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Repeating a little game theory

Do It Again

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The letter A! while ago, I began an occasional series on game theory, which readers seemed to like. I promised to return to game theory topics from time to time, and now is one such time. It won't consume the whole article; but it's certainly relevant.

One of the concepts I've explained is the Prisoner's Dilemma, where each of two players can choose either cooperation (with each other, to deceive the police) or abandonment (to confess). If they cooperate with each other, they earn a higher combined payoff – but if one abandons the other, he can achieve a higher individual payoff. If both abandon, they hurt each other badly. Each player has what's called a "dominant" strategy to abandon the other, which means more often than not they end up in a bad situation.

I bring up Prisoner's Dilemma again not for its own sake, but because it's a good example of a repeatable game. Repeatable games are – big surprise – games that happen over and over, giving the participants time and opportunity to strategize over the long term.

Applying the filter of Magic, "repeatable games" and "long term" may mean over the course of several games – but for this article, I'd like to focus on games that repeat within a single Magic multiplayer game, and where long term means the duration of that single game. Short term, therefore, would mean something like the duration of a round, or only a turn, or maybe even just a spell and a few more on the stack.

Now with some terms defined, let's take a look at one of the most important skills of multiplayer Magic: repeating yourself.

Bugging You, Again And Again

Imagine a group free-for-all game where one player keeps attacking you with a Villainous Ogre. The good news is: you have two Grizzly Bears. The bad news: she has a seemingly endless supply of ogres: every time you block with a Grizzly Bear, she plays a new Villainous Ogre. Soon, you're running out of blockers, and her ogres will have a free path.

Now, instead of just Grizzly Bears, suppose you also have a Myr Matrix (and the mana to power it). Every time you lose a 2/2, you can make another one. It doesn't matter if your opponent throws four ogres in a row at you, and then follows them up with a Python – you have a truly endless supply of blockers.

As readers familiar with my Multiplayer Card Hall of Fame know, Myr Matrix is what I would call a first-rate "cockroach" card. Cockroach cards have one or both of two properties: first, they're hard to remove; and second, they replicate. Matrix meets both of those criteria very well: it repeatedly creates creatures without fear of vulnerability.

Not every "cockroach" card is quite so good…though they can be very good. Looking at cards similar to the Matrix, Phyrexian Processor can create very large token creatures – but it must tap to do so, and it's unlikely to last as long as the Matrix. It's still a solid cockroach card.

So is Darksteel Brute – but for the opposite reason. Instead of being vulnerable to disenchant, it's quite permanent and should last a nice, long time on the board. But it can't "breed" as fast as you'd expect a cockroach to. Sure, you can activate it multiple times – but you still get a single creature, and that's it.

Why should you care about cockroach cards? Three reasons:

  1. All other things being equal, a card with lasting effects – which usually means one that stays on the board longer – is more useful than a card without. You can also think about this in reverse: a card that only trades one-for-one is usually not good enough to help you last against multiple opponents.
  2. Cards that let you replace themselves (or the tokens they create) also have a certain "rattlesnake" aspect to them – they tell your opponents in so many words, "don't bother…go somewhere else." This gives you more time to replicate more things with the cockroach aspect, which reinforces the rattlesnake aspect, and so on.
  3. You can play around with game theory.

What For Tat?

Suppose you have a Myr Matrix in your free-for-all five-player game, and another opponent has a Myr Matrix as well. You each have enough mana to make two myr tokens per turn. The other three opponents each have five 1/1 goblin tokens. (Apparently, someone had fun with a Hunted Phantasm or two earlier in the game; but those are long gone.)

You and the other Matrix controller have a basic choice for the next couple of turns: you can make 3/3 myr tokens and ram them into each other; or you can make 3/3 myr tokens and hold them back against the tide of goblins. If you ram them against each other, one of you risks being Overwhelmed by successive goblin attacks. If you hold them back, you're letting the other guy keep up – and risking an alpha strike if something goes wrong.

We don't have to do a Zvi-level analysis of the math to see the right course of action here: it makes sense to hold the myr tokens back, because it's safer to deal with the threat you're sure of than the threat that might or might not happen. So you make your tokens, and you hold back.

But then your opponent surprises you – when he makes his myr tokens, he attacks you.

Yes, we all know it happens – some people just can't abide logic. Why is this guy attacking you? Is he stupid? Is he ticked at you? Has he had brain parts removed? It doesn't matter – you're on the defensive.

As you replenish your army with available mana to warn off any goblins (you do save your mana during your turn so you can do things at instant speed, right?), you might be thinking, well, heck. If he's going to attack ME, then I'LL attack HIM.

And many game theorists would agree with you. After all, what we're describing here is a "tit-for-tat" strategy. If an opponent does something to you, you do it back – myr token for myr token, damage for damage, card for card. It's not that bright in a group game; but sometimes you may feel like you have no choice. And hey, at least with a cockroach card like Myr Matrix, you're not wasting tangible resources on each other – just opportunity and tempo.

But if you don't want this to go on forever – or until someone with a goblin token does something dangerous – then you may want to establish a new pattern. You could hold back again at some point, and see if restraint isn't contagious this time around. If it is, then you can continue the tit-for-tat strategy more productively: each of you makes a myr token, but keeps it for defense (or throws it into a goblin horde).

The myr situation isn't an exact parallel of the Prisoner's Dilemma we referenced earlier; but the basic principles are the same: there are games with repetitive characteristics, where you have the chance to learn to cooperate. You have a better chance of playing (and winning) these mini-games if you use cockroach cards.

Cockroaches In The City

When I first took a look at the new expansion, I was surprised with how many cards which were good in multiplayer, were so because of their "cockroach" aspect. Naturally, a huge part of this is the Golgari guild – black-green's recursion dynamic is very cockroach. (Just look at cards like Genesis or Haunted Crossroads.) Since the Golgari cards are a bit obvious – and since we'll be covering that guild in the very near future anyway – I thought I might illustrate more of the cockroach aspect by using cards outside of the Golgari guild. They're certainly out there, in every color and color combination. You just have to keep your eyes open.

This will not be an exhaustive list. I left many cards off of it, just to annoy you. Yes, you, over there, waving your [cardname].

Firemane Angel . There are at least three ways in which the angel exhibits repetitive and/or enduring effects. First and most simply, it's a creature that can attack or defend multiple times (and a pretty good one at that, even without the other stuff). Second, it breaks completely new ground in offering an ability that gives you the same benefit whether it's alive or dead. That's extraordinary, even for the modest life tick.

Third and most notably, the angel is extremely hard to do away with permanently. Ten mana is quite achievable in multiplayer Magic, and not too many opponents are going to bother to kill this unless they (a) must do so out of desperation; (b) can do so convincingly and repeatedly; or (c) aren't paying attention.

Flickerform . This aura is useful on its own; but it really shines if you are using comes into play effects. Imagine using it on a Flametongue Kavu enchanted with Flight of Fancy, or on a Nekretaal enchanted with a Galvanic Arc. Sometimes, you can just plain build a better cockroach!

Selesnya Evangel . Everyone's already talked about this card plenty. I'll just note how happy I am that it has to tap to activate its ability, and then I'll move on.

Cerulean Sphinx . While not incredible in the cockroach department, I like mentioning cards like the Sphinx in lists like this because (a) it's a sphinx, and (b) this thing is incredibly hard to kill. Just like a cockroach.

Anyway, back on the sphinx thing – does anyone else really hope that future (blue) guilds feature multiple sphinxes? We already have two in the block, so I'm hoping there are more!

Circu, Dimir Lobotomist . Cockroach effects that don't cost anything extra are, well, extra-nice. You just play the spells you'd probably play anyway, and Circu starts lobotomizing an opponent's deck. Good stuff. Circu himself may be a bit fragile – three toughness is not invincible – but with a little protection at his side, he can stick around long enough to get some real work done.

Szadek, Lord of Secrets . Exactly what is so secret about this guy? He comes across like a library bulldozer, doubling the damage to the defender's library each time. If you play him on the seventh turn and attack on the eighth, your first opponent will have drawn about 15 cards, and therefore the loss of five means 20 gone. Then another ten, then another 20, and then you're done against most constructed decks. While you have to attack to get the ability moving, the fact that Szadek accelerates the milling process without you having to do anything unusual is a huge boon. And he grows to boot – which makes him harder to remove. (Not many cards can deal with a black 20/20 flyer.)

The guildmages. All four guildmages (yeah, the Golgari one too) are all excellent examples of good cockroach cards. While most opponents will take accurate shots at them when they first arrive, they start doing wonderful things if left unmolested for a couple of turns.

Duskmantle, House of Shadow . Any of the other three uncommon "guild" lands would also fit in this slot, of course. Or any lands, when thinking of cockroach cards! They're terrific at durability and repeatability – even basic lands keep tapping for mana.

Next week Wizards of the Coast is moving to their new building, so the site will be taking a week off from new content. When we return the week after that we're likely to continue our discussion of cockroach cards as we explore green-black cards in Ravnica (and elsewhere). I'll pay close attention to the message boards and emails, if readers have any insights on the cockroach element they'd like to share.

Don’t Forget Your Format!

I haven't heard much from readers on the new, reader-inspired format. Let me remind you what it is:

Working Name: "2000+"

The format is a multiplayer, free-for-all format with tournament-legal cards and sets. Whenever a player casts a spell, any player may play the following ability:

Pay one mana, remove a card in your hand from the game: change target spell of the same type, which an opponent controls, to a copy of the removed spell.

Control of the spell does not change, and the original caster chooses any targets beyond the original, if called for.

And now I'll encourage you, once more, to take some time and test this format! (One reader, for example, has found a problem with Phage the Untouchable. This is the sort of thing that's pretty easy to fix – but we need to learn about it.) Send your thoughts to the message boards, or drop me a line. If you've tried it, I'd like to hear from you. Thanks.


Anthony has been playing multiple Magic formats for several years, and has been writing for much longer than that. His young adult fantasy novel JENNIFER SCALES AND THE ANCIENT FURNACE, co-written with wife MaryJanice Davidson and published by Berkley Books, is available now.

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