# Probability in abstract strategy-Synchromy

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chris_mancini
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Joined: 05/01/2015

I have recently completed a prototype for an abstract strategy game called Synchromy, and I wanted to reach out the the community to see if there are any math whizzes out there to help me (as I am weak in all calculations except geometry!)

The game is for 2 players.
The game board features a 6x6 square grid.
The pieces are transparent primary color tokens: 30 each of red, blue and yellow.
These pieces can be stacked to create 3 secondary colors: orange, green and purple.

The game begins by each player blindly drawing which 2 of the 6 colors noted above they will be playing. These are kept secret from the other player at all times. Players will never play the same color, and only 4 of the 6 available primary and secondary colors will ever be in play for points, though all colors are likely to be on the board as the game progresses. This introduces opportunity for bluffing and misdirection between players.

The object of the game is to have the most of one color on the board while also having the least of another color at the end of the game. Which color serves which goal is up to the players after they have drawn their 2 colors.

Players may take 1 of 6 actions per turn:
1. Draw a color token blind from the bag and place it on any open space on the board.
2. Move a single token from its space to any open space on the board (tokens may only move in a straight line or diagonally).
3. Draw a token blind from the bag and place it on top of a previously placed token, creating a secondary color combination (only 2 tokens may ever be stacked, and only in a combination which creates a secondary color).
4. Move the top token from a secondary color combination to an open space on the board.
5. Move the top token from a secondary color combination on top of another single token, creating another secondary color combination.
6. Move a stack of 2 secondary color combination to an open space on the board.

The game ends once all spaces on the board are occupied. Given the range of moves available, this often if not always is a decision by a player to end the game, based on the layout of the board and whether or not a player believes they have won.

Score is calculated by taking your "most" color number and subtracting your "least" color number. There are also secondary goals, such as bonus points for groupings of 4 or more, and creating an edge-to-edge line of your color.

I think that's all I can tell you guys at this point...my biggest question is, is there an imbalance inherent between primary and secondary color goals? For instance, if player A draws blue and yellow, both only requiring a single token, and player B draws green and purple, both requiring 2 tokens and both also using blue to create them, how does this affect probability and balance? Does the range of movements available on a turn serve to equal things, as all tokens on the board have the ability to be manipulated?

any insights, opinions or criticisms are welcome and most appreciated...tear it apart, break it, say it sounds interesting or profoundly boring...whatever comes to mind will help!

MattPlays
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Joined: 04/12/2015
hmmm

Had to read it through a couple of times to get the hang of it. Well, as its abstract it has no theme attached to it so some people wont be interested but being abstract it doesnt necessarily discount any demographics either.

For the colour choice at the start I assume that would be drawing pieces out of a bag then replacing them before the game begins?

The tactics could be interesting depending on if you get two primary colours or a primary and secondary but this needs a lot of play testing and maths o see if that is balanced.

JohnMichaelThomas
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Joined: 05/30/2015
There's probably some imbalance, but possible tweak to fix it

I thought about this quite a bit, and while it seems like there might be a slight imbalance toward primary colors (since by definition a primary color must be placed on an open space before a secondary color can be created), any imbalance seems slight and impermanent. You'd probably need alot of playtesting and keeping track of the color draws and use of primary or secondary colors as most and least colors to figure out if there's a noticeable imbalance. There are 8 possible combinations of primary/secondary/most vs. least, so you'd need alot of plays of each combination to get enough data to figure it out. You might be able to do a monte carlo simulation to try and get some idea, but that's alot of work.

The one thing you might do to prevent the possibility of a primary/secondary imbalance is to have each player choose 1 primary and 1 secondary color instead of 2 random colors. This would make it slightly less mysterious what color combinations your opponent has (since they could have 1 of only 4 possible combinations instead of 1 of 6 possible combinations), but it would practically guarantee there's no imbalance.

JohnMichaelThomas
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Joined: 05/30/2015
One correction

JohnMichaelThomas wrote:
There are 8 possible combinations of primary/secondary/most vs. least...

My bad, there's actually only 6 combinations of strategies.

Each player has 4 strategies (2 primary, 2 secondary, primary most + secondary least, secondary most + primary least).

And that results in 6 strategy combinations which might produce an imbalance:
2 primary vs. 2 secondary
2 primary vs. primary most + secondary least
2 primary vs. secondary most + primary least
2 secondary vs. primary most + secondary least
2 secondary vs. secondary most + primary least
primary most + secondary least vs. secondary most + primary least
(There's another 4 combinations where both players use the same strategy, but those by nature won't be unbalanced).

Still alot of plays to find any patterns.

wombat929
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Joined: 04/17/2015

chris_mancini]... only in a combination which creates a secondary color...[quote]</p> <p>Do you need to include this caveat? Is it possible to stack two tokens in a way that doesn't make a secondary color?</p> <p>[quote=chris_mancini wrote:
The one thing you might do to prevent the possibility of a primary/secondary imbalance is to have each player choose 1 primary and 1 secondary color instead of 2 random colors. This would make it slightly less mysterious what color combinations your opponent has (since they could have 1 of only 4 possible combinations instead of 1 of 6 possible combinations), but it would practically guarantee there's no imbalance.

This is exactly the sort of thing I think rules variants are for. On first blush, I'd say having two secondary colors would be harder than having primaries. Another thought, what if you used "goal" cards that gave points to three colors instead of two? You could pick combos that were mathematically equal, perhaps.

Last, have you thought about how to make this game color-blind accessible? Overall, 7-10% of men have some form of color blindness. At first glance, it seems like using translucent tokens would make this easy to be color-blind accessible -- just add interlocking shapes to the tokens. Use a square, a circle, and a triangle, and have the secondary colors be square/circle, square/triangle, triangle/circle.

chris_mancini
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Joined: 05/01/2015
Thanks

Very helpful insights all... Much appreciated! I agree John that the blind draw could provide imbalance if it happens that a particular color is somehow drawn at a far reduced frequency...you need blue but just aren't pulling them.

Wombat I like the idea of using cards to assign goals...this could speed up play, give a little added difference each time and perhaps compensate for the imbalances as they are further identified. I'm going to seriously look into this...thanks very much!

As for the issue of color blindness, it is one I hadn't thought of, but certainly worth considering. I recall Tom Vasel recently commenting on an abstract game in a similar fashion; recommending perhaps adding simple icons or shapes. You know what they say about great minds!

So much testing yet to be done...this game has provided a unique challenge in that I cannot play against myself like other games I've designed or even bought. finding live testers has been, as I'm sure many of you have encountered, a challenge without a regular, seasoned gaming group. The few I know act like MTG is the only game in existence! Maybe I'll start a separate thread to see how many BGDF members are in the Los Angeles area...I think a solid group dedicated to play testing would be a hugely valuable resource!

debiant
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Joined: 05/03/2015
I'd be interested to play

I'd be interested to play this to see if I would constantly be trying to keep track of my score or whether I could play on feel. On first read through I missed how it was scored. I think the hidden scoring is clever. Unfortunately I don't have any mathematical advice for you.

chris_mancini
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Joined: 05/01/2015
Stacking tokens in more than secondary combos

I'd considered the optional rule that players may stack 2 tokens of the same color, thereby "locking" them in (as only 2 may ever be stacked); of course by the rules as they are, a player may just as easily move the top token, thereby "unlocking" the stack. Other than this, any 2 colors will create a secondary color, so at least the stack mechanic is controlled within a closed system.

I definitely think the thing to do with a game of such variability is to test specific situations, as well as some organic play to see what comes up. You guys have been very helpful in identifying some of those specific situations...I'll post more once I've run some sessions!

MattPlays
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Joined: 04/12/2015
I think

this game would translate quite easily to an App. Something to think about?

wombat929
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Joined: 04/17/2015
Color-blindness and UnPub

chris_mancini wrote:
As for the issue of color blindness, it is one I hadn't thought of, but certainly worth considering. I recall Tom Vasel recently commenting on an abstract game in a similar fashion; recommending perhaps adding simple icons or shapes. You know what they say about great minds!

For me, it was Daniel Solis' interesting piece on designing for c.b. that got me interested in it.

Have you looked at UnPub? The website makes it sound like you can host your own UnPub event and publicize it there. Your local library or community center probably has a room you can use for free or cheap, and if you get a couple other designers to set up there too, you can do it that way.