christian freeling
Netherlands

The previous thread
Once more from the top. The Starweb board has 18 corners, 12 outward and 6 inward ones.
Rules The game starts with a pie and the players, black and white, take turns to place one stone on a vacant cell. Like coloured connected stones form a group. A group containing n corners is worth Σn points, that is n*(n+1)/2. (It means that the first corner is worth 1 point, a second corner 2 points, a third one 3 points and so on). A player may pass without losing the right to move next turn. The game ends when both players pass on successive turns. The winner is the player with the highest score. If scores are equal, the player who placed the second stone on the board wins.
Here's my homemade board. I've indulged in a litte frivolity by highlighting the corners.

Paul Kreutzet
United States

if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?

christian freeling
Netherlands

ftstevens wrote: if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?
An extra rule to limit options? I don't think so. Actually the difference between Othello and Reversi is the same, in a nutshell. Your idea is represented by Othello with its fixed four in the centre. Reversi however offers just one alternative, Starweb many. A small section of those concerns positions in which preventing a connection may have priority over occupying a corner. Also, in a pie a corner may not be the smartest option.

Russ Williams
Poland Wrocław Dolny Śląsk

silly_sad wrote: what _IS_ a corner? At least on this map, it is any of the 18 hexes which touch an odd number of other hexes.



ftstevens wrote: if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?
This reminds me of Global Connection, a sadly neglected game where the perimeter of the board is covered with any multiple of four "islands" alternating in color. I find it to be a very intriguing generalization of Hex.
While I'm at it, it occurs to me that it could also work without the initial islands if ties are turned into wins for the player with more pieces in the perimeter. If still tied, the player who occupied the last perimeter cell loses.

christian freeling
Netherlands

luigi87 wrote: ftstevens wrote: if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?
This reminds me of Global Connection, a sadly neglected game where the perimeter of the board is covered with any multiple of four "islands" alternating in color. I find it to be a very intriguing generalization of Hex. While I'm at it, it occurs to me that it could also work without the initial islands if ties are turned into wins for the player with more pieces in the perimeter. If still tied, the player who occupied the last perimeter cell loses. 'Value cells' tend to be at the perimeter (although not necessarily so). YvY was also thought out by going in the same general direction. What actually seems to provide this simplicity to Starweb is something that wasn't considered before, because 'group penalty' as a means of connective scoring was never challenged: the new scoring system. The board is arbitrary but this particular size and shape gives 18 nicely distributed value cells and a board that has the same number of cells as a base9 Havannah board. That's a nice size to give scope to strategy and tactics. Ed's on it!

Jesse
United States Kelso Washington

I can't even figure out the math equation required to score this game...

Russ Williams
Poland Wrocław Dolny Śląsk

jpj2 wrote: I can't even figure out the math equation required to score this game...
Do you mean you don't know what n(n+1)/2 means?
It means n × (n+1) ÷ 2
i.e. multiply n times (n+1), then divide that result by 2.
This happens to be equal to 1+2+...+n.
Does that help?

christian freeling
Netherlands

russ wrote: jpj2 wrote: I can't even figure out the math equation required to score this game... Do you mean you don't know what n(n+1)/2 means? It means n × (n+1) ÷ 2 i.e. multiply n times (n+1), then divide that result by 2. This happens to be equal to 1+2+...+n. Does that help? It also means that for any group, the first corner is worth 1 point, the second 2 points, the third 3 points and so on. That may be easier to visualise than an equation.

Michael Howe
United States Cromwell Connecticut

luigi87 wrote: ftstevens wrote: if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?
This reminds me of Global Connection, a sadly neglected game where the perimeter of the board is covered with any multiple of four "islands" alternating in color. I find it to be a very intriguing generalization of Hex. While I'm at it, it occurs to me that it could also work without the initial islands if ties are turned into wins for the player with more pieces in the perimeter. If still tied, the player who occupied the last perimeter cell loses.
re: Global Connection. Is the simple scoring rule of "fewest groups wins" enough? What would be the strategic difference between this and n(n+1)/2 scoring?
I remember browsing a game in Cameron Browne's book about connection on a hexhex board with players played perimeter goal pieces within constraints as part of the game and then had to connect them. I'll see if I can find my copy of the book and provide a name.

christian freeling
Netherlands

mhowe wrote: luigi87 wrote: ftstevens wrote: if he players are always likely to spend their first several turns claiming corners, maybe start out with those pieces on the board already in some configuration?
This reminds me of Global Connection, a sadly neglected game where the perimeter of the board is covered with any multiple of four "islands" alternating in color. I find it to be a very intriguing generalization of Hex. While I'm at it, it occurs to me that it could also work without the initial islands if ties are turned into wins for the player with more pieces in the perimeter. If still tied, the player who occupied the last perimeter cell loses. re: Global Connection. Is the simple scoring rule of "fewest groups wins" enough? What would be the strategic difference between this and n(n+1)/2 scoring? I remember browsing a game in Cameron Browne's book about connection on a hexhex board with players played perimeter goal pieces within constraints as part of the game and then had to connect them. I'll see if I can find my copy of the book and provide a name. There are two issues here, the goal and the presence/absense of an initial position. If a game features 'connective scoring', then it logically is about a 'score'. The biggest or smallest group seems hard to align with this, but 'the number of groups' might maybe play a role. Regarding an initial position my position is that if it can evolve as part of game play, then this is preferable above an initial position. A pie or some other balancing mechanism would seem to be required in either case.



russ wrote: silly_sad wrote: what _IS_ a corner? At least on this map, it is any of the 18 hexes which touch an odd number of other hexes.
Quote: A group containing n corners
so this is a connectcorners game? players try to connect as many corners as possible with as few adjacent stones as possible.
right?

christian freeling
Netherlands

silly_sad wrote: so this is a connectcorners game? In general it is a connect 'value cells' game. In Starweb they happen to be corners.
silly_sad wrote: players try to connect as many corners as possible with as few adjacent stones as possible.
right? In general one would try to get as many corners as possible in one group, because for any group the first corner is worth 1 point, a second corner 2 points, a third one 3 points and so on. Thus two groups of three corners each, sum to 12 points, but one group containing six corners is worth 21 points. Hence the incentive to connect.

Tony van der Valk
Netherlands Den Haag

Quote: In general one would try to get as many corners as possible in one group, because for any group the first corner is worth 1 point, a second corner 2 points, a third one 3 points and so on. Thus two groups of three corners each, sum to 12 points, but one group containing six corners is worth 21 points. Hence the incentive to connect.
Hey, now I get it. For me this is the (informal) description that makes me want to play this game.
Next I wonder why not to play it on a standard Havannahboard. Maybe because more corners bring more strategic possibilities?
Christian explains that a "corner"  "is any of the [] hexes which touch an odd number of other hexes". So a corner could also be in the middle of the board like in the PolyY board.
Still there is a lot of resemblance with the Game of Y and PolyY
The majority of corners rule of PolyY is a little easier to grasp than calculating combinations of 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120...
Let's play all of these games!

christian freeling
Netherlands

Tony van der Valk wrote: Quote: In general one would try to get as many corners as possible in one group, because for any group the first corner is worth 1 point, a second corner 2 points, a third one 3 points and so on. Thus two groups of three corners each, sum to 12 points, but one group containing six corners is worth 21 points. Hence the incentive to connect. Hey, now I get it. For me this is the (informal) description that makes me want to play this game. Next I wonder why not to play it on a standard Havannahboard. Maybe because more corners bring more strategic possibilities? Christian explains that a "corner"  "is any of the [] hexes which touch an odd number of other hexes". So a corner could also be in the middle of the board like in the PolyY board. Still there is a lot of resemblance with the Game of Y and PolyYThe majority of corners rule of PolyY is a little easier to grasp than calculating combinations of 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120... Let's play all of these games! Hi Ton,
There were two thoughts coming together that led to Starweb. The first one was that the Superstar board has twelve outward and six inward corners. The second and crucial one was the use of the triangular series for 'connective scoring' in a 'Star like' game, instead of the 'group penalty'. Holding on to the latter without ever questioning it had previously gotten me into a dead end.
I then morphed the Superstar board into the Starweb board. The corners are evenly divided but six are nearer to the centre. The center is still big, but not too big. Actually the number of cells of the board equals that of a base9 hexhex board. Of course the board is arbitrary  but it's nice. One could however imagine any board and any kind of 'value cells', including wholly arbitrary ones.
Your series of triangular numbers is correct but a bit long. If you get half the corners into one group, which isn't very likely in a balanced game, then your score is 45. This is a game with lowscoring. You need only a point more to win or even an equal score if you're the second player. Totalling the score of two or three groups shouldn't be a problem.
The 'odd # of neighbours' definition of corners is by Russ, and very convenient in Starweb's case. But in principle we're talking about 'value cells'. Note that in Symple all cells are value cells, so thinking of them as 'different from connection cells' is a choice, not an inherent restriction.

Russ Williams
Poland Wrocław Dolny Śląsk

Noting that "value cells" is of course a more general concept than just corners leads me to wonder about an initial placement phase, in which players alternately choose and mark the 18 (or however many) value cells for that session.

christian freeling
Netherlands

russ wrote: Noting that "value cells" is of course a more general concept than just corners leads me to wonder about an initial placement phase, in which players alternately choose and mark the 18 (or however many) value cells for that session. The reason I brought the general idea of 'connective scoring' to the forum's attention again is because it might be a more rewarding concept than generally thought, especially because there now have appeared interesting alternatives for 'group penalty' as the incentive to connect. So I'm glad it made you wonder and yes, that's an interesting idea.
Edit: The first thought about it is "why not 'mark' all value cells close together". There happens to be a way to avoid that: the 'oneboundonefree' opening protocol. The bound one is a value cell (so the opponent chooses its position, more or less). I'm not playing around with it any further, just thought I'd point it out.

christian freeling
Netherlands

Here's our first Starweb game. Corners should probably be a shade darker rather than lighter.
(Edit: Done).
Commentary I don't think allowing me to swap an inward corner was Ed's best option. With 8.J7 White declined taking a corner on strategic grounds. There are four vacancies left so I can still get half of them but it will be hard for Black to avoid having one more isolated group than White.
position after White9

Michael Howe
United States Cromwell Connecticut

What's on P7?
Clearly black is going to try to make a 7 or 8 corner group on the right and white will try to do the same on the left. So I guess it comes down to who can successfully invade and cut? I actually imagined the game with more of an alternatecorners opening.

christian freeling
Netherlands

mhowe wrote: What's on P7?
Clearly black is going to try to make a 7 or 8 corner group on the right and white will try to do the same on the left. So I guess it comes down to who can successfully invade and cut? I actually imagined the game with more of an alternatecorners opening.
Indication of the last move made.
There are a few interesting aspects to strategy that can be explained without a lot of experience. I'll have a go at it later.
Ok, I'm back. Black has actually taken 11.G16, the corner inside his 'territory'. Now White takes the last corner and Black is saddled up with an isolated group. It could have gone vice versa but then White would have taken G16 because thought it's only 1 point for me, it's 8 for Black. Black would have had two isolated groups then.
White aims at connecting nine corners while Black has eight. I feel I already have a won position.

christian freeling
Netherlands

This is to get my own thoughts straightened out.
In a pie you have the cutter and the chooser. For our purposes the 'cutter' is the player who places the first stone.
Strictly symmetric play requires that the player performing it has a stone in the centre so let's assume the first stone is placed in the centre.
 If the cutter wants to play symmetrical he's dependent on the chooser.  If the chooser wants to play symmetrical he's dependent on the cutter.
And why would anyone play symmetrical in the first place, if it loses the game? Because the other player, observing the first and maybe second symmetric reply, can play at one side of the board so that the centre stone will not get any cutting role, and thus win with an equal score.
In a more general context, the second player has enough at an equal score to win, so employing a 'one sided' strategy aiming at getting 9 corners connected, even if the opponent can do likewise, is advantageous. Therefore it is in the interest of the first player to cut the second player's position, for instance as in the above game by isolating a group.
Finally, the pie in Starweb is interesting because of the diversity of the cells and because both players know that the second player only has to get to an equal score to win.

Michael Howe
United States Cromwell Connecticut

christianF wrote: mhowe wrote: What's on P7?
Clearly black is going to try to make a 7 or 8 corner group on the right and white will try to do the same on the left. So I guess it comes down to who can successfully invade and cut? I actually imagined the game with more of an alternatecorners opening.
Indication of the last move made. There are a few interesting aspects to strategy that can be explained without a lot of experience. I'll have a go at it later. Ok, I'm back. Black has actually taken 11.G16, the corner inside his 'territory'. Now White takes the last corner and Black is saddled up with an isolated group. It could have gone vice versa but then White would have taken G16 because thought it's only 1 point for me, it's 8 for Black. Black would have had two isolated groups then. White aims at connecting nine corners while Black has eight. I feel I already have a won position.
Seems like this is going to come down to a sente battle, to use a Go term. Each player has to decide if his opponent's last move demands a reply or whether he can respond with his own cutting attempt.
If this sort of opening is a win for one side and results in less than interesting play, maybe the idea of fixed alternating corners could be reconsidered.
Or maybe, and this is a much bigger change, you could change the definition of corner ownership to something like polyY. A player owns a corner if he encloses it with a group that also connects to or encloses a different corner. Player could then attempt to influence and claim corner without occupying them. No more initial cornerclaiming phase.

christian freeling
Netherlands

mhowe wrote: Seems like this is going to come down to a sente battle, to use a Go term. Each player has to decide if his opponent's last move demands a reply or whether he can respond with his own cutting attempt.
If this sort of opening is a win for one side and results in less than interesting play, maybe the idea of fixed alternating corners could be reconsidered.
Or maybe, and this is a much bigger change, you could change the definition of corner ownership to something like polyY. A player owns a corner if he encloses it with a group that also connects to or encloses a different corner. Player could then attempt to influence and claim corner without occupying them. No more initial cornerclaiming phase.
White needs to reply 'locally' if Black threatens to cut off a groups, like 13.F2. I think I got this under control. My strategy was to nibble off one group, all else being more or less equal, and that succeeded. I don't need more than one group.
This obviously is a game between absolute beginners, but also fairly seasoned Havannah players used to 'reading' a hex grid. I think Ed played for 'security' and payed a small price  and I needed only a nibble. I don't think this type of opening will be at all typical. (Edit: Black13 already will cut off a white corner, a simple trick that I didn't anticipate. Now should I do the same ...?)
As for your suggestions, I'm not quite that far. I feel I can trust the game and that deepening understanding of its strategy will see these issues straightened out. But trust is not transmissible

christian freeling
Netherlands

mhowe wrote: If this sort of opening is a win for one side and results in less than interesting play, maybe the idea of fixed alternating corners could be reconsidered.
Here's something I expected to happen, a sudden leap in insight such as happens frequently to beginners in any strategy game. There has been so much talk about 'groups containing corners' that I had temporarily forgotten about groups that don't. Purely defensive groups, the 'value' of which is only in the devaluation of the opponent's score, by isolating groups.
In the game we play Ed invaded with 13.F2 which gives the option to disconnect either D1 or G1. I made an escape for G1 and now try the same trick at N18. But there are more such vulnarabilities at both sides. This game shows an understandable lack of strategic insight on our behalf rather than a problem regarding corner claiming. I remember that our first games of Havannah also illustrated a quite formidable degree of naivety. We can't quite see the shape of things to come ...


