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.
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.