Tuesday, 26 December 2017

Option Density

There is an old MtG rule of thumb that says the player who spends more mana in a game of magic wins the game. While certainly a long way of 100% accurate it is still a strong trend. Magic is incredibly resistant to general rules, the game is so broad and complex there are (paradoxically) always exceptions, there are times to split Fact or Fiction 5-0 and such! It is best to avoid making sweeping claims or statements involving the dreaded "always" term when discussing magic. With that all in mind I have been observing an incredibly strong trend in cube. As the title might have hinted at, the player with the greatest option density is the one who is most likely to win. This is certainly a less strong trend than the mana spent claim but it does have some nice insight to offer just in understanding it as a core aspect of magic.

Renegade MapI started to appreciate the concept of option density when I was trying to break down and understand the card quality effects on offer in the game. The better ones typically gave you more options and that rather obvious nugget of insight has stuck with me since. Then, more recently I was wrestling with the issue of why one drops are just so damn good in the cube. When a mere three drop needs to be off the charts good to get a look in to the cube but basically any one drop with 2 power, 2 damage, or the words "draw a card" on it and you have not just a cube playable card but a card that will often see a lot of action. Renegade Map gets cast well in excess of ten times more than a bomb finisher card like Hazoret and is also played well over four times as much. It rather all fell into place in my head. The strength of one drops derives significantly from the greatly increased option density they bring to a game of magic. The underlying reason for one drops being good is revealing of an aspect of magic that is both obvious but also ethereal. When I say that the player who won had more option potency over the course of the game that sounds entirely reasonable but not something you can then imagine a way to replicate. When we start to look at it in terms of option density we can begin to understand how we are going to take advantage of this. Good choices and lots of them leads to winning in magic.

I do need to caveat this whole essay. It is very much one of those near impossible to measure things. It only holds true that many good choices leads to winning when you are able to do so while keeping all other things equal. Like, if all things are equal, the better player wins. You can measure the option density easily but you cannot so easily ascribe value to those options. More critically you cannot have all other things equal and yet have differing option density. Other things have to be different to give you those greater options! Further more, the concept takes no account of matchups. Option density works quite well in cubes and in limited and in some constructed formats however in something like standard it rather falls apart. You may well have a fairly option dense deck that just has a weak matchup against an option light deck. More contained metas will not so readily adhere to the trend of option density leading to greater chances of winning. Option density is one of those more fundamental things in magic, like mana curves or consistency, or power to cost ratio, it is just something you want to understand and appreciate. It is an SI unit of magic. It is often the reason to why a card is so good or why a line of play is optimal. I find I often take a "needless" hit in combat when I have instant removal in hand. I let them hit me, I see what they do post combat and then I remove their dork in the end step. The reason is often put down to information but I also like to think of it in terms of increasing my option density. I am paying some life to have more options. I am happy to pay a few life to upgrade the potential target value on my removal spell in a lot of situations.

Adanto VanguardSo, let us consider what many would think of as a great opening hand. We will have in it an Elite Vanguard, an Adanto Vangaurd and a Brimaz, King of Oreskos. With this we will have three Plains and for your last card you can choose between another Plains or any four drop of your liking! This is perfect mana efficiency and curve with nice high power level cards that all work towards the same end. So, in a classic sense this is a great hand however I think conventional wisdom misleads us. Now when I look at this hand what I see is a hand with basically zero option density. The only option you have at any stage before turn four will either come off the top of your deck or it will just be doing nothing instead of something, which is rarely going to be strong... My ideal openers for most archetypes in cube would typically be 3 lands, a pair of one drops and a pair of two drops. This kind of hand simply has a much higher option density than the former hand. Not only does it offer four ways of curving out to turn three with perfect mana efficiency (as opposed to just one) but it also accommodates potential draws more kindly. Again, this must be understood in terms of averages, having two comparable one drops is less valuable than having the option on a proactive threat or some disruption, the latter will be a much more meaningful option generally.

Now the real difficulty is evaluating the worth of an option. Not all choices are equal and so you want powerful options rather than just as many as you can get your hands on. Most things in magic are partly quantifiable, you can asses their worth in mana terms or card terms or some amalgamation of physical resources. Information and options however are incredibly hard to quantify. These are the ethereal resources in magic. To make matters even more complicated these effects will not have a fixed value. There are times having a look at someones hand will be worth almost everything you have, perhaps 19 life and the rest of your hand and mana! Other times a look at someones hand will be utterly worthless. The same can be true of physical cards and effects that are more tangible but it is usually less dramatically so. I cannot really offer much in the way of a guide to evaluating the worth of options and information with them being so vague and varied. The only real thing to do is play lots and think about things. Experience and practice will improve the worth of options and information to you as well as help you guess at their value. The more you understand the core concepts in magic, such as option density, the more value they will have to you and the better you will be able to judge that value.

Glasses of UrzaI can at least provide a nice illuminating little example of how information and options scale with each other very well. Let us try and consider the relative value of a Gitaxian Probe for the two starting hands we discussed earlier. In the aggressive white hand with zero options a look at their hand may give you a good idea if you are going to win or lose that game but it isn't going to have a significant impact on the game because your hand has such limited alternate lines of play. You may elect to not run out your Adanto Vanguard because you see a Disfigure and you want to try and bait it with something else. Your Probe can give you information that does give you a relevant choice. It turned the previously bad do nothing line of play into one with some merit. For the hand of one and two drops however the Gitaxian Probe is far more likely to have a relevant and significant impact. Based on what you see you can much better evaluate the real values of your four distinct lines of play and choose the best one with greater confidence. The more information you have the better your options become. Information can make a seemingly terrible play become good in the case of the do nothing instead of making the Vanguard. All options gain value with information and often the low value options gain the most. This demonstrates that having options is of value even when they don't seem like good lines of play.

You don't need Probes, Inquisitions or Glasses of Urza to obtain information in magic. Information is available in many ways. It comes naturally as your opponent physically shows you things by playing them or revealing them with effects. It can be inferred by the decks people are playing which lets you make educated guesses about what might be in their deck which in turn can be used to predict what is in their hand based on how they have played thus far. You can just bypass or supplement this logical inference and try to read what people have by their body language and tics. You will get information as the game goes on and therefor the more options you have at your disposal the more you will be able to scale it with the information you glean.

Izzet CharmA good way to get a foothold into understanding the value of options is to look at modular cards. If you break them down and turn them into parts you can get an insight into what you are paying. Izzet Charm is a nice easy example. The card is borderline cube worthy which makes it a pretty decent card. Broken down however it is pretty much a Shock, a Spell Pierce or a Careful Study each for an additional mana. Your extra options are seemingly worth half a mana each what with there being two of them! Now, that isn't fully revealing as to how the cost of options scale as this is half a mana nominally or it is +50% of the cost of the effect. It is harder to test so easily further up the curve as there are no cards so convenient as Izzet Charm for dissection in the four mana range. You can also look at it as just an option on not-Careful Study rather than two alternate options and this would make the nominal cost of an option closer to one mana and not the half mana the other method suggests. The reality is somewhere in between with jsut these two effects and with many more other effects also further changing it too! Suffice it to say it seems much more like a nominal mana cost all the way up. Abrade and Doomfall suggest the cost of the option is a little higher at a full mana but then they are offering more powerful pairings in a single colour. They support the argument for looking at the cost of an option in terms of a not X as opposed to specifically Y. You would then look at Y and consider the value of not Y and factor in both.

Good options can be well worth an extra mana but it is not quite that simple. As already stated, there is a huge range on the value of options. A fixed mana cost can only be ascribed to an average result, or better still, an acceptable extra cost on the base effect for when the option holds no value. The option on a card might be game winning but the card isn't going to be playable if mostly that option is blank and it costs more than a mana more than a card that does the same except for this rare bonus option. An option should be looked at for cost purposes as if it were a blank meaning that a good option should be affordable when operating at its floor. The power of the option is measured by the ceiling, scaling and frequency of the good outcomes. You need to have it all, the low cost and the potential for good to come of it. If you can perfectly evaluate the value of everything else the value of options becomes simple algebra. If mode A on a binary card is consistently useful and powerful (in other words comparable to something you would play without option B attached) with an average value X and mode B has zero value 90% of the time and 5X value 10% of the time then the value of mode B is 1.5X. You add them together due to the broad playability of mode A and as such the high variance mode B offers quite a lot of value to the card. This gets less simple when we start to consider increasing instances of mode A not having value and the resulting value of the modal card is more like an average of the expected value from modes A and B.
Cryptic Command
This is all well and good when contained within some modal one off card but for yet further complexity we should be considering the interaction of all of our cards. If we can get increased value from the effects of a spell due to the flexibility of that spell then we can do the same with our whole deck. This is where we really come back to the one drops. One drops have the most modes of interaction with your other cards than anything else (other than free spells of course, but I don't need to write a dissertation on why those are great!) and as such they afford the most scaling of extra value due to extra options with your other cards. Elite Vanguard and Shock turn out to be good for surprisingly similar reasons to why Cryptic Command is good!

We are happy to pay up to an extra mana on cube worthy effects for the option on another option! We are also happy to throw a card payment into the mix with examples like Vampiric Tutor and Faithless Looting supporting that assertion. With mana and cards being the two primary resources in magic and options being worth either or both of them it is pretty clear options are a big deal. Cards like Ponder do nothing but give options! It is easy to look at a modular card and see three or six distinct modes or however many ways to play it there are. It is relatively easy to count how many ways you can differently do a card quality spell too. These are the one shot option injections some spells provide. Typically the cards that offer the most options are things that are in play for a while. Ideally those with abilities, perhaps free ones you can use at any time. A card like a Carrion Feeder, Cryptbreaker, Kytheon or a Mother of Runes, a Grim Lavamancer or a Town Gossipmonger. These cards will generally out option density the biggest names out there because they come down early and offer all the typical creature options as well as bonus ones for lots of turns. One of the biggest strengths of the energy based midrange decks in standard at the moment is that they have a lot of cheaper cards that have insane option density. When you are sat on a pile of energy and can turn it into 1/1 thopters or +1/+1 counters as you see fit at any point in the game you have a lot of opportunity to outplay people and make the best of the situation. Planeswalkers feel very option dense and in some respects they are. The thing is they don't come down super early, they get killed very quickly or they simply end the game pretty quickly. I suspect the average activations for planeswalkers is going to be around three. It might seem like a lot because more text is involved, the options are more distinct and so forth. In practice however a vanilla creature probably has comparable options over the course of a turn. Attack or not? Planeswalker or face? Block or not and so forth.

Fatal PushVanilla creatures and planeswalkers offer ongoing options fairly slowly. They also both do so at a predictable rate. You know when the walkers are triggering, what they can do and so forth. Their options are all restricted by turn phase and game rules. These kinds of cards are one kind of option density, then you have modular spells that can do different things and that is a different kind of option density. Then you have very narrow spells that do exactly one thing like a Fatal Push. They provide option density by giving you the option on when you do what that card does. Fatal Push has a much greater option density than an Oust despite having a narrower range of potential targets due to the greater number of occasions you can cast it. Even so, having either in hand increases your overall option density when they have targets. Fatal Push has higher option density than Oust as it is instant over sorcery. It also has a greater option density than another instant card with greater target range such as a Hero's Downfall due to the much lower cost. Not only can you Push things from the start of the game but you can also do so in combination with doing other things at the same time with much greater ease further increasing the option density difference.

The last distinct type of option density generation I touched on earlier, they are the things in play with the cheap, instant speed, repeatable abilities. Lotleth Troll is a good example as is Arguel's Bloodfast, Walking Ballista, Deathrite Shaman etc. They have repeatable, instant, and cheap (or free!) effects that can be used at any point in time. The option density is pretty extreme with such cards and it is a big part of why these cards shine. The key thing to remember is that it is not just how many different things a card can do or how many times it can do them that lead to option density. Simply being able to do one specific thing at a wide range of occasions is a great way to obtain option density as well.

Thraben InspectorAnother good way to understand option density is to appreciate why Thraben Inspector is so good. Broadly speaking the card adds up to a Merchant of Sectrets, that extra toughness is not the reason one is a world better than the other. Thraben Inspector is a great deal better than Sea Gate Oracle as well and it adds up to rather less than that. What makes Inspector such a great card is the huge array of relevant options he brings at such a negligible cost. His option density is very high indeed, even discounting when you use the clue. Just when you make him combined with the many things you can do with a dork in play each turn add up to a lot pretty fast. Sure, it is not anywhere near the option density of a Deathrite Shaman but then that is one of the best cards in magic. Deathrite is also not a free inclusion as it doesn't come with that redeeming clue. You don't always run the Shaman when you can because your deck might not support it properly. All you need to support Inspector is white mana!  It is his low cost that ensures you can make him from the get go, you start the game with the option to use him at most stages. He is a lot more option dense than a seemingly more option dense cards like Savage Knuckleblade simply because the Inspector is relevant in hand and play from that much sooner. Thraben Inspector is not powerful much like Merchant of Secrets is not powerful, Inspector is good because it is option dense. It has very little impact on your resources and returns a significant array of options making it one of the most playable, sought after, and played white cards in the cube. It it not really more option dense than any other one drop dork, that is a strength they all share. Option density I would say counts for more than the mana efficiency reasons of why you play one drops so heavily in magic. So, yes, all one drop dorks are on average decently option dense over the course of an average game and this makes them valuable. Inspector is so good because it provides this value at a negligible card cost.

Understanding option density and the relevant impact it should have on a game should help in all areas of your magic game. It is useful for card evaluation, it is useful in deck design and useful in making in game choices too. I think all magic players are all well aware than options are valuable, how they get them and so forth. The reason there is plenty of discussion and content on things like mana curve but little to none on option density is not ignorance in the community but the ethereal nature of option density. You cannot so easily put numbers to how valuable an option is and it is all so entirely contextual. For the most part "options are good" has been simple and accurate enough to be all that is really needed on the matter. It is all you can say in the general sense and beyond that you need an exact context to be defined to say anything else of use. This essay has been fairly hard work writing and probably comes across a lot like a first draft! Ultimately all I feel like I have written is "options are good" and "as you get better, you will get better". I am not sure I offered any concrete and practical ways to implement the understanding of option density. The hope is simply that any greater understanding is part of what leads to getting better and that by reading this you have gained some insight into the game and are now better!

No comments:

Post a Comment