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Rip Apart My Game - Simple Abstract Strategy Board Game

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Steve
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Joined: 07/29/2008

UPDATE JULY 5, 2012 - At this point, the original file attachment is obsolete as the initial board game had a flaw, for which I thank everyone for pointing it out to me. The original instructions have been taken down and I'll rework it.

I have no idea where to place this topic. It looks like playtest requests now go here and so this is where I'll place it. The moderators can move it if there is a better forum for this.

This is one of my board games. The complete rules are in the attached PDF but here is the overview - It is a two-player, abstract strategy board game. Players sit between a 3-space hexagon (3 spaces on each of it's 6 sides for 19 spaces overall), taking turns placing pieces (for instruction sake, red and blue pieces) down onto empty spaces of the grid. The object is to make the last legal move or, in other words, you win by not losing. For the red side, you must avoid making the corners of an equilateral triangle with your pieces. For the blue side, you must avoid placing three of your pieces in any given row (horizontal, forward diagonal or backward diagonal). Gameplay example and play variants are in the attached PDF.

NOTE - I'm working on a more complex variant of this game; The PDF isn't complete yet but for those who want to see the incomplete PDF, private message me.

Thank you in advance and I look forward to everyone's feedback.

TLEberle
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Joined: 08/10/2008
Settlers Island Abstract

This sounds very fascinating; I don't think you'll get much in the way of "rip apart my game." I do have some questions: are both sides balanced enough? What happens if you can play all nine of your markers?

Here's something: what if in order to win you have to "hold serve" and win from both sides consecutively?

(drop me a line at traviseberle [at] gmail.com if you want some playtesting help, because this looks like it has legs.

Cheers,
Travis

suf
suf's picture
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Joined: 07/26/2010
Played about 6 games with

Played about 6 games with alternating starting color. Game is interesting and we definitely enjoyed it.

However, triangles are definitely harder to spot and it seems like the game is balanced towards the 3-on-a-row player. Except for the 'warming up' first play, the triangle was always formed first. Perhaps with more plays this would change.

Three types of 3-on-a-row are specified in the rules, but there is one fourth case where the three hexes are one side apart each other. Perhaps adding that might shift the balance a bit.

As a fan of abstract games I like the idea and feel like you're on the right track. We'd love to see a bit more strategy in the game.

Good work!

akanucho
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Joined: 11/10/2009
Looks slightly unbalanced to me

There are four types of location on the board: C - Corner E - Edge I - Interior M - Middle

  C E C
 E I I E
C I M I C
 E I I E
  C E C

As it is, the game looks slightly unbalanced in favor of the lines player. Each corner is part of exactly 8 straight lines (along one of three diagonals) and exactly 8 triangles. Each edge is in 7 lines and 9 triangles, Each interior location is part of 12 lines and 13 triangles, and the middle location is part of 18 lines and 18 triangles.

  1 1 1
 3 3 3 3
6 6 6 6 6
 3 3 3 3
  1 1 1

First I counted in how many horizontal lines each location participated, and then I added the other two rotations. Each corner is 1+1+6 = 8, each edge is 1+3+3 = 7, each interior is 3+3+6 = 12, and the middle is 6+6+6 = 18. There is one middle, but 6 each of corners, edges, and interior, so there are (6*(8+7+12)+18) / 3 losing patters, or 60 possible losing lines (20 along each of the three diagonals).

For triangles, it was more complex. For each corner, I looked for locations that would (with the starting corner) form the first edge in a triangle (assuming that each triangle was counterclockwise from the starting edge). There are 8 such locations.

  0 0 0
 0 0 0 0
0 0 1 1 1
 0 1 1 1
  X 1 1

For edges, there are 9.

  0 0 0
 0 0 1 1
0 0 1 1 1
 0 1 1 1
  0 X 1

For interiors, there are 13.

  0 0 0
 0 1 1 1
0 1 1 1 1
 1 X 1 1
  1 1 1

For the middle, all 18.

  1 1 1
 1 1 1 1
1 1 X 1 1
 1 1 1 1
  1 1 1

For triangles there are (6*(8+9+13)+18) / 3 losing patterns, or 66 losing triangles. In order to balance the number of losing patterns, I suggest adding in six more losing lines.

  X . Y
 . . . .
. X . Y .
 . . . .
  X . Y

and the other 2 rotations. This leaves the weights of the locations slightly different between the two players (the interior and middle locations are at 13 and 18 losing patterns for each, but corners are in 9 lines and 8 triangles and edges are in 8 lines and 9 triangles), but the number of losing patterns is equalized at 66 losing patterns each. The only tricky issue with those 6 lines is the three lines parallel to those new diagonals that include the middle location, they cannot also be valid losing patterns or else there would then be more losing patterns for lines than triangles.

Steve
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Joined: 07/29/2008
Replies

First, thank you for your responses so far.

@ TLEBerle -

Concerning a tie - During my testing, I never encountered a tie. If anything, including 9 pieces for both sides is more for completeness than necessity as my test games usually ended before either side needed a ninth piece.

Concerning your winning strategy - I'm not sure if I understand what you mean by "holding serve." Please elaborate.

@ suf -

Concerning your views - Yes, I concur that triangles are initially harder to spot, especially the "crooked" triangle. In my defense, I found that with successive testing, they became easier to spot to the point where the added difficulty was negligible. If this continues to not be the case, that is a cause for concern.

Concerning a "fourth" 3-in-a-row case - If I understand you correctly, you may mean a case where the pieces are not touching each other. In a typical hexagon grid, this would translate to individual spaces touching only at points and not at edges which would not constitute the row as specified. I will have to make more observations about that.

Concerning lack of strategy - As stated, this is a simple strategy game. I am working on a more complex variant of the game and will hopefully reveal those rules soon. thank you for your interest.

@ akanucho -

Thank you for your analysis. Unfortunately, my mathematical notes for this game are not available to me right now. When I performed my own analysis, I remember both sides being equal with 60 possibilities each. In an effort to field a response, though, I've recreated some of that analysis.

For the 3-in-a-rows, our numbers concur at 60 although you performed different operations to arrive at your conclusions. I will admit that I merely performed a brute force method of counting out all of the possibilities for one set of rows and then multiplying them by 3 (3 different sets of rows).

For the triangles, I also performed a brute force method to obtain all possible triangles and then doubled the result (some triangles are flipped horizontally, others vertically and one diagonally). That number also turned out to be 60 although you came up with 66. Broken down further, the individual triangle types had 24, 14, 12, 6, 2 & 2 possibilities (from smallest triangle to largest) which summed to 60. Do you see more then six triangle types?

TLEberle
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Joined: 08/10/2008
"Holding serve"

>>Concerning your winning strategy - I'm not sure if I understand what you mean by "holding serve." Please elaborate.

Gladly!

One of the issues that can come up with an asymmetrical game such as this is that one side has an easier go of it than the opponent, for whatever reason. Netrunner has players play a game from each side, and if you win both games you take the match, and if there's a split whoever got more points wins the game.

In tennis, it is understood that the player who is serving for a game will be more likely to win the game, so you have to win by two. The person who wins the match is the one who can "break" his opponent by winning a game from the receiving side. You hold serve by keeping your opponent from taking away the advantage. (This is how you got that famously long tiebreaker fifth set at last year's Wimbledon: each player refused to drop the service game and it went on for days.)

This is a whole bunch of words to say that you might consider a victory condition as the first person to win two games consecutively: one as red and one as blue.

akanucho
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Joined: 11/10/2009
Only six types, but....

Side Length = 1: x24

  . . .
 . . . .
. . . . .
 . X . .
  X X .

Side Length = sqrt(3), or ~1.7: x14

  . . .
 . . . .
. X . . .
 . . X .
  X . .

Side Length = 2: x12

  . . .
 . . . .
. . X . .
 . . . .
  X . X

Side Length = sqrt(7), or ~2.6: x12

  . . .
 . X . .
. . . . .
 . . . X
  X . .

Side Length = 3: x2

  . X .
 . . . .
. . . . .
 X . . X
  . . .

Side Length = sqrt(12), or ~3.5: x2

  X . .
 . . . .
. . . . X
 . . . .
  X . .

I, too, missed at first the fact that there are two sqrt(7) triangles for each corner.

  . . .
 Z Y . .
. . . Z .
 . . . Y
  X . .

Marvelously well designed game, by the way. I love how deceptively simple the game seems at first. I had a blast calculating all the winning odds, and at first I found 60 vs. 60 patterns as well. I had a large bit of text that said explained how I proved that the two sides had completely equal odds at winning, and I had to delete it all after I realized that I'd flubbed and missed a case. I'm sure that there's a clever way to balance the two sides; good luck in finding it! I look forward to seeing what you come up with!

akanucho
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Joined: 11/10/2009
I'm not sure this is a

I'm not sure this is a completely valid way to measure balance, but it seems like the Lines player has a single token advantage, in that they can place one more token than the Triangle player in both the best case (most tokens placed where next placement loses) and worst case (fewest tokens placed where next placement loses). At least, these are the best and worst cases that I could find; they are certainly not definitive.

For Lines, best case (10 tokens placed):

  X X .
 X . . X
. . X . X
 X . . X
  X X .

For Lines, worst case (6 tokens placed):

  X . X       . . .       . X .
 . . . .     . X X .     . X . .
X . . . X   . X . X .   . . X X .
 . . . .     . X X .     . X . .
  X . X       . . .       . X .

For Triangles, best case (9 tokens placed):

  X X X
 X . . .
. X . . .
 X . . .
  X X X

For Triangles, worst case (5 tokens placed):

  . . .
 . . . .
X X X X X
 . . . .
  . . .

I have a few suggestions for variations that adjust the balance. I hope I'm not out of line by mentioning them: 1. Lines player always places first. 2. Lines player places first and places two tokens on their first turn. 3. Triangle player plays first and places a Lines token on their first turn. 4. Lines player places first, but Triangle player places one of each token on their first turn.

Steve
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Joined: 07/29/2008
Missed It By That Much!

Again, thank you for all of the responses so far.

@ TLEBerle -

Thank you for that explanation. It makes sense to me now. I'll know what others are talking about when I see that again.

@ akanucho -

Thank you for pointing out the other six possibilities. I had not seen that. In the words of Maxwell Smart, "Missed it by that much!"

Oh well... things that are broken deserve to be fixed. I'll have to see what I can do to balance the two sides out while attempting to retain the simplicity. This probably puts my more complex variant in jeopardy as well (read: breaks it thoroughly), so it's back to the drawing board for me. Some ideas do come to mind...

I thank everyone for catching the imbalance.

Steve
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Joined: 07/29/2008
Two Possible Solutions

I do not want to disparage any of the attempts to correct the imbalances of the game so far - I thank everyone for their suggestions. I just wanted to make my own attempt at correcting the imbalance and I may have two additional solutions.

SOLUTION #1 - Keep the grid as is, create a new rule for the "line" player.

There are 66 losing conditions for the triangles, 60 for the lines. So, the logic was to increase the number of losing conditions for the lines.

The result was a new rule - In addition to the line player not being able to place 3 pieces in any given row, the line player must also not place 3 pieces in consecutive outer corners. The corners are now their own "row" but, unlike other rows where the pieces can be anywhere in the row, the pieces must be consecutively placed in the corners. For instance...

..XOX
.OOOO
XOOOO
.OOOO
..OOO

The "X" represent pieces in three consecutive outer corners.

The good - Keeps the grid as is; Keeps the # of pieces as is; Evens out the losing conditions for both sides exactly.

The not-as-good - Adds an additional rule to memorize (albeit a simple one, but a rule nonetheless).

SOLUTION #2 - Alter the board to even the two losing conditions out.

There are 66 losing conditions for the triangles, 60 for the lines. So, the logic was to equalize them both by altering the board. The result was this:

..OXO
.OOOO
OOOOO
.OOOO
..OXO

X represents a space that can not be played on. The resulting board has 46 losing conditions for each side.

The good - Evens out the losing conditions for both sides exactly; Keeps the rules exactly as is.

The not-as-good - Grid now feels almost too small; Smaller grid = Even shorter playing time... Too short?

Anyway, what do you guys think? I have some ideas for additional solutions and I'll let you know if any emerge that increases the strategy without altering the game significantly.

akanucho
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Joined: 11/10/2009
A variation along the lines

A variation along the lines of Solution #2 would be more my preference, as the rules are wonderfully simple and it'd be a shame to complicate things. I don't know if removing the two locations you've indicated have the result you think it would. Since each edge location is in 7 lines and 9 triangles (I think), wouldn't removing those two change the number of losing patterns to 46 lines and 48 triangles?

You'll have to double-check my maths, but I tried calculating losing patterns after adding one location to each row, and I got 108 losing lines and 104 losing triangles. However, if I removed just the location added to the middle row, the number of losing lines and triangles both dropped to exactly 96.

  . . . .
 . . . . .
. . . . .
 . . . . .
  . . . .

I'm not sure if adding new locations actually makes the game longer or shorter. The fact that there are so many more losing patterns at first sounds like the games would actually tend to be shorter. But if you don't play in the new locations, the game lasts the normal length of time. I'm guessing that the new locations have very high weighting towards forming losing patterns, but I haven't calculated that yet.

Likewise, if you remove the two locations you suggested, you're only removing two locations, but you're eliminating a large number of losing patterns, so wouldn't that actually make the games last longer, not shorter? Since each location is part of fewer losing patterns, each placement would actually have a smaller chance of ending the game, extending gameplay. I'm sure there's a good explanation for which would extend the game, adding or subtracting locations, but I don't have it. Not yet, at least. I'll be working on this for a while, methinks.

Steve
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Joined: 07/29/2008
You beat me to it again! :)

You are right. I messed up on my numbers for my proposed solution #2. That's twice now I messed up on my math. Ugh. Just more proof that I need to double-check my math on a spreadsheet before I write.

Not only that, but I was beginning to add spaces to the original design to see if I could solve the dilemma in that direction. The closest I came was a diamond formation with the two extreme top and bottom tips cut off. Which, before you ask, doesn't work (96 lines, 92 triangles). I'm glad that you proved that it could be solved by adding spaces. I'm sure there's a mathematical formula that would make this easier but I'm not that fluent in that area.

I crunched the numbers on your board and it seems to work out as detailed - 96 each.

At any rate, I'm a little relieved that there's a board to match the game now. I'm still going to see if there's other solutions but I probably won't be as fanatical as I was in the past few days. I was losing too much sleep going through all the possibilities manually - Probably a poor method but the only one that I could rely upon. Thanks for all the help so far.

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