Casual Fridays #56: SORRY, YOU HAVE THE WRONG EXTENSION

How far should you extend your forces in a multiplayer game of Magic’ The secret formula lies within.

First, a housekeeping item.

Some of you noticed a wee little fly buzzing around our collective Internet heads last week. Todd Petit, formerly ‘Theo,’ has cast off the shroud of secrecy surrounding his identity and offered you all a glimpse of my ‘true nature.’

Todd was kind enough to warn me about the article, and I know for a fact that he took great pains to avoid hurting my feelings and inject a sense of humor into the writing. (These things don’t come naturally to actuaries, folks. Credit where credit is due!) And of course I got a good chuckle out of his efforts.

Actuaries are people, too, and are entitled to their opinions. I occasionally get on Todd’s bad side because I don’t play enough blue, or I point out he’s the best player among us at inconvenient times, or I believe stopping his combo locks BEFORE they happen is a good idea. All of these misunderstandings are, of course, grounded in faults completely mine. Anthonytopia is well-mapped territory. Theotopia is largely uncharted, so I can understand if you would like to give him the benefit of the doubt.

But there is one clarification I need to make – not because I care what a reader believes about me or my Birds and Bees deck, but because I care about what a reader believes about threat control.

The Birds and Bees deck, over perhaps fifteen games so far, has never been the first, or second, deck to be eliminated. Winning percentage is well over .600. Tranquil Grove has been specifically targeted (Disenchanted, that is) exactly one time – most people, and Todd’s philosophy works great here, are content to ride on my coattails as I get rid of pesky enchantments FOR them. The Ensnaring Bridge is a more frequent target, since the deck often needs it to turn the mediocre creatures I use into a capable fighting force.

When you decide not to put at least two or three cards in his deck that can respond to threats because ‘someone else will,’ you run a calculated risk. You are calculating that you have no room in your deck for threat control after you stuff it full of combo support, or fatties, or whatever. You are calculating that your creation will go off before a nasty threat hits the table and hampers you. And you are calculating that a more prepared player will find it in their interest to remove the offending threat for you.

This strategy, after calculations, can work. It can work real well. Todd’s success rate in our group is evidence of that.

But if you like to control your own destiny in most games, make no mistake: When you have four Tranquil Groves, and the person in your group who loves combos with enchantments tells you that your deck really could do just fine with just one, DON’T leave three in the box.

One last comment on Mr. Petit’s literary chef d’oevre. Todd and I laughed about this after I read the article; and he knows quite well that I have tried very hard to avoid any kind of ‘King of Casual Play’ title. You will NEVER see me refer to myself that way. There is no such thing. Just a bunch of friends getting together, over a kitchen table or the Internet, to show each other who really has this game down. In our tiny corner of the world, Todd wins some of the time, I win some of the time, and we both lose plenty of times.

Let’s move on to theory.

YOU HAVE THE WRONG EXTENSION

Dave (yes, I’m back to fake names’ it’s a habit now) made mention in a reflective email after an evening of play that he sometimes ‘overextends,’ and thereby loses the game after an efficient sweep of the table. We all do it at one time or another. It is a very common error, because it is very difficult to predict when a cataclysmic event is going to shake the table.

To illustrate, here are some of the calculations that need to go into such a prediction:

What decks are my opponents playing’
How much mana do they have available’
How much mana do they need to ‘shake the table”
What card are they likely to use to do it’
What will be left after that card plays out’ What will I be able to do in response’
What are people’s life totals now’
How much damage can I do between now and the time the first opponent can ‘shake the table”
If I can, should I kill that first opponent’
If so, how many creatures/resources will it take’
What are my chances of drawing, playing, and retaining those resources’

I’m pretty sure that’s just a partial list.

You can make all of the right decisions and naturally, just as in a duel, fate will deal you a cruel judgement. One opponent will play a Bottomless Pit, forcing you to extend out your hand before it gets discarded; and the next will play a Wrath of God, clearing the board of everything you thought you had ‘saved.’

But it’s not completely hopeless. Let’s take a look at how we might figure out how far to stick our necks out, and how to judge the sharpness of the axe waiting for us.

BASIC EXTENSION MODEL

As we go through this basic model, it will help to make some assumptions. They’re pretty stringent but we can relax one at a time later’

All creatures in the game are 2/2 vanilla creatures costing three mana (Grey Ogres);
Everybody is playing 20 creatures, 24 lands, and 16 creature removal (let’s say 12 spot removal, four mass removal) spells;
Any removal spell is capable of dealing with any creature;
Damage via creatures is the only way to win the game;
Everyone’s drawing one card per turn;
Everybody acts, without collusion, to maximize their chance of winning the whole game.

We need a formula that tells us, ‘How many creatures should I have out on the board”

We can build a rather winding train of logic. Hang with me; it’s not a perfectly fit chain and it jumps a bit here and there. But it pretty much stays within spitting distance of the tracks.

You need your creatures to deal 20 damage to each opponent. That means the more opponents you have, the more creatures you need to have out OR the longer they have to last. It also means you can’t just let your creatures sit there on defense forever.
Every move you make on offense weakens you on defense. If you attack with a creature, you won’t be able to block with it. These are vanilla creatures, no Serra Angels (yet).
Therefore, you have to have a certain number of creatures reserved for attacking, and a certain number for blocking. Players who act to maximize their chances to win generally won’t ‘suicide attack’, so leaving a number of creatures back equal to the number of possible attackers from one opponent is sufficient. Without collusion, you know one opponent won’t come at you just to clear a path for the next guy.
Still with me? Let’s keep going
If you are holding removal, your opponents probably are too. The percentages across all decks are the same, remember. So if you’ve got two spot removal and one mass removal card in your hand, you can expect every opponent to have the same.
If an opponent waxes one of your creatures, you are likely to wax one of his creatures. So spot removal will only get played if someone has a clear advantage over someone else; and mass removal will only get played if someone has a clear disadvantage against one or more players.
Therefore, everyone will tend to have the same number of creatures on the board. The player who rushes ahead risks triggering a mass removal from a panicked opponent; and the player who doesn’t commit enough troops faces a battle of attrition (via removal) that she is likely to lose.
I don’t think I’ve truly surprised anyone yet. Let’s carry on’
You need to maintain the force you have. If you lose a creature through spot removal, you will need a creature card ready to put in its place. If you lose all of your creatures through mass removal, you will need to have a creature card ready to start the cycle over again.
Your opponents need to maintain their forces. See #4; this is a parallel idea.
Therefore, everybody will keep a number of creature cards in their hand equal to the number of removal cards they have. This won’t always be exactly true, of course: if you play a mass removal spell, other players are holding on to their mass removal but still playing creatures out. That means they have a slight removal edge on you from that point. Over the course of many turns, though, the ratio of creature to removal cards in everybody’s hand should be about 1:1.

All of this leads us to our answer:

Every player wants to have a number of creatures on the board so that (1) she has as many creatures as everyone else and (2) she has enough creatures in her hand to ‘support’ her removal at a 1:1 ratio.

This should hold true regardless of the number of opponents you face, or the formation of teams, or whatever else.

So are you automatically overextended if you have four creatures and everyone else has only two’ Not necessarily. You can be in a number of positions:

EVEN CREATURE:REMOVAL (C:R) RATIO:

If you have as many creatures as each other opponent, and you have a 1:1 ratio of creature:removal in your hand, you’re KEEPING PACE. You want to just MAINTAIN your position and outlast all of the players who are out of balance.
If you have MORE creatures than any other opponent, and you have a 1:1 ratio of creature:removal in your hand, you’re looking like someone who wants to KEEP ORDER and stay at the top of the heap. You can afford to NIBBLE, or push a bit against the player you perceive as your greatest threat.
If you have LESS creatures than any other opponent, and you have a 1:1 ratio of creature:removal in your hand, you’re looking like someone who is getting nibbled at. You will probably need to HOLD your TEMPER for a little and ACCEPT the attacks that come your way, until the balance in your hand can help adjust the board situation.

LOW C:R RATIO:

If you have as many creatures as each other opponent, and you have a low (less than 1:1) ratio of creature:removal in your hand, you’re SEEKING HOLES in an opponent’s defense. If you’re comfortable with the idea, you might use your relatively strong spot removal to punch through prior to an attack, and create a new player who has to accept nibbling.
If you have more creatures than any other opponent, and you have a low (less than 1:1) ratio of creature:removal in your hand, well you’re the overextended one. You are RISKING A SWEEP and your best course of action, at this point, is to pick your largest threat and OVERWHELM him. Use those creatures while they’re still out there! If your creatures get removed bit by bit instead of by sweep, don’t try to replace them. Just gently ease into the hole-seeker role, thank your lucky stars, and wait to topdeck more creatures over time.
If you have less creatures than any other opponent, and you have a low (less than 1:1) ratio of creature:removal in your hand, you make like a turtle and CONSERVE resources. Play defense, protect your creatures by using your relatively strong removal to get rid of attacking creatures (rather than blocking), and last as long as you can.

HIGH C:R RATIO:

If you have as many creatures as each opponent, and a high (more than 1:1) C:R ratio, you may be SEEKING A FIGHT to show off your ability to replace creatures. You might PROVOKE someone into attacking you, or simply attack yourself and replace the losses with impunity.
If you have more creatures than any opponent, and a high (more than 1:1) C:R ratio, you are flooded with creatures and can afford to be RELENTLESS. Pick a target and start beating down. PUNISH anyone who removes creatures from you by simply replacing them and retargeting your attack. If the game is young, though, consider easing into an order-keeper or fight-seeker role as you replace some creatures.
If you have less creatures than any opponent, and a high (more than 1:1) C:R ratio, you are in the best position to SHAKE THE TABLE. Use a mass removal spell to SWEEP if you have one, and then start plopping down creatures faster than anyone else.

I found it helpful to make a cute little chart.

In hand on board	< 1:1 (C:R)	= 1:1 (C:R)	>1:1 (C:R)
> each other player	RISKING SWEEP: OVERWHELM	KEEPING ORDER: NIBBLE’	RELENTLESS: PUNISH
= each other player	SEEKING HOLES: REMOVE’	KEEPING PACE: MAINTAIN	SEEKING FIGHT: PROVOKE’
< each other player	CONSERVING: PROTECT	HOLDING TEMPER: ACCEPT’	TABLE SHAKER: SWEEP

Words can be imprecise when lonely, but I tried to use the single verbs that captured best your recommended course of action.

The question marks, where you see them, are intentional. The ‘hole seeker’ and ‘fight seeker’ have the toughest choices to make because their creatures are in balance (so they look like they want the status quo), but their hands are out of balance (so they don’t want the status quo at all). It’s easy to come up with a case where the ‘hole-seeker’ would NOT want to punch through a defense with removal and then attack; or when the ‘fight-seeker’ would similarly want to stay put. Likewise, the ‘order-keeper’ and the ‘temper-holder’ don’t follow my advice as often as the other categories might. They’re aware of balance they have that others don’t see.

By and large, each player is taking action – aggressive for those with more creatures to spare, defensive for those with less – that increases their chances of moving into the center cell, where creatures are in balance on board and in hand.

Okay, that’s the basic model. Now let’s let go of an assumption or two.

ADJUSTING THE MODEL: CREATURES BECOME MORE COMPLEX

The largest assumption we’ve got means the most change to the model when we let it go. One Serra Angel can do the work of four or even more smaller, tapping, non-flying creatures. How on earth do we count cards in balance when we’ve got a Multani to compare with a Morphling’

This was never a precise model, and we just have to deal with a bit more imperfection. But we can follow some broad guidelines:

A 2+X/2+X vanilla creature can generally count as two 2/2 vanilla creatures, where X is the number of opponents you are facing. This is because fewer big creatures aren’t a perfect replacement for more small creatures. They can be removed more easily, you can’t hold half of one back to attack with the other half, and blocking one is easier than blocking three.
An untapping 2/2 can generally count as two 2/2 vanilla creatures, since it perfectly simulates ‘one attacking while one stays back to block.’
A flying or trampling 2/2 can generally count as one-and-a-half 2/2 vanilla creatures, since they’re far more reliable on the attack. Shadow also gets a bonus – maybe 25% instead of 50% due to the inability to hold back and block.

(Notice that by the logic so far, a Serra Angel is worth four-and-a-half 2/2 vanilla creatures in a three-player game: With two opponents, the Angel’s 4/4 is enough to get the double value under first criteria, untapping gives it two more, and flying adds another 50%. In a four- or five-player game, the Serra Angel starts to lose more value, as you’d expect.)

Creatures with activated or triggered abilities are typically more valuable as blockers than attackers (especially if they tap for the activated ability). They count for less when they’re on the board (remember, we’re still assuming you win through CREATURE DAMAGE), but for more in your hand. 1/1 creatures with moxie, like spellshapers and Soul Wardens, can count as equal to a 2/2 vanilla creature when in your hand, but as 1/1 vanilla creatures when on the board.
However, if they have REMOVAL capabilities, in essence they raise the number of creatures you have relative to other players, pushing you into the more aggressive boxes in the chart above. Count 2/2 removal creatures (like Arc Mage) as two 2/2 vanilla creatures, whether in your hand or on the board.

That leaves us three more categories of variables: mana cost, power/toughness inequalities, and miscellaneous abilities. (There might be more to explore; but you can’t take any model too seriously. Like I said, these are broad guidelines.)

Mana cost really only applies to cards in your hand. If you can’t play the creature next turn, the creature is worth half of what it normally would be to you.
Not all creatures have equal power and toughness, of course. I think we can keep things simple and make a 2/2 equal to a 1/3, 3/1, and 0/4. Too much offense or defense, though, pushes you toward the more aggressive or more defensive boxes. No formula here – just try to balance the creatures you have on the board so that half can attack and half can block capably. For more unusual P/Ts like 2/4, 5/3, etc., just treat every 0/2 or 2/0 increase as a 1/1 increase.
There are tons of other factors creatures can bring with them: comes-into-play abilities, untargetability, self-recursion, and so on. I’d generally treat well-respected, benign abilities as equal to flying or trample. (That is, one 2/2 untargetable creature is like one-and-a-half vanilla 2/2s.)

In my first draft of this column, I inserted here a really long and involved example of calculations using different creatures in hand and on the board. Really, I don’t think doing that much math is necessary. Just scan over the cards in your hand, rate the above categories of cards a bit more highly than vanillas, and adjust accordingly. It’s a good idea not to let any card – the Avatar, the Morphling, anything, count for more than 4 or so, especially when you’re holding it in your hand. When in doubt, rate the creature lower. You will be less likely to overextend.

Don’t worry. The rest of the model adjustments are far less complicated.

ADJUSTING THE MODEL: PEOPLE PLAY DIFFERENT KINDS OF SPELLS

You do have to mind the addition of fancy stuff like enchantments, artifacts, and non-removal sorceries and instants. But the model doesn’t change TOO much. For example, Stasis acts much like a board clearer (or the threat of one). Creature enchantments simply add functionality to the creature – adjust the rating of the creature based on its new abilities.

Non-creature artifacts are a varied lot, but most simply either give some mana or card advantage to a player (e.g., Diamonds, Mercadian Atlas) or set up a condition that is threatening to your game plan (e.g., Winter Orb). You may have to change your strategy a bit from your ‘cell’ designation to reflect the more serious threats; but these artifacts, apart from Nevinyrral’s Disk, typically don’t affect your expansion calculations. Keep moving to the center cell when you can.

This is a good place to mention creatureless decks. Creatureless decks are, ironically, virtually constantly in the ‘sweep’ cell in the lower right. They play like they have a bunch of creatures to play out of their hand, but of course they’re sweeping simply to keep the field equal at zero until they can set up their non-creature threats and win condition. These are the blue-whites with Wrath of God or Evacuation, or the Red-Blacks with Ensnaring Bridges or Pestilence. Note that the very presence of a deck like this tends to push everyone else closer to the top row. (If you don’t understand why the presence of a strong control deck almost always means your moderate control deck is now a furious beatdown deck, or why the presence of an unusually aggressive deck puts every other deck into control mode, see ‘Who’s the Beatdown” from Mike Flores in the Dojo archives. This doesn’t change too much in multiplayer, at least not until the extreme player, be she extreme control or extreme aggression, is out of the game.)

Ugh. It’s been a while since we’ve had fun in this week’s column, hasn’t it’ Let me throw another cute table at you. Find the smart-ass comment that best applies to your situation:

If you…and if you…

…love theory…

…hate theory…

…win most games:

No doubt you’ve caught my earlier work. No need to thank me; your success is all the gratitude I can stand.

Ah, the Miles Davis of M:tG. Well, don’t let us keep you. Go visualize your card-patterns, or whatever the hell you do.

…loss most games:

Why are you wasting time in this stupid graphic’ Read, damn you, read!!!

Perhaps you should warm up to theory. Keep reading, Dubbya..

ADJUSTING THE MODEL: REMOVAL SPELLS CAN VARY

Not every removal spell can get rid of every creature, of course. They differ in degree (Shock vs. Fireblast) and method (bounce vs. burial).

We could rate removal spells, make Shock the ‘vanilla’ and grade ’em on a curve, like we did creatures. But do you really want to’

How about this. Permanent removal that does at least three damage, steals, or generally guarantees a trip to the graveyard (including Counterspell) counts as serious removal to be counted fully in your ratio. If it does two or less damage, or simply bounces, or gives the target a choice (e.g. Diabolic Edict), it’s good but don’t think of it as quite equal to a vanilla creature in your hand.

ADJUSTING THE MODEL: PEOPLE MAY BURN OR MILL YOU

Here’s where it gets a little dicey again, but we can maneuver.

When you encounter a player who is trying to mill you, you essentially need to break your deck down into ‘life chunks’, and think of his spells as creatures capable of taking away those chunks. A Millstone is not unlike a Grey Ogre, in this respect. Analyze accordingly.

Burn is trickier to gauge, since a Lightning Bolt can serve as either removal or a quick 3/x creature. I have to think a bit more about how to treat burn in this model; for now, I would suggest that burn mages tend to have less creatures, which gives you an opportunity for aggression with your own creatures. This in turn forces the burn mage to burn your creatures instead of you, effectively emptying his hand of ‘creatures’ without giving him the benefit of holding back removal. So perhaps when facing a burn mage, a more aggressive stance with your own creatures is in order. Count every creature on the board as worth an additional 25% vanilla 2/2.

ADJUSTING THE MODEL: SOME PLAYERS DRAW MORE THAN ONE CARD PER TURN.

If the number of cards drawn by players is not equal, then the model starts to break down a tiny bit. Some players will have more capability for aggression or control than others, and not everyone will be seeking to keep the same number of creatures on the board (and 1:1 ratios in hand). Watch the card-drawer and see which edge of the matrix she shoots for: She is likely to try to stay there the entire game and win from that more aggressive or defensive position.

ADJUSTING THE MODEL: PEOPLE COLLUDE, EXPLICITLY OR IMPLICITLY.

As much as I protest that politics in multiplayer are overrated, there are undoubtedly times when two or more players realize at the same time that it would be in everyone’s best interest to get rid of the third.

This is the least complicated, but most damaging, element when added to the model. In essence, when more than one player begins to focus on you, you need to keep resources on the table at X times the speed you normally would, where X is the number of consistently colluding players. (By consistently, I’d say over a span of two or three rounds, or more.) That means you will almost certainly overextend, intentionally.

What THAT means, in turn, is that your days are numbered and it is time to start thinning the ranks of the colluders. You must enter aggressive mode almost immediately, if you are at all capable of doing so, and you must slash and burn as quickly as possible. Every creature in your hand loses value and every creature on the board gains. Every removal spell in your hand loses value and every one you use gains you position.

There is a defensive version of this desperation, but it requires global clearers (or freezers), and plenty of them. For example, a Stasis lock, with sufficient numbers of Rescue, Ensnare, and ACC countermagic can theoretically hold down the fort against several players. There are other decks using False Prophet, Living Death, etc. I want to make sure I give full marks to decks that manage to pull this sort of thing off. Whether aggressive or defensive in nature, decks that manage to avoid – or take advantage of – overextension in the face of collusion are impressive indeed.

COMING SOON: Break this Card returns in a couple of weeks! And with the imminent arrival of Invasion, the Multiplayer Card Hall of Fame is almost ready for its facelift. Viva version 3.0! Nominations (particularly from Prophecy, which has not been integrated yet) are welcome over the next month.

Also, if you write to me, please let me know what you think of Parallax Survivor, which I am co-authoring here on StarCity with Anthony Boydell. (As to our working relationship, we’re getting along fine, thank you very much, though I have to stop the man from footnoting every half paragraph, and he has to continually explain his obscure European references to my uncultured American mind.) Your feedback is welcome on that, on Casual Fridays, on anything really, anytime. Goodness knows I don’t want folks thinking of me as some sort of, well, monarch.

Peace,
Anthony Alongi
Dictator of Casual Play
[email protected]