# Card Probability Mechanic

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Tbone
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Joined: 02/18/2013

Essentially the game at its core plays like Chess except each card has a specific type of card it can kill (there are abilities and other classifications of the cards but for now I'm worried about the probabiities).

The card types are correlated directly to the amount of cards of that type are in your deck. Each player may pick 2 cards of each type/abundance. There are six types.

Abundant - 6 cards
Common - 5 cards
Base - 4 cards
Scarce - 3 cards
Rare - 2 cards
Legendary - 1 card

In total there are 42 cards.

There is also a seventh type that only has one abundance and the player may only chose one, this is called the Monumental which will always be on the field because it holds the end game condition (not the winning condition) for that player. This will total the cards for each player at 43.

The decks are shuffled and 16 are put on the field including the Monumental.

Here is the type vs. type arrangment...

Monumental-Abundant-Common-Base-Scarce-Rare-Lengendary-Monumental

My question is this...

Does this make sense in terms of probability? More importantly is it balanced?

I can profide more information if needed but essentially its "high probability cards kill low probability cards" where high probability cards will typically have weaker abilities.

let-off studios
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Joined: 02/07/2011
Sense

This makes sense to me.

In terms of being balanced and fair, I suppose if the players have a chance to use their entire deck, regardless of the order the cards come out. Abilities are what would concern me, since they may change the odds and/or effectiveness of a given card significantly. For example:

• Do you have any abilities that let the player look at the deck?
• Do you have abilities that change a card's effectiveness based on position on the board and/or relative to the card(s) it is next to?
• Do you have any abilities that let the player take something from a discard pile/use an exhausted card again?
• Do you have any abilities that let the player manipulate the odds? For example: an ability that lets the player draw three, pick the one they want, and return the other two to the bottom of the deck.

I would think that those kinds of abilities would require a considerable amount of testing and balance before everything looks okay.

Good luck on your design, Tbone. :)

James Allen
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Joined: 08/07/2014
A Way Of Calculating Balance

Like let-off studios, I think it depends entirely on what abilities the cards have. I'm going to assume that a turn consists of selecting one of your cards to take an opponent's card.

The question of whether or not this is balanced, is really whether or not the imbalance created when players draw cards is strategically surmountable. The assumption here is that if one player's draw can be so much more powerful than his opponents that no amount strategy can overcome it, the game will be unpleasant.

Before looking at that, if player's can only pick 2 cards of each abundance to make their deck with, that's only 12 cards and 12 cards aren't enough to place 16 cards on the table. Also, since there are only 2 Legendary cards in total, it's not clear how each player can choose 2 legendary cards. To fix some of that, I'm going to assume you mean each player draws 7 cards from their deck and places those plus the monumental on the table. And I'm going to assume that each player just gets one legendary card.

Okay, so let's speculate how imbalanced can the initial draw be? One way to think about it is to do some extreme cases. (Just to make this all easier to write, I'm going to refer to each abundance type by it's first character; call all the cards in play, a “field”; and the player's PA and PB).

PA.field(M,A,A,C,C,B,B,S) # gets all the common cards
PB.field(M,B,B,S,S,R,R,L) # gets all the rare cards

One way to measure this is by calculating the number of possible takes given each player's card types.

PA's takes:
PA.A takes PB.M
PA.M takes PB.L

PB's takes:
PB.B takes PA.C
PB.S takes PA.B
PB.R takes PA.S
PB.M takes PA.A

This isn't exactly right because each player can have multple opportunities to take a particular type, and multiples of the same type to take. One way to represent that is to count up all the possible combination of one type taking another.

PA's takes:
PA.A takes PB.M
PA.A takes PB.M
PA.M takes PB.L

PB's takes:
PB.B takes PA.C
PB.B takes PA.C
PB.B takes PA.C
PB.B takes PA.C
PB.S takes PA.B
PB.S takes PA.B
PB.S takes PA.B
PB.S takes PA.B
PB.R takes PA.S
PB.R takes PA.S
PB.M takes PA.A
PB.M takes PA.A

We can represent this as odds in the form of good outcomes for PA versus good outcomes for PB, and get 3:12, or 1:4. So, the worst case imbalance is 1:4 (maybe there is a worst case). Is that acceptable given game play and the abilities on the cards?

Side Notes: is there a reason why “base” isn't called “uncommon?"; and note that the selection of two cards for each abundance nullifies the distribution in quantity across abundances.

Tbone
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Joined: 02/18/2013
I Appreciate the feedback

Thank you for your insightful input.

The thing Im weary about is the fact that I dont want the game to rely on the random factor too much.

To further explain, it is very difficult to get more than the 15 (or 16 if you count the Monumental) on the field.

To help get a better understanding of the cards each have these characteristics...

Value: how many points you get for killing the card

Abundance: how many can be present in the Deck

Mobility: how it can move around the board

Abilities: unique mechanics that alter gameplay

Predator: what cards can kill it

Prey: what cards it can kill

The object of the game is to end the game with the most points. Usually you end the game by either killing the enemies Monumental or fufilling the winning condition on your specific Monumental. (Note that killing the enemy Monumental or fufilling the end game condition does not necessarily give you the win, you must have the most points at the end of the game)

Generally a higher value card means it is more powerful. But it isnt what balances the card. I could have a card with an incredible ability and give it a value of 100 but if its impossible to kill then there is no point in giving it the value...

Is there some other attribute I can add to further the balanci g capabilities and will this Predator Prey system work with the abundance factor?

Thanks.

Masacroso
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Joined: 05/05/2014
Tbone wrote:Does this make

Tbone wrote:
Does this make sense in terms of probability? More importantly is it balanced?

I can profide more information if needed but essentially its "high probability cards kill low probability cards" where high probability cards will typically have weaker abilities.

It is the opposite but I understand anyway: low probability cards of high value, kills high probability cards of low values.

The probabilities are linked to the mechanic. For me 86 cards on play seems too much, think than chess have just 16 pieces per player. What probabilities you want to know? Probabilities on composition of hand? I need to know the large of the hand or some more mechanic.

(But from my perspective I would narrow the number of rarity and cards on any set of the same rarity. But it just an opinion with little info about the game.)

From your second post the value of a card is more than just his rarity cause they are mechanics that change the game.

Some ideas: for me the real POINT of competitive games is the possibility to predict the cards/moves will play the opponent(s) and, at the same time, evade excessive predictability to a desired level and second-nature-skills to play a deep strategy game.

To achieve the big first point you need a game where the players knows the plays than the other people can do, going from a large degree of freedom to some narrow, maybe with a little tweak adding real randomness in some point.

If you dont knows the cards/plays of your opponents then you cant try to predict anything. Some similar mechanic of prediction, but weaker, is based on rarity. You can think that you can play some cards with some degree of security because are hard to counter/be killed by others plays/cards cause rarity.

The key here, to understand how all of this works, in the coefficient of variation (related to standard deviation): if you have a long number of cards the cv will be high so your ability to predict something lowers.

So to make a good game based on rarity and dont make all completely random you must control de cv to a desired level, i.e., you must see which is the number of cards (in this disposition of frequency (=rarity) and value (=power over other cards)) where the cv is good for some ability to predict things.

Tbone
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Joined: 02/18/2013
You do not have any cards in your hand

The 16 cards that are in play are already on the field.

The board is set up like so...

Your Territory (where your 16 cards will reside). 8 spaces divided into two rows of four with the four spaces facing you.

The Battle Grounds. Four by four spaces - this connects the two opposing players' Territories.

You might ask "how do you fit sixteen cards on eight spaces?"... Well there two "states" in which cards can be in: Activated(card facing up) and Deactivated(card back facing up).

When setting up the game you will shuffle you deck, put 8 cards deactivated, one on each territory space. Then you will put four deactivated cards on top of the deactivated cards on the row farthest from you in your territory. Finally you put the last four cards activated (including your Monumental) on top of the deactivated cards on the row closest to you.

You may also ask "how does one 'activate' Deactivated cards?"

Here are the types of actions you can preform on your turn (you may only chose one per turn)...

1) Activate a Deactivated card
2) Kill a card (which would most times require you to move the card)
3) Move a card
4) Use an ability (if it requires you to move)

Some abilities are easier to execute then others... for example...

Ability 1: Card can capture enemy cards

is much easier than

Abulity 2: When the card reaches enemy Territory it can control enemy cards

Ability 1 is inherited once it is activated while Ability 2 needs to be triggered...

Sometimes I feel the game is too difficult in a sense that its too easy to kill cards but not easy enough to execute abilities.

Would giving the player more actions per turn help?

Masacroso
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Joined: 05/05/2014
I have a idea: test the games

I have an idea: test the games with rules than emphasize one aspect of the game or the other and try to find what you think is better.

Example: low the conditions for actions or make them stronger. Or make the process to kill something more difficult in some way.

Tbone
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Joined: 02/18/2013
Cost/Resources

One of my options...

Give each card a cost and also give them a resource value. Cards need to be paid for in order to activate them. Resources also can be used to pay for actions such as abilities with a specific cost and movement.

Resources are obtained by taking a turn to draw from the deck. Instead of using the card as an active card on the field you would use it as its resource value, kind of like a mana system.

The only problem (maybe) is the fact that the strategy behind this game is already pretty intimidating. Adding resource management might be too much but it would help balance abilities and cards.

This way I can even mess with the Predator/Prey system by giving a cost to killing a card. In reality the cost is action points...