ktkenshinx wrote: ↑
2 months ago
(the linear to nonlinear spectrum): How many different decision trees does a deck pose in any given game/match? (Of course, this might be matchup dependent)
(the unfair to fair spectrum): How far ahead of the one card per turn, N mana on turn N, and N mana in total spells does the deck get?
(the non-interactive to interactive spectrum): How frequently/infrequently does or can the deck interact with resources on the other side of the board?
I want to write a bit about decision trees, because this is something I actually looked at rather in depth a couple years ago. People may (or more likely, may not) remember some of my writings back on MTGS where I went about making a somewhat rudimentary AI that could take lists of cards and play Magic. I would have two decks play each other with various deck lists, then analyze them for what cards over/under performed in each list. Decisions were made by a heuristic of clock speed, essentially, winning before your opponents estimated turn to win. This only worked for non combo decks (aggro, midrange, and control all handled this heuristic very well), but it gave a lot of insight into decision trees.
As I would look over the data from matches, there would naturally be decisions on each turn. Where you had various sequences of plays available, each of which could lead to different results on the heuristic. Most decks that I examined, followed a pattern of having their number of good options gradually increasing as the turns went by until about turn 4 or 5 (it has been a while so I don't remember the specific turn in detail). At that point mana would cease to be the limiting resource and card rate would instead become the limitation. As such, the decisions that needed to be made shifted from making plays from your hand, to attacking and blocking.
After realizing this, I started playing a lot with the idea of card velocity. Certainly not a new concept by any means, but I would brew decks that essentially would focus on trying to play a lot of low mana cards each turn that could replace themselves, plus some ramp to actually get there. I played with this concept a lot in Nic Fit in Legacy but tried it in Modern too with Experimental Frenzy in both Jund and Affinity to good success.
So, I want to apply this to the definition here of being linear and how you best measure that. Think of the game like a tree, lets say that an opening hand is 3 lands (fetch, shock, basic), 2 1 drops, a 2 drop, and a 3 drop. So your turn 1 decision is playing a land, which leads to 3 decisions, and a 1 drop (for the sake of simplicity lets say both 1 drops can be cast by the basic), or no play. So you have 3 decisions for the land, 2 decisions for the 1 drop (I'm going to ignore the no play option). So turn 1 for that deck results in 6 distinct outcomes.
At some point I built a spreadsheet and some formulas to measure score in this form. I called it a complexity score, based off of the idea of decision trees. It's modeled fairly closely on the game complexity idea, which can be read about here: https://en.wikipedia.org/wiki/Game_complexity
Actually, while I was doing this, I had emailed MaRo at one point (I used to email him about Magic AI all the time) and even had a short private discussion on this concept (he usually doesn't respond to emails but he did to this one), and it turns out that internally Wizards has these metrics on cards/decks to some extent though I'm unaware as to how much they use them, or how they're measuring it.
This probably wouldn't help much as far as the fair and interactive criteria go, but linear by the definition provided is something that very much can be quantified, meaning that statistics can be compiled on it and it can be measured.