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The Beautiful Struggle – Lost in the Shuffle

I am coming to you today with a shocking revelation: sometimes, Magic Online players do not draw enough lands. I know that this must be an unknown concept to you, since we all have drawn sufficient lands in every single game of paper Magic that we’ve ever played. However, I assure you that every time I log on to Magic Online, there are people who are complaining about this odd phenomenon, which has acquired the nickname “manascrew.”

As I mentioned in my last round of dailies — My last daily ever, I guess, until The Great Scouse figures out what he wants to do with that article format — I recently obtained Magic Online, and I like it a lot. It’s just like playing Magic in person, except I can do it any time I want to. I feel like MTGO has made me a lot better as a player, although I have had to spend a fair amount of money for that experience.

I am coming to you today with a shocking revelation: sometimes, Magic Online players do not draw enough lands. I know that this must be an unknown concept to you, since we all have drawn sufficient lands in every single game of paper Magic that we’ve ever played. However, I assure you that every time I log on to Magic Online, there are people who are complaining about this odd phenomenon, which has acquired the nickname “manascrew.”

Okay, enough with that joke. I doubt I could have filled a whole article with it anyway. I’m sure you can tell where I’m going with this. Everybody complains about their mana problems, but when you have that many games of Magic going on in one day, you get a lot more complaining on the whole.

Manascrew happens in every format except Momir Basic; you can’t prevent it. One of the first tough lessons that we learned when we started playing Magic is that losing with uncastable cards in hand is a terrible experience. Most Collectible Card Games are themselves defined by the possibility of resource screw. Although I played VS System briefly because I had been told “you can’t get manascrewed,” it turned out that many decks depended upon curving out perfectly, so you could get creature-screwed by missing your curve at a key point.

It’s often said that the skill most important to the best players is the ability to mulligan correctly. The gain from mulling well is that you are able to avoid manascrew (or at the very least, minimize the damage you take when you are manascrewed). Thus, whenever I have these problems, I’ll occasionally complain, but I’ll also try and look at my own games, to see if mistakes might have been made that resulted in the mana problems.

This applies equally well to the opponent’s mana problems. A good example comes from an RGD 4322 that I did about a month ago — yeah, yeah, I know there’s no profit in the 4322 queues, but what can I say? I love drafting RGD — where I had a typical all-colors-but-Green deck that made it into the finals against an opponent with a quite spicy U/B/R deck. In game 1, his rather blah draw was destroyed by my Ribbons of Night; in game 2 he owned me with his Red cards, which included Electrolyze, Steamcore Weird, Ogre Savant, and other first-picks.

In game 3 I kept a slow draw, but my opponent’s draw was practically inert: he played Island, Swamp, Island on the first three turns. On turn 4 he did a main-phase Train of Thought for one, and then played a second Swamp. On turn 5 he transmuted Netherborn Phalanx into Twisted Justice (which didn’t make much sense to me since my turn 4 play was a Soulsworn Jury) and had no subsequent land drop. He did not draw a Red source for the remainder of the game, and upon conceding he revealed a hand that was obviously full of spicy Red cards. He was not pleased about this turn of events…

[name withheld for privacy’s sake]: this is crazy good luck for you
mm_young: maybe u kept a bad hand if u have no plays turns 1-3?

When you do the math, you see that my opponent was probably right that the odds were in his favor. I assume my opponent kept two islands, a swamp, Train of Thought, and unplayable cards on the draw. He has three draw steps to see a Red source while he plays the lands in his hand, and then a fourth draw step on the turn where he played the Train of Thought. He claimed to have eight Red sources in his deck including Izzet Boilerworks. So, the odds of not hitting a Red source on or before turn 4 are (25/33) * (24/32) * (23/31) * (22/30) = 31%.

Additionally, if my opponent had drawn a Blue source on or before turn 4, he could have spent turn 4 by playing Train of Thought for two; this would not have guaranteed a Red source, but it’s a play that will justify most keeps for that format, in my opinion. If my opponent had a total of eight Blue sources in his deck (the amount I would play if I had Train of Thought and as many important Blue cards as he had shown me), that’s one of fourteen cards that he needed to hit on his first four draws (if you thought it was sixteen cards, you counted Izzet Boilerworks twice and you forgot that he had an Island in the opener). The odds of this not happening are (19/33) * (18/32) * (17/31) * (16/30) = 9.5%. I needed a calculator for precise figures, so I’m not saying you should be able to do this math in your head during a game, but I was able to estimate within one percent using pen and paper, via the fact that 24/32 = 3/4 and 18/32 = 9/16 = 3/4 squared.

So my opponent definitely made a reasonable keep on the numbers. You could argue that my post-game comments were still relevant: even a good keep on the numbers is still risky if you have absolutely no plays in the meantime. Or, you could argue that the keep was just fine; as I said before, the Train of Thought might have motivated me to make the same decision my opponent did. I’m sure I’ll get comments to either effect in the forums.

The point is that you can’t expect to win off either decision. You can be around nine-to-one to hit a useful land in his first four draw steps, like my opponent just was, and still not get there. Conversely you could get there on the Red source and then subsequently be mana-flooded. It’s the nature of the Beast.

Of course, when you’re playing in person the Beast consists of your own two hands, but it’s not so on Magic Online. When you have an automated shuffling system, complainers have a ready-made target for their wrath. Let’s face it, the MTGO shuffler is a pretty easy target for bullying: it can’t run away, it can’t fight back, and it’s always sitting there acting like it’s all better than you and stuff.

There are players who would like to think that Magic Online is such a cash cow for Hasbro and Wizards of the Coast, that they would have no problem with a little corporate skullduggery to protect it. The rancored_elf lawsuit is all the proof these players need that the WotC can be ruthless when dealing with consumers, if it needs to be. These people are obviously willing to believe all sorts of stuff about how cheap and / or dishonest the WotC might be…

[name withheld for privacy reasons, commenting after a server crash]: hey, they just make millions of dollars a day – no reason to ever upgrade or maintain enough bandwidth!

However, the Legends fiasco also taught the WotC a useful lesson: your players have the capability to prove when something goes wrong, and they love the game so much that they will sue the pants off of you if they can prove you messed with it. Of course, they also know that a nontrivial number of us players are mathematicians and / or computer programmers. So it does not make logical sense for the WotC to engage in any skullduggery with the shuffler, since the potential financial retribution would make the bath they took on the Legends sorting look like a Turkish massage.

(Personally, I believe that any corporation is capable of skullduggery — plus, I just like the word “skullduggery” — but it’s not like the WotC are Enron, where the whole of their business depends upon the alleged dishonesty. No reason to muck with the shuffler when you’re making a ton off of paper Magic, I say.)

Putting aside the pop-psychology about whether or not the shuffler would be messed with, the software end is fairly well-documented. Unlike most online poker sites, MTGO does not have an easily-accessible page from which you can find out the technical information about their card-randomization techniques. However, all MTGO Adepts have a link which they can give you in this situation (Thanks to Adept_Sentinel for being the one to give it to me), leading you to this Wizards message board with information about the shuffler.

If you don’t want to click the link or navigate the lengthy thread, I can respect that: one of the reasons I’m here is to do that for you. The shuffler uses the Knuth mathematical technique, which was created in 1958; according to Chris Green at Leaping Lizards, he first implemented the shuffler in code in 1981. Green also relates a few tales of LL programmers who, unconvinced with the shuffler’s unbiasedness, ran some tests that confirmed the proper randomization within “a miniscule fraction of one percent.”

One thing you realize is that most people who are unhappy with the MTGO shuffler don’t understand the meaning of the following phrase, from the very first post on the linked-to thread: “Most people are under the misconception that a random distribution means an even distribution. Random distributions have natural clustering.” In other words, the random number generator returns values evenly along the interval [0, 1], but when the “shuffling” code applies those values to the cards in your deck, clumping can occur, the same as it does in real life. Even if we assumed the MTGO shuffler was not perfect, a “perfect” one using the Knuth method would not evenly distribute land throughout a deck.

Another thing that you realize when you read the giant shuffler thread is that most of the people who are unhappy with the MTGO shuffler are not programmers, statisticians, or mathematicians. Many of them have personal stories, which may be related in detail, but which still don’t cover a sample size of any value. For example, a story like (I’m paraphrasing one comment early in the shuffler thread) “when I added a card to my league deck, that always made it certain that I would not draw it in my next match” might sound damning, especially if related in the right way, but the fact is that one person’s collection of matches for the entire duration of multiple leagues is not a sufficient sample size for demonstrating shuffler problems. Hell, four or five people’s collections of matches for the entire duration of multiple leagues is not a sufficient sample size.

Now, that’s not to say that there couldn’t be problems with the shuffler. Multiple responders to the shuffler thread mentioned the “Asheron’s Call bug,” where the random number generator was in error such that a small number players of that online RPG always got attacked by monsters, to a degree exceeding that of other players. But, as for evidence that this is happening with the MTGO shuffler… well, one poster said it best by quoting incompetent attorney Lionel Hutz from The Simpsons: “Well, Your Honor. We’ve plenty of hearsay and conjecture. Those are kinds of evidence.”

(Note to those folks responsible for the MTGO-related parts of the Wizards’ website: although the thread answered many of my questions, a page similar to the ones the online poker sites have would still be a good idea. Here is a high-quality sample, laden with technical details, from the first widely known online poker site Paradise Poker. Here is a low-quality example — almost no technical information of any value — from Party Poker.)

Now, I’m not saying that if you’re manascrewed or flooded, you should just sit back and take it. Nobody likes losing in such a fashion, and I’ve complained about it more than a few times myself. The difference is that I’m not blaming my opponent, the shuffler, or even myself for the manascrew. I’m not blaming anyone, because blame is irrelevant. Bad luck will get you with or without the blame, and all you can do is accept it and move on. That’s the discipline.

This article written while channel-surfing, and catching a very young Christian Slater skateboarding in “Gleaming the Cube.” Man, I’m getting old.

mmyoungster at aim dot com
mm_young dot livejournal dot com
mm_young on MTGO