Modelling a game format

[-Griffin]

People like discussing 'good for the game', 'bad for the game', ect, without defining what 'good for the game' really means. This is an attempt to roughly mathematically model what a 'good format' is in a CCG (it should be general enough to extend outside of Yugioh), and we can then toy with it to see what type of changes work the best.

 

Here's an initial draft of a model:

 

A Format is a set of Deck Types.

 

A Deck Type has a Popularity [0..1] (how often it is played in the format), a pair of Fun [pair of 0..1] (how fun it is to play, and how fun it is to play against), and a list of Matchups [list of 0..1] (its winrate when played against each other type of Deck.) and a Relevance [0..1] (average winrate in the format)

 

By multiplying each of a Deck's matchups with the other Deck's popularity, you can find the Deck's Relevance. This can be compared to its Popularity, and you then update its Popularity if appropriate (Decks that win a lot in the format get played more, Decks that lose a lot get played less). Fun should also impact its Popularity, but should never be treated below a certain value (say, 0.3), the 'Ignore Fun Value', where people will play a Deck because they like the theme, or because it gets wins, or because it makes them feel special, even if it's a chore to play. Repeatedly applying this update should converge to a steady state of popularities, aka, 'The Meta'.

 

We then need to define what the goal of the format is. Some candidates are:

 

"Popular Decks are fun to play and play against" Σ Popularity*Fun1*Fun2

 

"There is variety in Decks played" 

 

"Decks are balanced against each other well" ΣDeckΣwinrate*(1-winrate)

 

Once we have a definition for a format and a heuristic for the goodness of a format, we can see the impact of "applying a 'nerf'/banning a card" by picking a Deck (most Relevance, least Fun, ect), and reducing its winrates across the board by a certain amount (say, 1%-5%). This would also likely cause a small randomness to its Fun. We could also do things like add new Deck Types, "add new cards to a Deck/Buff a Deck" (buff winrates, randomly adjust Fun). and give the community 'learning periods' between the changes we apply to see how often it's good to make changes compared to how quickly players learn to optimally play a format.

 

I might or might not have a Simulation & Modelling exam this week. Discuss how dumb this model is and make a better one below. 

 

[Slinky]

Basically, its generally like this:

 

If it encourages interaction; its good for the game

If it does not encourage interaction; its bad for the game.

 

of course, there are exceptions.

[-Griffin]

Basically, its generally like this:

 

If it encourages interaction; its good for the game

If it does not encourage interaction; its bad for the game.

 

of course, there are exceptions.

 

Aye, and how well does this encapsulate the situation where it makes a Deck popular that doesn't encourage a ton of interactions, but all the Decks that fare well against it are super-interactive and so the overall interactiveness of the format is boosted? It also implies that a format with exactly 1 'very interactive' Deck is better than a format with 50 'almost as interactive' Decks, because the first has more interactivity by definition. 

 

We could easily add 'intractability' as a feature of each Deck Type, if it's important for our model (although it might have large overlap or be equivalent to the 'fun to play against/fun to play' features).

 

It's not hard to actually run this simulation once you have good models for things, and from there you can test strategies to change the format (make popular Decks more fun/interactive while slightly randomizing their matchups, make strong Decks weaker while slightly randomizing their fun/interactivity, ect), and see how that changes your heuristic. It might turn out that nerfing/banning un-interactive cards is far more effective than adding new interactive cards, or vice-versa.