Saturday, May 24, 2014

In General: Advantage Theories: Metrics

Hello and welcome to In General. In this series we talk about broad topics related to the game of Magic. In today's article we will be discussing advantage. Advantage is a word that gets used a lot in coverage or commentary on games. It is simple in theory: the person with the advantage is the person more likely to win that game. The tricky bit is to analyze the game state and decide who has the advantage. Boards in Magic can get very complex. Even at their most simple, they are constantly changing as players acquire new cards and can take more actions on each turn.

Many Magic writers have discussed the topic of advantage theory throughout the games history. Names like Zvi Mowshowitz, Michael J. Flores, Patrick Chapin (congrats on the PT Win), have had formative influences on the development of these theories. Treatise on this subject have been as specific as single game analysis and as broad as full-length novels.

No single theory is perfect for determining a victor ahead of time and there are several different metrics by which we can measure who has the advantage. Let's take a look at a few important ones:

Advantage Metrics

Mana Advantage - Who has access to more mana? This implies that more mana means the ability to make more plays or more impactful plays. This is a good metric for control mirror matches, but isn't as good when lands are 'dead draws' such as in aggro decks or late game limited scenarios. If you find yourself wanting to draw a land at all points in the game, that is a good signal that the having the mana advantage is important to winning the matchup.

Card Advantage - This is about who has access to more cards. Count up all the physical cards that you have in your hand and add that to the number of cards you have in play. Whichever player has the higher total has the advantage in cards. This is an important statistic in any mirror match, or in any match where the winner is likely to be decided by the 'last threat standing'.  Any deck that mixes both threats and removal cares about card advantage because having more of either means you can simply overwhelm your opponent. There are problems with this though:

1. This metric assumes all cards have a standard value or are at least similar in value. This isn't true; value is both quantum and variable. Island has less impact on the game than Cruel Ultimatum, but early on the game you would rather have the Island because you can't even cast Cruel Ultimatum yet.

2. Some strategies don't depend on using their cards in an economical way. Mono Red Burn for example. This deck operates by discarding its own cards as they are played, exchanging cards for the opponent's life points. It is true that it takes a certain amount of burn spells to kill and thus some measure of card advantage is worth counting, but every card over that theoretical 20 damage mark is simply irrelevant.

Sometimes it is better to discuss Virtual Card advantage. This takes into account a more detailed assessment of the game state and the decks that are involved. Excess lands aren't useful to an aggro deck, so they won't be counted as cards. Creature tokens can be relevant to the board state, but they aren't a physical card. There are more examples to explore, but in short: a virtual card is something that isn't a card, but still 'counts as a card'. Conversely, even if you lose access to a physical card, it may not be a loss in card advantage if that card was already dead, i.e. not useful.

Resource Advantage - Resource advantage or materiel advantage is simply an aggregation of all your resources. Whoever has more of these total resources has the advantage. The problem with this valuation is deciding what weight to place on each resource. Simply put, not all resources are equally valuable to each deck. Storm Combo needs a critical mass of card draw and mana, but doesn't really care how many cards are left in their deck. Ad Nauseum requires a high life total, but once you translate that life into dozens of cards every other resource becomes abundant. Dredge would rather have cards in the graveyard than in the hand and some Dredge decks don't even require any mana to operate. What is the pattern here? 'Unfair' decks tend to be hard to evaluate from a resource angle because they are using specific combinations of cards that, when utilized in concert, create more than the expected value of those cards.

Tempo Advantage - Tempo or time advantage is a measure of how many turns a deck will need to win. The deck that can win in fewer turns from the current board state is advantaged. This is much better for evaluating unfair decks, but there are still a few problems. For one, tempo doesn't necessarily have to come in full turn increments. Sometimes you can pick up bits and pieces throughout the game that will eventually snowball into a large advantage later. Secondly, some decks don't have a specific time frame for when they want to kill the opponent. Consider the match-up of aggro vs. control. Aggro wants to kill a.s.a.p., but control decks only try to end the game once control of the game has already been established. In many of these games it seems as though things are 'over' long before the game actually ends. Either the aggro deck has tons of burn left in hand to kill the opponent whenever it is convenient or, on the opposite side, the control deck might be slow rolling a board sweeper which will make the game unwinnable for the opponent, but doesn't actually kill them.

Fundamental Turns - What we are discussing here is the Fundamental Turn. A turning point in the game that signals when advantage has shifted firmly into one side's favor. An example: Modern Splinter Twin combo. On turn four they will create infinite Pestermite tokens and attack for lethal. If they get to untap on turn four unmolested, they can simply combo off and win immediately. You must do something to disrupt them by that time or lose the game outright.

Inevitability - A consequence of the fundamental turn is Inevitability. If an aggro deck doesn't win in the early turns of the game, their chances of winning drop dramatically. This is the idea that, rather than trying to win by a specific turn, some decks chances of winning go up incrementally as long as the game goes on, edging ever-closer to certain victory. Take a look at this totally scientific chart that I made to illustrate:


What are the inflection points on this graph and what do they mean? Well, the aggro deck will be amassing forces and attacking throughout turns 1-3. On turn four or so though, the control deck will cast a board sweeper which dramatically disadvantages the aggro deck. Turns 4-5 are spent doing nothing or casting more Creatures which are now irrelevant. On around turn 6 or so the control deck will deploy a massive finishing threat that the aggro deck cannot beat, which further drops their chances of winning near to zero. Ever resolute, note that the chance of winning approaches, but never actually reaches zero. THERE IS STILL HOPE! A top-decked burn spell or Haste Creature can still offer some small chance of victory.

Are you confused? Do you not quite understand what the fundamental turn is? Can two decks both have inevitability? Grandpa, why are you so bad at using MS Paint? Not to fear Zoners. These questions will all be answered in due time. Specifically, future In General articles.

The main idea that I want you to take away from today's post is this: there are many ways to think about advantage in Magic, many ways to GET an advantage, and each has specific strengths and weaknesses as a system of measurement. Next week we will be discussing two more advantage theories in-depth. Interaction Advantage and Mana Sum Theory. I am singling these two out because they are the most advanced, most developed, and most accurate predictors of success that we have.

See you next week.
-GG

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