake due to 23. L04.
23. M06
Defends against L03 by creating the follow-up scoring threat of L04.
23. ... M07
24. M08 B12
White decides it's time for fresh action. This move begins an offensive network in conjunction with the G12 and B02 stones.
25. E02 G03
26. B08
If your defensive moves double as offense, you are more likely to gain an advantage. This move is an example, as it both intercepts White's stones and works with the G08 and E11 stones.
26. ... G13
This fork was just waiting in the wings.
27. E13
This blocks White's larger threat.
27. ... I13xG12-I13(2)
28. H12xH11-J12(2)
Black cancels out White's scoring. Note that no scoring can be done at H13 because White has a claimed tile at G12-H13.
28. ... E10
With the idea of G09.
29. J02
Black delays the action in the top-left.
29. ... I02
30. H11 G09
31. H08
Guards against E09, but not I10. Better might have been H10, where scoring at E09 is followed up by scoring at E10.
31. ... I10xG09-I10(2)
The score is now 14-7 in favor of White.
32. G09 F09
33. E12
Scoring at H09 is easily made meaningless by follow-up tactics by White.
33. ... F12
34. C12 D12
35. H09xG08-H09(1) I07
36. H05
The idea is that 36. ... J05xI05-J07(2) is now followed by 37. J05xH04-J05(2). Neither player at this time sees White's follow-up strike at G04!
36. ... G09
A nice little fork.
37. G11 F07xF07-G09(2)
38. C03 J05xI05-J07(2)
Now White gets wise to the tactics.
39. J05xH04-J05(2) G04xG03-K04(4)
The score is now 22-10 in favor of White.
40. M02 M03
41. K13 G03
42. C11 C10
43. F04 F03
44. G02 K02
45. I07 I08h
There exist tactics that will cancel out Black's I06 idea.
46. I06xH06-I07(1) K04
Also possible is 46. ... H06. After 47. H05 G07 48. H07 F06, White will gain a point. This little 3x3 maneuver is a recurring pattern.
47. L03 N07
Scoring at L05 would have been a mistake.
48. N08h L05xK04-L05(1)
White does not fear L04 now, because his previous move at N07 creates a follow-up strike at N03.
49. L05 K05
50. M05xL05-M06(1) M06
51. K14 J13
Stopping E14, but Black has an ingenious move up his sleeve.
52. M13!
White cannot stop both M14 and N13.
52. ... M12
Of course, White defends against the larger threat and tries to create as much counterplay as possible.
53. M14x K13-M14(2) K12
54. N13
Stopping M11 via the follow-up M13.
54. ... L06xL06-M07(1)
55. C02 D02
56. M09 N09
57. C09 C08
58. M11 G07
59. H05 F06
60. F07 F05xF05-G06(1)
61. G05 G04
62. B03 B04
63. B05 J12
Black is down 14 points to 25, and there is not enough potential left to overcome such a deficit at this stage in the game. Black resigns.

Title: Re: Rekushu
Post by Arimabuff on May 30^th, 2009, 5:21am

on 05/29/09 at 18:34:15, The_Jeh wrote:

...Of course, I do not pretend to know what either of us were thinking during the game...

Well, I assume you know what YOU were thinking... ;)

Title: Re: Rekushu
Post by The_Jeh on May 30^th, 2009, 7:03am

on 05/30/09 at 05:21:33, Arimabuff wrote:

Well, I assume you know what YOU were thinking... ;)

Well, one does forget. :)

Title: Re: Rekushu
Post by Fritzlein on Jun 3^rd, 2009, 4:35pm

Thanks, John, for posting the moves to a game of Rekushu with some commentary. That's a great way for a newcomer like me to get off the ground. Unfortunately, I don't have a 20x20 board handy to replay the moves, and I can't figure out how to replay it on iggamecenter. The URL http://gc1.iggamecenter.com/gm.phpgid=63&sid=76170&place=0&lang=en gives me a 404. I tried to sit down at a Rekushu board at iggamecenter to enter the moves manually, but it won't let me play against myself. Also I found the game in your game history (assuming it finished 5/28) but from your game list I can't get to a board for replaying. Any suggestions?

Title: Re: Rekushu
Post by The_Jeh on Jun 4^th, 2009, 2:28pm

Hmmm... The game must disappear from iggamecenter's archives after a period of time. I will try to find a place online to view or replay it. Otherwise, remember that the game was played on a 14x14 board, not 20x20.

Title: Re: Rekushu
Post by The_Jeh on Jun 5^th, 2009, 8:03am

I sent my program to your Yahoo account, by the way, in case you don't check it.

Title: Re: Rekushu
Post by The_Jeh on Sep 1^st, 2009, 9:44pm

I was so inspired by chessandgo and Fritzlein's excellent videos, that I decided to make a video commentary of a live game of Rekushu. You can view it here:

http://www.motionbox.com/videos/7a99ddb51f1eedcbf5

I hope it goes some way towards attracting new players.

Title: Re: Rekushu
Post by clauchau on Sep 2^nd, 2009, 5:40am

Wow, thank you a lot for that warm demonstration. By watching it, I immediately get convinced Rekushu is an elegant, fascinating, deep, classical new game. I love it. Congratulations.

Title: Re: Rekushu
Post by Hirocon on Oct 29^th, 2009, 9:59pm

I haven't played this yet, but it seems like it would be very easy to force a draw by playing completely defensively. Just place your stone as close as possible to the last stone the opponent placed, on the side that blocks off as many partial score threats as possible. I challenge The_Jeh to a match where I will play completely defensively.

I suggest adding a rule: you can't place a stone immediately adjacent to the last stone the opponent placed. This would allow the first player to easily force a 1x1 score, but maybe that is not such a terrible thing.

I suggest adding a pie rule: at the beginning of the game, allow the first player to place one black stone and one white stone, then let the second player choose to play as either black or white.

Playing on a board with an even number of vertices along edges will not prevent ties, because it is unlikely that all tiles on the board will be occupied when the game ends. Since ties are unavoidable, you could just allow draws, or you could just pick one of the two colors/players to win in the case of a tie.

I suggest getting rid of the rules against mirror moves. Mirroring is only really a problem if the second player does it for the entire game, because if the symmetry of the board is broken anywhere at any time, the mirroring strategy will not be guaranteed to work from then on. With the pie rule suggested above, the first player could prevent mirroring by placing the first two tiles asymmetrically. Mirroring also wouldn't be a problem on a board with a center vertex, which, as I describe above, is no more susceptible to ties than a board without a center vertex.

Title: Re: Rekushu
Post by The_Jeh on Oct 29^th, 2009, 10:58pm

on 10/29/09 at 21:59:21, Hirocon wrote:

I accept your challenge, although I don't know when I'll be available. Fritzlein and I already played a game in which he played completely defensively, following the same strategy you mentioned. In the end, I was always able to forcibly score. That is not to say you can't obtain better results, however, so I look forward to the challenge.

on 10/29/09 at 21:59:21, Hirocon wrote:

I suggest adding a rule: you can't place a stone immediately adjacent to the last stone the opponent placed. This would allow the first player to easily force a 1x1 score, but maybe that is not such a terrible thing.

That's an interesting variant and worth trying. Still, the ability to play adjacent to a stone is part of what creates the "feel" the current version has.

on 10/29/09 at 21:59:21, Hirocon wrote:

I suggest adding a pie rule: at the beginning of the game, allow the first player to place one black stone and one white stone, then let the second player choose to play as either black or white.

In general, I find the pie rule to be somewhat of an ugly patch. But it could be included as a match rule if both players have a preference for it. Actually, I think a komi would be a more fitting correction, but I would prefer to have zero komi unless the need becomes obvious. In my experience, the game is fairly balanced from the beginning, with almost all opening moves, except those very close to the edge, being roughly equal.

on 10/29/09 at 21:59:21, Hirocon wrote:

Playing on a board with an even number of vertices along edges will not prevent ties, because it is unlikely that all tiles on the board will be occupied when the game ends. Since ties are unavoidable, you could just allow draws, or you could just pick one of the two colors/players to win in the case of a tie.

I know this does not prevent ties. That is not the intention of having an odd number of tiles. Draws are already allowed, and I wouldn't have it any other way, as I believe an ideal game should be a draw with perfect play, and therefore the rules of a game should render it at least possible that perfect play results in a draw.

on 10/29/09 at 21:59:21, Hirocon wrote:

I suggest getting rid of the rules against mirror moves. Mirroring is only really a problem if the second player does it for the entire game, because if the symmetry of the board is broken anywhere at any time, the mirroring strategy will not be guaranteed to work from then on. With the pie rule suggested above, the first player could prevent mirroring by placing the first two tiles asymmetrically. Mirroring also wouldn't be a problem on a board with a center vertex, which, as I describe above, is no more susceptible to ties than a board without a center vertex.

I'm not sure that the presence of a center vertex would eliminate mirroring. It might just make it so that the first player can do the mirroring - play in the center and then play the rest of the game mirroring the second player's moves. Sure, I could then disallow the first player from playing in the center, but I don't really like the idea of having a central point at all, because I'd rather the set of a species of points have an even number of elements. The central point would be one-of-a-kind, so only one player would be able to use it. I agree that the mirror rules are a tad inelegant. On the other hand, they are only rarely invoked, and it is exceptionally rare that they actually prevent a player from playing where he would like to play. I'm not sure what the effect would be of a game without the mirror rules but where at least one deviation is forced. It could turn out to be as acceptable as the effect in Go, or it might be that the mirror rules mix the game up just enough in a justifiable way.

Title: Re: Rekushu
Post by Fritzlein on Oct 30^th, 2009, 4:41am

As a casual observer, my reaction is that a pie rule is less of a kludge than the current mirror rule. That's just my intuition, though, and others may feel differently. I might even suggest a three-stone pie rule, i.e. one player places two black and one white stone before the other gets to choose.

I am curious as to whether Hirocon will have better luck playing defensively than I did. I'm eager to hear the results of your game.

Title: Re: Rekushu
Post by Hirocon on Oct 30^th, 2009, 4:44am

After experimenting some more, I've changed my opinion about defensive play. Defending forever is not trivial (though it may still be possible). I wrote very simplistic defensive AI for the white player using the following evaluation:

I define a "threat" to be a rectangle with no white corners and no stones of either color in the interiors or edges.

1) Minimize the number of threats with three black corners

2) Among all moves satisfying (1), minimize the number of threats with two black corners

3) Among all moves satisfying (2), minimize the number of threats with one black corner

4) Among all moves satisfying (3), minimize the number of threats with zero black corners

When this AI searches only one move ahead, it puts up a very strong defense, but with some work I was able to score against it. It usually played immediately adjacent to the most recent stone I played, but not always. I modified the AI to always play immediately adjacent to my most recent stone, and again I was able to score against it.

I still think it is much easier to defend than to score, and it may in fact be possible, with perfect play, to defend forever. But I no longer believe there is a trivial way to do it.

Title: Re: Rekushu
Post by The_Jeh on Oct 30^th, 2009, 8:59am

on 10/30/09 at 04:44:42, Hirocon wrote:

I was hoping that someday there would be an AI to play against, but I lack the skills to create it myself. If this simplistic white-playing AI's defense is as strong as you say, I would love to test myself against it. Better yet, feel free to use it as a tool when we play.

Title: Re: Rekushu
Post by Hirocon on Oct 30^th, 2009, 6:01pm

The_Jeh played against my AI today. He was able to score against it pretty quickly.

This is a fun game. My only concern when I read the rules was that it would be too easy to defend, but after playing it I see that isn't the case.

Title: Re: Rekushu
Post by morat on Jul 31^st, 2010, 12:09am

I just came across this thread. The game looks interesting and I'll have to give it a try soon.

Particularly since several people suggested a triangular grid, I thought I'd mention that the game has some similarity to a game called Fencing which John Brunner invented for his book "The Shockwave Rider".

It also strikes me as having some relation to Mark Steere's Quadrature and another game, Quads and Quazars, by G. Keith Still.