Utter Beatings – Average Case

Average Case

It may be cool to hate on Lotus Cobra now, but the initial hype surrounding the card was just absurd. The Magic community honed in on Cobra’s potential, what it could do at its best. People weren’t looking at decks Cobra would actually fit into, or how it would realistically play; it was all turn three Ultimatums and Baneslayers.

It’s not like Lotus Cobra is the only card this has happened with; most every new spoiled card receives the same treatment (though none really present such enticing best case scenarios). Now there is nothing wrong with getting excited about the potential of new cards, to think of what they can do when maximized, but that is no way to go about honestly evaluating cards.

Lotus Cobra is symptomatic of a flaw in how we think about Magic: we tend to be pretty bad at thinking in terms of average case. We do a good job of thinking about the best and worst case scenarios for cards, but the average case, the true value of cards, proves to be pretty elusive.

Take a look at what happened with Tarmogoyf. It’s not like we didn’t see the potential of a two mana 5/6 or better. It’s just that we also saw the potential of a two mana 0/1, and the worst case scenarios seemed so much more likely. It took quite some time, and presumably a fair amount of play with the card, for us to catch on to how good Tarmogoyf was on average.

It is completely understandable that we are bad at thinking average case. It is easy to imagine the best possible scenarios for a card, as well as the worst. It’s easy to see that Lotus Cobra could possibly fuel turn three Ultimatums, and it is also easy to see that at its worst Lotus Cobra will be a vanilla 2/1 for two. It’s also easy to see that neither of these cases is especially realistic. Honing in on what exactly is realistic – that’s more difficult. We can’t just think of one scenario that will demonstrate the average value of a card like we can for the best case and worst case.

Our inability to think in terms of average case is not terribly problematic when it comes to individual cards, as we can reason through how good a card will be on average by comparing it to similar cards. A card like Lotus Cobra shouldn’t be too hard to correctly evaluate, as we know how good so many similar cards are: Birds of Paradise, Noble Hierarch, Devoted Druid, Bloom Tender, Smokebraider, etc. Devoted Druid in particular gives a great anchor for Lotus Cobra. Sometimes Cobra will generate more mana, and sometimes less, but a Devoted Druid that can also swing for two a turn is a pretty reasonable way to look at the Cobra. (And note that Devoted Druid has seen tournament success powering out [card Regal Force]Regal Ultimatum[/card], even almost realistically on turn three, so it’s not out of the question for Cobra to be found doing something similar. But Devoted Druid hardly resembles something broken, and neither does a small upgrade on it.)

For cards without close siblings, like Tarmogoyf, the first Planeswalkers, Path to Exile, the new “quest” cycles, and so on, we are much more lost. With no comparison point to anchor our valuation, we are left to actually work through how good on average a card is going to be, and these cards are evidence of just how bad we are at that.

Where we really get wrecked by thinking in terms of best case and/or worst case is not in evaluating individual cards, but in evaluating matchups and how games tend to play out. Failure to think average case hurts us most when it comes to building and selecting decks. It’s not your deck’s best draws that matter, as those are going to win the majority of games without help. It’s not your opponent’s best draws you need to be concerned about beating, as those are highly unlikely. It’s all about what happens on average.

Be honest with yourself. When you are a brewing a list, are you thinking about consistency, about what your opening hands are going to look like, about how you are likely to curve out? Or are you instead thinking of all the cool things you can do, of what your best draws will look like? Which approach do you think is going to lead to building better decks? When it comes to thinking about matchups, do you focus on the opposition’s best draws, and figuring out how to beat those? Or do you instead have a good sense of what a regular draw looks like, from both your side and theirs?

It’s easiest to think about how decks draw at their best, as that is something we can easily glean from just looking at a decklist. Players who don’t play a ton of Magic, but do spend a lot of time thinking about it (you know who you are), tend to suffer the worst from this. It’s too hard to get a feel for what an average draw is without plenty of play. Jamming a bunch of games can get you a pretty good sense of how games realistically play out, and give you a proper springboard for your thoughts. Without actual experience reigning in your expectations, it’s just too easy to get caught up in what every deck is capable of. Thinking about one deck’s nut draw versus another’s is counterproductive, as it’s irrelevant which deck nut draws better. It is especially important to realize that the best draw versus best draw is not at all representative of how games usually play out, or of the favorite in a matchup. A deck’s very best draws are not only quite rare, but also have no bearing on how well the deck typically draws.

Five-color control, throughout its life in Standard, had the worst nut draws in the format. Literally every single other deck nut drawing would completely smash Five-color’s very best draws. And that never stopped 5cc from being one of the top decks. Against a deck drawing perfect amounts of mana and spells, with a perfect curve, all those [card Esper Charm]draw twos[/card] and [card Vivid Creek]CIPT lands[/card] sure look real awkward. But most often, decks would have holes in their curve, and not hit the perfect number of lands at just the right times, and 5cc would be able to keep up. Suddenly all those [card Mulldrifter]draw twos[/card] and [card Vivid Marsh]CIPT lands[/card] are no longer awkward, but instead are ensuring consistency. Those cards didn’t do 5cc’s best and worst draws any favors, but they sure did make its draws on average very good. It seems like control decks in general are often underrated because their best and worst draws are so unimpressive, even when their average draws are completely dominant.

Don’t focus on beating your opponent’s best draws, as they don’t come up often and you won’t be beating them often no matter how hard you try. If your deck on the draw can’t possibly beat turn two Bitterblossom into turn four Mistbind Clique with basically any other action, that doesn’t necessarily mean you have a bad Faeries matchup. This will only happen in roughly 15% of your games against Faeries, so there’s no reason you need to focus on winning those games. You are much better off thinking through the other 85% of games, which are both far more common, and where any deck changes you do make are much more likely to make a difference.

One last point I want to hit on is that as a general rule, you best improve your average draws by maximizing not your best draws, but your worst. If you have an above average draw, by definition you are a favorite to win. By maximizing your best draws you are gaining percentage points in the relatively small number of games that you lose with an above average draw, and you are probably doing so at the cost of your worst draws. If instead you make your worst draws better, and best draws worse, you gain percentage in a larger number of games. To illustrate, let’s say you are 75% to win a game with an above average draw, and 25% to win with a bad draw, and you can add a 10% chance to win a game you otherwise would have lost to either your good draws or bad draws. For your good draws, you get an extra 10% in 1/4 of your games, whereas for your bad draws, you get an extra 10% in 3/4 of your games. You clearly get more out of focusing on the games you were likely going to lose than the games you were likely going to win regardless (Time Warp in Faeries struck us as a good example of a win-more card during Nationals testing, and for that reason we ended up not playing any in our final version – LSV).

See ya in the comments, where I can’t wait to hear how average you thought this article was.

34 Comments Leave a comment

Matt T says: September 24, 2009 @ 9:16 pm

I was considering ragging heavily on this article until I read the last two paragraphs, which were actually really sound. I think, for the most part, the upper-level tournament community has EXACTLY the right read on Lotus Cobra and its role in the upcoming Standard environment. Nobody of caliber is buying into the Flores ZOMG! school of thought, and neither should anybody be quick to dismiss it. Conley gave one of the best analyses I’ve heard on the card in his article the other day and on the MtGCast on SCG’s site.

Dan says: September 24, 2009 @ 9:46 pm

“If your deck on the draw can't possibly beat turn two Bitterblossom into turn four Mistbind Clique with basically any other action, that doesn't necessarily mean you have a bad Faeries matchup. This will only happen in roughly 15% of your games against Faeries, so there's no reason you need to focus on winning those games. You are much better off thinking through the other 85% of games, which are both far more common, and where any deck changes you do make are much more likely to make a difference.”

When I play against Fae on MTGO, this that percentage seems sooo off. It’s more like 80% of the time XD.

No seriously, great article. Lotus Cobra is not broken by any means but I think it’ll find a home some midrange list since turn 2 Lotus Cobra -> turn 3 Baneslayer/World Queller doesn’t seem too farfetched at all (okay, less than 20% of the time but it’s a start right?)

Nick says: September 24, 2009 @ 10:00 pm

I think that with fetches lotus /will/ be powering out some five drops fairly consistently. I mean, how many lists have we seen that are mono or ally-colored that just run fetches for landfall abilities? Quite a few. Lets say its a naya deck, after a turn two cobra, you could have the red-white, or the blue-green. Even if naya isn’t running blue, it might have that fetch for plated geopede or cobra or somthing. So I do think that cobra will hit five drops fairly often.

That being said, it does comply to the standard ‘it dies to everything’ rule. Even pathing it is fine, since they would have had the mana anyway (presuming they had a land drop). This card is overhyped, yes. But now there seems to be a large number of artcles /under/rating it. There was the inevitable surge of overestimations, and now there are just as many underestimations. This card is great.

Nicholas Gulledge says: September 24, 2009 @ 10:06 pm

My very first thought when I read the Quest cards was “Oh, so it’s like Suspend 2.0″.

I’m pretty sure that when seen in such a light, as cards whose manacost is lower than the effect’s “proper” cost through the implementation of a variable time-cost, it becomes easier to relate to our previous experiences with such mechanisms and value these cards appropriately.

I enjoyed your article.

Andy says: September 24, 2009 @ 10:09 pm

I think a reasonable use for Lotus Cobra is just in zoo. I started thinking about the small things it can do for you, like equip a jitte on the third turn. Little stuff that make the card practical and not a crutch on a strategy.

Randy says: September 24, 2009 @ 10:32 pm

Yes lots of people are going bonkers for the cobra with all kinds of standard dreams.Unfortunatly for them lotus cobra is probably much better when looking at in an extended point of view.Zoo check Bant check some crazy blue green deck check.A great card yes but much better in extended.

Kenseiden says: September 24, 2009 @ 10:51 pm

I know it sounds off-topic, but I face a turn 2 Blosson very often, as ppl usually mulligans wildly into it.

I understand your point on thinking about good/bad hands, but I like to think in decks that can play decent magic against decent hands. Its not like turn1 careful study rootwalla rootwalla turn 2 mongrel, but I think you know what I mean.

also I think lotus cobra on turn 2 is going to be almost as feared as bitterblossom.

josh says: September 24, 2009 @ 11:00 pm

I personally find lotus cobra to be really strong, not for the fact that it powers out the nuts turn 3 baneslayer/ultimatum/etc. But because it allows naya zoo (and i suppose other cheap aggro decks) to play already undercosted spells, such as woolly thoctar, wild nacatl, and ranger of eos early and for less. With regularity as well, while 1 mana does not seem like much (only using basics as an example), that 1 mana is allowing you to play a ranger on turn 3 for 2 powered up nacatls, which are then going to be half price, you see how crazy cobra can be. Furthermore, lotus cobra is not required to make any of those plays impossible without it, it just allows the curve of an aggro deck to be so much father ahead than usual, and considering the whole point of aggro decks is to kill your opponent ASAP, getting to be 1 or 2 turns ahead while getting a 2 power guy is simply just crazy. while everyone is talking about turn 3 baneslayers, im guessing that the meta is going to be turn 3 ranger and nacatl

Adam K says: September 24, 2009 @ 11:22 pm

“I think a reasonable use for Lotus Cobra is just in zoo. I started thinking about the small things it can do for you, like equip a jitte on the third turn. Little stuff that make the card practical and not a crutch on a strategy.”

Actually Andy I think you are buying into a “best case scenario” with that thought. most zoo builds usually only play with about two jittes, so the odds are against your favor having jitte+active lotus on turn 3.

Instead, the extra mana you have on (some of) your turns might not be that helpful. zoo plays very very few lands so you won’t get much worth out of lotus after turn 3-4 ideally, as the deck is designed to not draw excess lands.

Chris Young says: September 25, 2009 @ 12:19 am

Thanks for this article. I think anyone who has played a lot of 5 Color control can really get this concept.

I think people are looking at Lotus Cobra all wrong and one of the comments touches a little on it. Its the little things it can do such as equip or drop another exalted or even be a free creature on the turn you play it. All these little things can add up. Even if its just pulling a path or a bolt out of a hand allowing for your 3/3 to enter play safe and sound. The card is really good and is no less of dead draw than any other accellerator or 2/1 during late game.

One of the things that it also does is allows to play a bit more blue counters without having to really commit to the blue side of the mana base as much.
I mean the fact that you can get a land to enter play with a spell on the stack means that even when hes only got a single mana showing negate can be at the ready still.

And its not like we needed to make Noble Hierarch even better but it does.

I think when you start to think about all the subtle ways a card can effect your average draw or average matchup cards like the cobra seem to be a bit better than you thought they were. No not the second coming of Goyf but not nearly as dismissable either.

The article is excelent and Id like to see more analysis on this with some more specific deck construction thoughts with this idea in mind.

Alex says: September 25, 2009 @ 2:41 am

“also I think lotus cobra on turn 2 is going to be almost as feared as bitterblossom”

And you know why? /Because people focus on best/worst draws!/ I really wish someone would right an article about why we shouldn’t do that…..

lewk says: September 25, 2009 @ 4:01 am

article was above average

Jim says: September 25, 2009 @ 5:02 am

I think this is the 267th article about how Lotus Cobra is overrated.

goldenj says: September 25, 2009 @ 6:45 am

Nice article, and some pretty original thinking and concept.

I think in the statistics at the end, though, you’re really looking at the difference between median and mean.

Increasing the quality of your good draws raises the mean but not the median. You’re arguing that the way to impact games is to move the median forward, which requires eliminating cards that contribute to below central tendency draws. The line about “If instead you make your worst draws better, and best draws worse” is a little loose. What you mean, I think, is that it would be worth lowering the quality of your good cards if it meant raising the median, not that lowering the expected value of some cards helps you win.

Of course, raising the quality of your good draws helps you in games where the opponent also had a good draw, which are some of the only games you will lose with a good draw. With highly tuned tournament decks, this is probably not inconsiderable.

It would be interesting to think about a way to measure, even qualitatively, how good a draw is, and how deck building choices affect it.

Shyft- says: September 25, 2009 @ 7:04 am

Nice article seÃƒÆ’Ã‚Â±or Wrapter. I’m a little sad you didn’t include Goblin Guide in this little exposÃƒÆ’Ã‚Â©. He’s another case of being sweet in the best case scenarios and terrible in average situations. Simply put, GG often is … for the person playing it.

ghweiss says: September 25, 2009 @ 8:34 am

Great article. I got two actual “lightbulb moments” out of it! Please keep writing, about anything.

Pete says: September 25, 2009 @ 9:38 am

“Lotus Cobra is symptomatic of a flaw in how we think about Magic: we tend to be pretty bad at thinking in terms of average case. We do a good job of thinking about the best and worst case scenarios for cards, but the average case, the true value of cards, proves to be pretty elusive.”

The number of comments that overlooked this (which was the point of the article) and instead agreed/disagreed with your Lotus Cobra comments are directly proportionate to the number of bad players commenting.

Great article; great thoughts about average pulls and consistency. Combo players probably have the best view of this idea. Most people assume combo players need “nuts” draws to win, but usually a combo deck’s goal is to make every average draw a winning hand. When you do that, combo wins (as does aggro and control, but combo is more reliant on making this a reality to be good).

Incidentally, this is why cascade (and BBE more specifically) is so good. If your BBE can hit a 3 drop that makes an average draw a good draw, then it single-handedly turns so-so draws into winning hands. And then you have a deck drawing “nuts” hands far more often–even when they don’t actually draw them–aka a good deck.

Good stuff.

Blind Fremen says: September 25, 2009 @ 11:10 am

I’m excited to see some type of “Cobra Affinity” deck that plays lots of lands/spells very quickly. I’m thinking Lotus Cobra, Quests, Harrow, Expedition Map, Armillary Sphere, Khalni Heart Expedition, Ior Ruin Expedition, Oracle of Mul Daya, etc.

Wes says: September 25, 2009 @ 11:55 am

Thanks for the article… It opened my eyes to 5-color… I guess I always understood what it was trying to do conceptually, but I just didn’t understand the how… the draws always seemed so underwhelming to me.. now I know why.

Amarsir says: September 25, 2009 @ 2:26 pm

Excellent article. I am sometimes tempted to build against those “nut draws” since I fear those losses, but you’re right that shrugging it off to play against the average is a better strategy.

McCombs says: September 25, 2009 @ 2:47 pm

I must have missed all of the over-hyping of Lotus Petal Cobra. I’ve easily read 10+ articles this week alone stating the opposite. I won’t even get into Sanchez’s numerous Twitters raging against the poor snake. I think that most players with a head on their shoulders and an ear to the ground see it for what it is… a good utility creature that can be used as a useful tool in the right decks but not as a card to act as the crux of your deck. That being said, I deffinitly want a play set of them but will be happily trading them away this weekend for multiple fetch lands to anybody who is still living in Magical Christmas Land.

JPirkey says: September 25, 2009 @ 3:49 pm

This was actually one of the best reads i’ve had in a long time. While not mind blowing information, it really brings to light a lot of things which go without thought in many people’s minds. Taking a lose less rather than win more approach is one of the least talked about winning ideas in MTG as we know it. Great Job.

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agz says: September 26, 2009 @ 3:18 pm

Lotus Cobra would be like Zoo’s Frogmite during stage one. If you can happen to pair it with Bob, it becomes more effective.

With Zoo being willing to reach into 3cc and 4cc creatures, the Cobra seems fine. This is just speculation given in passing, though, as I haven’t really looked to see if there’s any room for this card, though I would venture to say that such a tempo boost may be worth some slots. I’m getting the feeling from the general community that Cobra is a 4-of or no-of, but maybe this needs re-evaluating (sorry if I’m wrong in this assumption about the community). You don’t really want to draw the card in multiples, in my opinion (for decks like Zoo), but the random games where you drop it turn 2 and gain a tempo boost from it or just use it as some guy to carry a Jitte in the late game seem fine.

newager says: September 27, 2009 @ 5:44 am

I totally over-evaluated Bloodchief Ascension yesterday… I looked at it and said “I have 9 fliers, all with a power 2 or better, how hard can punching through for 2 be?” and I was right on that part. I maindecked it, and played it first turn of the first game of the first match. It was EASY getting it up to 3 counters and that was done by the end of my turn 5. Problem is, Limited is a creature heavy format! My creatures fly! I’m not going to sit back and let my opponent draw into an out before attacking me so I can get some use out of the Ascension, and they aren’t getting many cards into the graveyard otherwise (most of my removal came in the form of bouncing a Journey to Nowhere back to my hand with it come-into-play trigger on the stack. Had to get the judge to confirm to my opponent every single time I did that that it does in fact work). It did 4 damage the whole game and I sideboarded it out every single game 2 for another creature, which honestly would have done a lot more damage anyway. Fortunately, I didn’t draw it game one after that and never had to look at it again, but still…

Chris Young says: September 27, 2009 @ 8:02 am

I like most of the new kicker cards. Solid enough to play without kicker. And Goblin Bushwhaker is just such a good card. The 5/5 Shroud Sphinx was damn annoying. Just in the limited amount of cards Ive seen blue has the weakest common lot. Green seems to be really strong for limited play. Some of the equipment like Grappling hook is sick.

I didnt open fantastic broken stuff so I took this article into account and in the 5 rounds at our store I was never blown out of any game and went 3-2. Even though I sacrificed playing some of the strongest cards (the new Mythic Deamon) because it would add a 3rd color I would have to commit too heavily to for too few [7] cards. (The double/tripple black creature with Cruel Edict kicker)

By staying 2 colors I was able to play solid but not great stuff consistently. I specifically remember the article as I was trying to explain my choices later to other players. I undervalued my Green cards during deck construction and probably should have played them but it would have meant virturally no removal or tricks.

kakashi says: September 27, 2009 @ 3:34 pm

I think that Lotus Cobra is pretty good. It enables a deck to deploy its resources faster. It’s a threat, too. Does it deserve to be a mythic creature? Yes. The reason for this is that the utility creatures for mana acceleration are Birds of Paradise, Noble Hierach, and Llanowar Elves. Lotus Cobra is a creature that’s supposed to be mythic (and/or rare) in the sense that what it does is stupendous and over-the-top i.e. acting like a Black Lotus given the right conditions. It’s not meant to be easy to find and use effectively. In that sense, I can live with it being mythic and costing a ton of money.

I think the problem stems from us players seeing the card as very useful for our purposes and our need to acquire it at the least cost. In that sense, I can see how the feelings of betrayal come into play. Yet I would rather describe the creation of this card as well thought of, not only because it delivers profits to a company who enables fun times for its players, but also because WOTC R&D knew what they were doing. Not all mythics are created equal as can be seen with the 13 planeswalkers. Some are deemed truly useful while others lie in trade binders. That doesn’t make one planeswalker design wrong and the other right. It’s just the scale of value we attribute to cards that hinder us from seeing things in perspective–which I think is the theme of the article anyway.

John says: September 27, 2009 @ 7:34 pm

actually, I won my prerelease this weekend with a 4-0-1 where I was only playing one rare, which wasn’t even a “good” rare. The reason I beat other players was because

1) the deck I built had a low aggressive curve with equipment to support the creatures
2) each creature, though weak on its own, had synergy with other parts of the deck, be it maximing my landfall triggers, using allies strategically or walking past people’s defenses with otherwise evasive creatures.

contrast it with a sealed deck at a 2nd prerelease where I played various bombs and I lost because I built the deck to play the bombs as quickly as possible.

Of course, my average draw didn’t happen to include those bombs and I wasn’t able to insure against my worst draws, since I wasted many card slots to develop into the bombs. I went 0-2 drop.

Insuring against your worst draws is definitely a key to consistent winning magic.

Pingback Zendikar Set Review - White | ChannelFireball.com says: September 27, 2009 @ 10:48 pm

[...] Hitting on turn three with a Machete is pretty busted, but that is definitely best-case scenario. Wrapter wouldn’t [...]

NummaNumma says: September 28, 2009 @ 8:34 pm

“To illustrate, let's say you are 75% to win a game with an above average draw, and 25% to win with a bad draw, and you can add a 10% chance to win a game you otherwise would have lost to either your good draws or bad draws. For your good draws, you get an extra 10% in 1/4 of your games, whereas for your bad draws, you get an extra 10% in 3/4 of your games.”

Utter rofl at this. WOW. If it were possible to play the game, and if you lost, roll a D20 and on a 19 or 20 you win, this would be accurate. That is not possible. What is possible in magic is to add a 10% chance to win. Period. It would not matter if it was added to your good draws or bad draws.

Seriously, wow.

NummaNumma says: September 28, 2009 @ 8:39 pm

“Insuring against your worst draws is definitely a key to consistent winning magic”

Quoted from above. This is exactly as wrong as saying maximizing your best draws is the key to winning.

Maximizing winning is the best thing. Period. If improving your above average draws causes you to win 3% more, and improving your below average draws causes you to win 2% more, you should improve your best draw. This is inescapable.

Pingback How to Evaluate New MTG Cards for Constructed says: September 28, 2009 @ 9:52 pm

[...] Utter-Leyton on using the average case scenario for evaluating new cards instead of the best case or worst case scenarios: Lotus Cobra is [...]

lol says: September 28, 2009 @ 9:55 pm

scenario A-added to best draws-win total 55%
scenario B-added to worst draws-win total 55%

Grungedimi says: September 29, 2009 @ 3:22 am

Hey Josh, I really like this article and I can honestly say I’ve been following the ‘average-rule’ for quite some time now.

I immediately loved Lotus Cobra, but not for the turn 3 Ultimatum crap a lot of people are talking about. Sorry for the crude wording here, but I really really dislike it when players seem to think they will always draw their dream opening hand. That turn 3 Ultimatum scenario is incredibly unrealistic in my opinion.