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Deep Analysis – What Matters

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Friday, November 21st – In today’s thought-provoking installment of Deep Analysis, Richard focuses on What Matters. He discusses the true role of logic, chaos theory, and the effect of miniscule changes on any given game, match, or tournament. This excellent article is sure to elicit healthy debate in the forums.

I.

It is the deciding game in the semifinal match of a Pro Tour, and Wizards of the Coast has attached an expensive camera to the shirt of one competitor. The camera is trained on the cards in his hands as he performs the final riffle shuffle on his opponent’s deck before handing it back.

The camera zooms in, and the riffle shuffle progresses in slow motion. First the competitor’s left thumb moves up just a hair, releasing a card down into the mix. Then his right thumb moves up a mere millimeter, releasing another two cards. The left thumb releases another card, and we observe that it is a land. This process repeats over and over. Eventually the right thumb releases the twenty-first card from the top, a creature, and then the twentieth card, a burn spell. At length, he finishes the shuffle and hands the deck back to its pilot.

Fast forward several minutes. Olivier Ruel, the competitor with the camera on his shirt, is shouting “Don’t look, just slam it!” We are watching the semifinals match at PT: Honolulu. Craig Jones flips over the twentieth card in his deck: Lightning Helix – the burn spell we watched Olivier shuffle into that twentieth position – and the crowd goes nuts! Jones wins the match and advances to the finals!

Crazy. Crazy, but that was how it happened.

Okay, now back it up. Let’s put ourselves at exactly the same moment where Olivier is performing the final riffle shuffle on Craig’s deck. Slightly before we expect his right thumb to release Lightning Helix into the deck, imagine one miniscule change to the scenario: a piece of dust flutters into Olivier’s eye. He flinches, almost imperceptibly, and his right thumb releases the Lightning Helix one millisecond early. A card from the other thumb ends up on top of it, and Lightning Helix is now the twenty-first card in Craig Jones deck. Minutes later, when he flips over his twentieth card and slams it onto the table, it is a land.

Olivier wins and proceeds to the final. There, in this alternate reality, he may even defeat Mark Herberholz to become PT: Honolulu champion. All thanks to a piece of dust fluttering into his eye and altering, ever so slightly, the shuffle that determined his fate minutes later.

In chaos theory, the dust in Ruel’s eye is an example of the “butterfly effect.” The namesake story behind the phenomenon is that a butterfly flaps its wings and causes a cascading series of tiny changes in the wind and atmosphere that ultimately alters the course of something much larger, like a tornado.

Outside Magic, chaos theory is commonly used to predict the weather. It helps scientists look at all the relevant forces in play – a breeze starts out here, and heads southeast, while a tropical storm starts west of that breeze, and heads east, and so on – and then simulate how these forces will interact as time passes.

Say you work out that the breeze and the storm will collide in three days, and you also figure out exactly what type of weather phenomenon will result, and which areas it will impact. Repeat that process for all the relevant forces in the weather system (there are a ton of them to account for, as you can imagine), and you end up with a fairly accurate forecast of the weather in various areas.

The reason you never see the weather predicted much more than a week in advance is the butterfly effect, the dust in Ruel’s eye. Small things that seem insignificant when you’re starting out can come back to have a surprisingly large impact as time progresses. The further away you get from your starting point, the higher the probability that something you once thought was irrelevant will become seriously influential.

If I’d stopped the camera mid-shuffle, pointed at Ruel’s eye and screamed “There it is! There’s the speck that determines the match,” who would have believed me? What are the odds that such a tiny force would have any bearing on the result of the match? There are so many microscopic factors at play at the outset of a game of Magic, you often cannot tell which ones will be relevant later on until it is too late.

You mis-tap a land on your second turn, and you think nothing of it. You wouldn’t have played the turn any differently if you’d had the extra mana available, so it didn’t matter, right?

But it did. It mattered because your opponent noticed. He made a mental note of your mistake. It changed nothing about the next few turns – in fact, it changed nothing about this game. But the next game, when you were ahead and the opponent had the chance to turn the game around with a risky play, he remembered. For his move to win him the game, your play could not be tight. You had to overlook something, and he gambled that you would because he remembered that mis-tap from the first game. Turns out you do overlook it, and he does win, but he wouldn’t have even risked the move in the first place without some evidence that you would fall for it. At the time, you never would have put that mis-tap down as the play that cost you the match, but that’s exactly what it proved to be.

Anything can matter.

II.

In Magic, there are billions of tiny factors at work in every second of every game. You cannot take them all into account; the human mind is incapable of it. So to maximize your chances of playing correctly, you have to quickly eliminate as many irrelevant factors as possible, in order to give yourself enough time to figure out how the relevant ones will interact.

Once back in Kamigawa Block PTQ, I remember watching a player with Gifts Ungiven control facing off against a White Weenie player. The Gifts player was recurring Exile into Darkness to make the White Weenie player lose a man every turn. The opponent had two creatures on the table, one card in hand, and was in topdeck mode.

When White Weenie topdecked and played a Jitte, the Gifts player shrugged. He didn’t think it mattered – after all, WW had only one card left in hand, so even if it was a creature, the opponent’s team had only three or so more turns to live. The Gifts player could clear the two creatures away via the copy of Kagemaro, First to Suffer in his hand, but he wanted to save it for use as a finisher after he had Exiled all the blockers away. I thought ignoring the Jitte was a mistake, giving the opponent the out of drawing several creatures in a row to steal a game the Gifts player should have locked up.

So he didn’t use Kagemaro, instead Exiling a creature and passing the turn yet again. The opponent drew a card – another creature – played it, and equipped Jitte to his remaining man, adding two counters to it in the attack. Now Kagemaro was no longer a solution, as the WW player’s attackers had Flying, so he could just respond to its activation by pumping one creature +4/+4, meaning for six mana the Gifts player would still only kill one creature (so might as well use Exile into Darkness instead).

The game settled into a pattern. Gifts would Exile, WW would untap, draw, swing, and play another flyer to be the sacrificial lamb for Exile – an improbable draw, but exactly the type that would punish Gifts for letting Jitte get active. Gifts lost the match.

We all remember the times we overlooked something important like this, having filed it away as irrelevant when it turned out to be the very thing that ultimately lost us the game. These situations underscore the importance of only discounting a factor when you are certain it does not matter; if you get it wrong, the consequences can be dire.

Less often do we remember the times we failed to double-check that the factors under consideration were truly as relevant as we’d thought at a glance.

Sometimes you will sit and think for a full minute about whether to attack with that last 3/3 or to keep it back on defense. After figuring out how your opponent will block if you leave the 3/3 home, you conclude that a counterattack will leave you dead if you do not have a blocker, so you leave the 3/3 back and attack the opponent with everything else. He blocks with all of his creatures save his one remaining 2/2, and survives the attack at 3 life.

Had you swung with the 3/3, he would have been forced to chump, and could not have even performed the counterattack that you spent so much time accounting for. The time you spent thinking about how to attack had unduly factored in an irrelevant consideration; who cares what impact a theoretical alpha strike counterattack would do to you if you attack to make such a response impossible?

Jon Finkel sagely advises us to “focus only on what matters.”

To focus on what matters, you must first know what matters.

III.

Years ago, I was watching the finals of PT: Philadelphia with some friends. At the time, no American had won a Pro Tour since 1408, but Gadiel Szleifer was on a path to remedy that. Sporting his Taking Back Sunday (get it?) shirt and facing off against Kenji Tsumura, the best player in the world at the time, the stakes were high. We were all rooting for him.

“He’s got this,” I said.
“Knock on wood,” says a friend.
I chuckle. “Man, how crazy is it to see maindeck Time Stop in the finals of—”
“No, seriously,” the friend cuts me off. “Knock on wood, right now.”
“What?”
“Richard!” another joins in. “Just knock on wood!”
I cannot believe what I am hearing. Knock on wood? What, like he’s going to lose if I don’t?
“No,” I say. “I’m not going to knock on wood. I’m taking a stand against superstition. Now watch him win anyway.”
At this latest repetition of my prediction (apparently, each time I said this I was decreasing Gadiel’s chances of victory), someone actually ran the ol’ fingers-in-ears, “lalalalala can’t hear you” on me.

There was a wooden coffee table right next to me, but I had a point to make. When it became clear that I was not, in fact, going to knock on wood, they decided to “knock on wood for me.” I was skeptical that this would satisfy the strict requirements of the knock-on-wood superstition, but it must have done the trick, because – against all odds, considering I hadn’t personally knocked on wood – Szleifer won anyway.

Still, when you think about the butterfly effect… were they so crazy?

For me to rap my knuckles on the nearest source of wood – let’s say the coffee table – and to have the vibrations caused by this action set in motion a series of molecular domino effects that ultimately result in cards shifting miles away, and specifically enough of them shifting in just the right way that Kenji wins instead of Gadiel… this would be, shall we say, “somewhat unlikely.” Realistically, no matter the angle or ferocity with which I attack that St. Louis coffee table with my knuckles, I am not going to alter the outcome of Pro Tour: Philadelphia.

However, one could have just as easily the same of that fateful piece of dust that headed for Olivier Ruel eye.

In both cases, you have factors that seem so incredibly unrelated to anything you care about. A dust speck determining the finals of the Pro Tour? Knuckles on wood determining the finals of another? They both seem to have no impact whatsoever, yet one will make a very real difference and the other will not.

When evaluating each of the factors I’ve talked about today, I used deductive reasoning to choose the ones I thought mattered and the ones to ignore. Logic told me that the active Jitte could matter, that the counterattack resulting from holding the 3/3 back would not matter, that the dust speck headed for Ruel’s eye would not matter, and that knocking on wood would not matter. As the dust speck turned out to matter quite a bit, I got only three out of four correct. Could I have come to better conclusions? Absolutely; without question, I fell short of a perfect score. But to do better, I would have had to go against reasoning in the case of the dust.

In other words, I would have had to guess.

If, instead of reasoning out whether each factor was relevant, I had simply guessed on all four of them – or even just flipped a coin – I would have had a slim chance of getting all four correct. With logic, which should lead me to the same conclusion every time, I had no chance of getting them all right.

(One might argue, then, that I should have used logic to choose the first three, and should have only guessed on the fourth – you know, the one that logic was “going to get wrong.” Of course, as logically deducing ahead of time “which one your logic will get wrong” is impossible, that option is off the table.)

If you guess all the time, your odds of correctly pegging four different factors as relevant or irrelevant are very small. Your odds at getting three out of four are also small, and your odds of getting two or fewer correct is easily the most likely case. With good logic, however, you get three out of four every time.

Although in one isolated case, the person who guesses might happen to outperform the person who uses logic, the guesser will compare miserably over a longer period of time to the consistent three-out-of-four, three-out-of-four, three-out-of-four repetition of the one who sticks to logic.

When logic leads us astray – as it would have in the case of the dust speck – we should absolutely question our methods to see if our logic was faulty. However, many players fall into the trap of rejecting the methods outright when they lead to bad outcomes.

Say you play a deck that loses to Red but beats the rest of the field. As Red has been scarce in PTQ Top 8s lately, you conclude that it is nearly irrelevant for purposes of charting your path to victory. In the first round of the Top 8 of your next tournament, you are paired against the only Red player left in the room, and lose. You attend another tournament, and the same thing happens.

Your logic about the irrelevance of Red decks seems to have led you astray. Had you played a deck more prepared for them, you might not have been knocked out. (Of course, you might not even have made Top 8 – but that’s a whole different story.) So what should you do differently for your next tournament?

Nothing.

You brought a deck that lost to Red but beat the rest of the field, on the grounds that Red would be scarce in the Top 8 and therefore you would be unlikely to face it. That was exactly what happened. The only reason you lost was that, despite the unlikelihood of the event, you were chosen as the sole player to face Red in the Quarterfinals in both cases.

In both tournaments, you ended with essentially a one in seven shot at drawing the short stick of defeat… and while you drew the short stick both times, by switching decks, you might end up with even worse odds than one in seven. Question your methods, by all means, but be careful not to change them for faulty reasons – you may end up much worse off for it.

Good logic does not always reveal what matters, but it does better than any other method.

IV.

There are many things in each game that one can easily assume will have no impact on the final result. I talked about several of them in One Game. They can be difficult to find, but they are worth exploiting because they will be difficult to find for the opponent as well. When you make a clever move, or subtly alter your opponent’s perception of the game, he can always counter it – if he believes it matters. If he does not realize its relevance, he may ignore it… to your advantage.

Often, this circumstance comes about naturally. You make a play, such as casting a Jitte, and the opponent writes it off. He has a card in his hand that can make your play moot, but he does not think he needs to use it. This leads to your victory.

However, you can also take steps to increase the probability that your opponent will discount something relevant. What if, say, the White Weenie player had frowned when he played Jitte, grumbling “Come on, deck, I need something to sac to Exile, not this garbage.” If the Gifts player bought it, he could potentially convince him to ignore the Jitte when he had otherwise planned to nuke the board with Kagemaro.

A more recent example popped up in the forums of Riki’s article earlier this week. An Elves! player has cast Glimpse of Nature and is about to combo off with Mirror Entity, Wirewood Symbiote, Wirewood Hivemaster, and Nettle Sentinel. After the first activation of the Entity, his opponent says “Yeah yeah I know the combo. How many times are you going to do it?” The Green mage responds, “100.” The opponent says, “You’re dead,” and he is correct – Glimpse of Nature’s card drawing is not optional.

The Elves! player explains the key to his opponent’s success: “The reason…I got ‘gotten’ was the resigned tone of voice Pascal managed as if he was already in the process of scooping his cards.” The importance of this cannot be overstated. When Pascal asks his question, if he gives even the slightest hint that the number of repetitions chosen matters to this game, the jig is up. The Elves! player will execute the combo only as many times as he safely can without decking himself, and will easily win the game. Only by convincing the opponent that the number of repetitions is irrelevant – a non-factor in determining the outcome of this game, even though we know in hindsight it is the deciding factor – can he steal victory from the jaws of defeat.

You can influence your opponent’s perception of what matters.

Takeaways

I. Anything can matter.
II. To focus on what matters, you must first know what matters.
III. Good logic does not always reveal what matters, but it does better than any other method.
IV. You can influence your opponent’s perception of what matters.

See you next week.

Richard Feldman
Team :S
lcd_cow@yahoo.com