Comment by nwiswell
3 years ago
> My goal was to be able to compare decks to tell you which one was "better".
This would be a really out-of-the-box way to compensate for the deck quality bias I allude to in my other post -- normalize the effect of the deck on game outcomes by using a static "deck quality" score.
I suspect that coming up with halfway decent "deck quality scores" is an extremely difficult problem, though. It's not much of a leap from there to imagine using a computer to solve for the best possible deck in the format, the implications of which are terrifying for competitive Magic (and would be priceless to card speculators)
I think that it's not possible to normalize a single 'deck quality' score as the effectiveness of the deck depends on its opponents, you can have a deck that's good against some decks and weak against others in an intransitive manner; so the deck quality is conditional on the frequency of other decks in the 'competitor pool' i.e. the metagame. Game theory states that if there is not a single dominant deck (and I think that there would not in MtG) then there should be a Nash equilibrium of mixed strategies e.g. I pull out deck A with x% probability and deck B with y% probability, but with MtG rules that likely involves a distribution of many decks with different counterstrategies and counter-counter-strategies.
Deck quality scores is a huge problem, but you're absolutely right, it quickly bubbles out into exponential problem spaces. For example, even among a given Commander deck selected for a given matchup of `x` players, that deck list could have changed each of the last `n` games.
For this reason, the "assume a sphere with no friction" joke here is that deck selection, lock-in / mulligan processes, information asymmetry, and turn order, all being assumed to be equal and at that player's local maximum.
I was starting out with baby steps related to how well balanced your mana was. I would calculate the likelihood of a particular permanent being cast on turn #0-n. Never got to the point of creating a single index to score a deck overall. I had a long way to go. But I imagined taking some clever machine learning algorithms to help find suggested cards and swapping those in to create suggested decks.
And I imagined this all as a service people would pay for, lol.
I like analyzing any given permanents chance to be cast, that's neat. Did you model each card's power / importance at all or were they all treated as equal?
The player AI driving the game would score a permanent based on things like power, toughness, cmc with varying weights. And it would use that score to decide which permanent to play when it could cast more than one. A pretty simple model but probably an effective starting point.
Actually, it was a bit more abstract: it scored a game state where it considered this players permanents, the opponents permanents, this players life total, opponents life total(s).