Harald Korneliussen
Norway

Since the inventor and the implementor seemed to like Short Circuit, I figure I should to release my second one, although it's not quite tuned yet.
In the ball and chain pattern, the builder and blocker both have to construct two separate groups in their colour, a ball and a chain.
To find out whether a group is a ball or a chain, count its external faces, and subtract internal faces times three. If the result is positive, it is a chain of that size. If it is negative, it is a ball with size equal to the absolute value of the result.
Be careful to count faces, not neighbouring hexes.
This way of defining ball and chain size is the best one I've found so far that ensures that things which intuitively should be balls are balls, and chains (a la the rusty chain pattern) at get a good chain score. Some other things that do not look like chains also get a good chain score if they have a large surface area, so the name is a little inaccurate  but we can live with that
A player's score is the smallest of the largest ball and the largest chain in his colour, so they must try to strike a balance.
If a player has only one group, score is defined as zero. To win, the builder has to make sure the red score is higher than blue's.
I think this pattern should provide good opportunities for creative colour switching. If the pattern chooser wants to, it could also be played with a neutral color (green) that does not affect either player's score.
The blue group has 20 16 external faces and 11 internal.
16  7 * 3 = 16  21 = 5, so it is a ball of size 5.
The red group has 22 external faces, and 4 internal.
22  4 * 3 = 22  12 = 10 so it is a chain of size 10.
Edit: You're absolutely correct, Arty, I must have counted wrong somewhere. This means I have been thinking balls were easier than they are. Not sure that is a good thing... Edit 2: More errors?! Oops, looks like I copied the wrong figure from my notes! Here's the figure for which the first arithmetic was correct (in the original ASCIIart)
. . . . . . 1 2 2 1 . . . 2 X X X 2 . . . 1 X X X X 1 . . . . 1 2 2 2 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20  11 * 3 = 20  33 =  13, ball of size 13
Hey, what's the point of a code tag if it doesn't make text monospaced? Well, you get the picture, I hope.

Nick Bentley
United States Madison Wisconsin

this reminds me of one that I have in my notebook, where the builder must build two balls of sufficient size and then connect them. I never worked out the details though. I was going to call it big balls.

Harald Korneliussen
Norway

I looked at various forms of the idea that you must construct two groups which have opposite properties somehow, and then score according to the "smallest" of these. Ideally, building balls and building chains should be equally difficult, but I'm pretty sure chains are easier.
I also wanted to make a pattern that wasn't so devilishly hard to write a fast detection algorithm for

Arty Sandler
Canada Kanata Ontario

Hm.. are you sure the blue group has 20 external faces and not 16?
The detection algorithm is really easy to implement. The only question I have is how to rephrase the pattern description since there are no hexes on the MN board but circles.

Arty Sandler
Canada Kanata Ontario

vintermann wrote: Edit: You're absolutely correct, Arty, I must have counted wrong somewhere. This means I have been thinking balls were easier than they are. Not sure that is a good thing... Mmm.. so what about the pattern? Do you think this is good enough or not?
If yes then I would like to implement it But I need a short and more accurate description (i.e. there is a need to change "faces" to something else)

Harald Korneliussen
Norway

How about this?
Quote: "In the ball and chain pattern, the builder has to construct two separate red groups, a ball and a chain. The smaller of these has to be larger than the smaller of the blue ball and chain. If there is more than one chain or ball of the same colour, the largest counts.
To decide whether a group is a ball or a chain, we do as follows: For each cell, count the number of neighbouring cells which are of a different colour, multiply by 2, and subtract the number which are of the same colour multiplied by 3. For each group, add the scores of the individual cells. If the score is positive, the group is a chain, if it is negative, it is a ball.
The size of the ball/chain is the absolute value of this score.
If there is only one group of a colour, it counts as a ball and chain of size 0. "
This should be equivalent. We have to score it slightly differently when we count it this way, to account for internal faces being counted twice. You could replace 2 and 3 with M and N, to get a family of patterns instead. When I think about it, it doesn't need to be a problem that one kind of group is easier to make than the other. But then it really needs a better name.
Any ideas?

Arty Sandler
Canada Kanata Ontario

Hm.. Just paid attention.. Are you sure that the blue group has 11 internal faces and not 7 (or 14?) ?

Harald Korneliussen
Norway

I must have copied something wrong for my text file... Fixing it

Arty Sandler
Canada Kanata Ontario

Happens.
Well, this sounds better. I will implement it next week (or maybe even earlier).

Arty Sandler
Canada Kanata Ontario

Hm.. I assume that the board must be filled?

Harald Korneliussen
Norway

Yes.

Arty Sandler
Canada Kanata Ontario

Ok I am going to test it playing against myself in onetwo hours and then I will open it publicly.

Harald Korneliussen
Norway

Wohooo! thanks!

Nick Bentley
United States Madison Wisconsin

yippee! This is awesome. I know I said I would be back to playing, and I haven't, but that's because preparations for the oral defense of my dissertation have taken more time than I though. I do it on wednesday, and if I don't totally flub it, my PhD will be done with. THEN I will finally be able to come out and play again. whew.

Arty Sandler
Canada Kanata Ontario

yeah. I really need to test the patterns with someone besides myself
Good luck with your defense!


