# Card deck design - How many cards needed to express these 6 independent variables?

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Joined: 02/05/2015

My math and probability chops are terrible, so please bear with me...

I'm designing a card-assisted mechanic for a solitaire naval game in the age of fighting sail.

At the start of each two-week turn, the human player assigns each of his ships a mission and a zone of the game map to operate in. A face-down chit-draw mechanism then secretly assigns the AI enemy ships to map areas and mission assignments.

The enemy chits are revealed. If the human player and AI enemy both have a force assigned to the same map zone, there's a possibility of an encounter (die roll used with 50% chance).

I need an encounter mechanism to set the following 6 initial elements of the encounter:
V1.Wind direction (8 possibilities)
V2.Location of AI enemy ship (10 possibilities)
V3.Bearing of human player ship in relation to enemy ship (8 possibilities)
V4.Distance of human player ship from enemy ship along that bearing (15 possibilities)
V5.Enemy ship initial course heading (8 possibilities)
V6. Human player initial course heading (8 possibilities)

I'm trying to design an encounter card deck, where all these possibilities can be set by the draw of a single card.

One opportunity is that the game uses 1km grid squares, with 8 points of direction (4 sides and 4 corners). A card also has 4 sides and 4 corners. So, I'm thinking: Why not use the shape of the card to display some of the directional variables graphically?

A card could have colored tabs around the perimeter that dictate V1, V3, V5, and V6 for that particular card.

V2 (location of AI enemy ship) could be a number(1 through 10) on the card.

V4 (distance along the bearing) has the most possibilities, so I'd prefer to maybe randomize that with a dieroll or something rather than increase the size of the deck exponentially to accommodate all 15 distances.

Here's the critical question: How many cards would a deck have to have to express every possible combination of these six variables?
(I don't mind it it's a lot, since the game would be Cyberboard-only and the deck is not meant to be printed).

I know there's something called "combinations and permutations" that other threads have mentioned and offered a link to a calculator for.
But I don't even know whether this is a question of permutations or combinations, or how to use a tool of some kind to tell me exactly how many cards I need, and what should be on each of them.

xenosus
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Joined: 09/29/2012
Well, assuming I did it

Well, assuming I did it correctly, if you wanted each card to express all variables individually, you would need 614,400 cards. It'll be a whole lot easier to just make a deck for each variable and have the player shuffle after each use.

Miika
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Joined: 02/01/2015
Effect card deck

Hi,

Could you use one deck that has several values.. And maybe a small board that has like 3 places for cards and each card represents 2 of the values.. I did a quick sketch up, it has issues, but hope you catch the point.. Cards wouldn't have texts, i just put those in to show the example .. But with this kind of system, you have to adjust some values.. Like V2 would have either 8 or 16 possibilities... etc..

(hopefully this works)

This way you could do a deck with lets say 4 times 16 cards, with different variables..

-Eberhardt-
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Joined: 01/30/2015
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@Broadsword56 the game sounds very appealing.

@Xenosus wow that's a lot of cards (~166K). :)

@Miika that is actually a great idea. In speaking with Ruy343 and RadioPrime I have started to revise wording on cards in favor of symbols.

DifferentName
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Joined: 09/08/2013
Cyberboard

I was just writing about the importance of keeping in mind the limitations of a physical card game, vs a video game, and then noticed you mentioned the game would be on Cyberboard, so I guess it is a video game.

I don't know how cyberboard works, but if you have to actually make the cards, it would be a lot easier to make the 57 cards to have 6 separate decks for those variables, than to try combining them into 600k+ possibilities.

I think fast prototyping is emphasized more in board game design than video games, but I still recommend it for something like this. Try to get something playable with a few of the variables before making a ton of cards for them.

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Joined: 02/05/2015
Brilliant concept!

Thank you, everyone, for all these great suggestions.

@Miika - This is a terrific mechanic and I'm going to try it. Thank you so much!

I can easily reduce the number of possible locations per map encounter zone to 8 instead of 10.

For the human distance from the enemy ship, I came up with something I like even more: The number on the card is a negative modifier that you always subtract from the number 20. So, for example, if you draw the card with 15 you place the human player's ship 20-15 = 5 squares distant from the enemy AI ship along the bearing line.

(This is based on the fact that the absolute maximum spotting distance to see a sail on the horizon on this lake, in the summertime, for ships of this type, would have been 20 km, max. So the card number simply reduces a random amount from the maximum possible visibility. I don't need it to generate distances less than 4km, because once the encounter is that close, it's a tactical battle that uses a different mechanic (battle movement) to establish the AI ship's initial orders and heading.

Dagar
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Joined: 01/23/2015
Why do this subtraction

Why do this subtraction thing? As long as your vision range is a constant 20km, a -15 will always mean 5km. Why do you not want to simply put the '5km' information on the card? K.I.S.S.

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Joined: 02/05/2015
Dagar wrote:Why do this

Dagar wrote:
Why do this subtraction thing? As long as your vision range is a constant 20km, a -15 will always mean 5km. Why do you not want to simply put the '5km' information on the card? K.I.S.S.

It's because the simplicity of the cards 1-16 means each card will have only one number on it (the number 1-16). The same numbered card serves a variety of purposes, depending on which of the three variables boxes it's drawn for.

Example: I draw a card for the wind direction/distance box. I draw a card with the number "1" on it. The box says distance is "20-#" So my distance would be 19 km. Otherwise the face-value 1 on the card would give me 1 km, and I don't want distances that short.

I need the drawn card to generate deployment distances of >16, up to 19 km, the max clear-weather vision range. And I don't want distances under 4 km.

Dagar
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Joined: 01/23/2015
Okay, all clear, neat simple

Okay, all clear, neat simple system.

Miika
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Joined: 02/01/2015