Graveborn Musings – Game Theory, Not Politics

Have you ever heard people say that multiplayer is no fun because politics always determines the outcome? I’ve run into that idea so many times that I think it might be the number one misconception about multiplayer. Sure, there’s some interaction at the kitchen table that might be called politics, but not nearly as much as people think. What multiplayer does have is more strategic complexity – much harder to say than politics, and I know it sounds disturbingly philosophical, but when you say “I love multiplayer because anything can happen,” you’re talking about strategic complexity.

Today, I want to look at a game that I won recently – not the win itself, as there was more than a little luck in the cards that came up, but the strategy that I pursued to get to the win – and then I’ll use that example to illustrate how the complex strategic environment of multiplayer can lead to strange plays that are actually the right plays.

Game Theory, Not Alliances

Tonight, I won one of the funnest games I’ve had for a while. My winning had nothing to do with it being fun…mainly it was three cool guys (plus me) showing off four interesting decks. The play order (names and generalscommanders) was:

• Brent: Kaervek the Merciless
• Brian: Bosh, Iron Golem
• Me: Molimo, Maro-Sorcerer (slightly outdated decklist here)
• Dan: Sliver Overlord

I was scared of Brent’s deck – global damage, tactful use of Kaervek and usually a pretty quick Grafted Exoskeleton – although it’s probably as weak a deck as he is capable of making, and it isn’t overpowered, really. I hadn’t seen Brian’s deck before but I respect him as a clever and über-tricksy deckbuilder. Dan was new to the format, playing only his second EDH deck, but he was still playing Slivers. The funny thing about playing Slivers: you usually get marked for death once you have about four creatures in play. Dan is a super-cool guy who really gets the format, so he promised no accidental “oops, I win” combos, but of course Sliver decks are capable of some fairly explosive deliberate wins when given even a little bit of breathing room.

I kept a hand with three lands, a Cultivate, Plummet, Moment’s Peace and Praetor’s Counsel (so much I want to say about this card!!), but everyone else had a bunch of mana ramp on the table before I did – although I was able to follow up a third-turn Cultivate with a topdecked Skyshroud Claim and a fifth-turn Molimo. Dan had a Sliver Overlord, Brent had Ashling the Pilgrim on five counters and a Koth on five loyalty, and Brian had Mind’s Eye and a nebulous aura of menace. Even at this stage, it was clear that both Brent and Brian considered Dan to be an immediate threat. The plan was to dog-pile Dan, and I was expected to go along with it.

Before saying what I should do, look at my hand again and ask yourself if that would make you want to be more or less aggressive; to push or be patient? Plummet is a card looking for a big target, and it’s almost guaranteed to find one in the late game, Moment’s Peace is the ultimate insurance, and Praetor’s Counsel is whispering in my ear that if there’s a lull in the game, such as might be caused by a late-game sweeper of some kind, I’m going to be able to cast it and get virtually insurmountable card advantage. So even before the first spell is played, I’m in no itchin’ hurry, because I feel my hand gives me an edge in the long game.

Stall…stall!!

Then look at the threat that Dan poses. With a little bit of time and breathing room, he’s going to be able to unleash a horde of creatures, get them pumped up to ungodly proportions and swing for the win. Each of us recognizes that he is probably the most likely to kill any one player, and most likely to sweep the table, but I can’t think of anything that would allow him to take out more than one player next turn, and he’d have to get very lucky to pull that off.[a] Should I join the others in trying to kill Dan?

Let’s look at a little bit of game theory here. Basically, you should assume that your opponents are rational decision-makers: they have a goal in mind and they’re going to find the best options they can find to achieve that goal.[b] In this case, all three of us shared the goal of killing Dan before he could build up his board presence. Brent and Brian know that Dan is the threat, and it would take a major change in the board state for them to turn their attention away from Dan and towards me. To summarize then, I know what my opponents are thinking, I know how they’re going to act based on what they’re thinking, and that knowledge gives me the opportunity to pursue other interests.

And I do have other interests. While I want Dan dead, he’s not such an immediate threat to me, since I’m holding the best Fog effect in the game, as well as having more/better blockers than the others. Moreover, with at least two other players working against him, I’m confident that the threat Dan poses will be minimized or at least delayed. At the same time, I don’t want to let the other guys build up their board positions to the point where they can end the game by burning me out. The ideal situation for me would be if they struggled to kill Dan over a couple of turns, used up more of their resources, and generally didn’t try to kill me, so that’s what I tried to achieve.

First, I played a Wickerbough Elder and swung at Koth with Molimo. I said to Brent, “Sorry, Dan still has to die, but Koth is scary…hey, at least you aren’t taking general damage!” In other words, I reassured him that Dan was still the biggest threat to him. The trick in this situation is to weaken your opponents without changing their strategic assessment about who the biggest threat is. Sure I attacked Brent with a 9/9 general, but I didn’t do damage to him, and he had every reason to expect me to attack Dan next time. Sure I used my Wickerbough to destroy Brian’s Sol Ring, not Dan’s, but those were pinpricks – as far as Brent and Brian were concerned, I wasn’t doing enough damage to them to change the basic calculus that Dan should be their first priority.[c] They didn’t fully appreciate that while I was messing with them, I wasn’t messing with Dan; if I’d joined them in focusing exclusively on Dan then he would have quickly crumbled under our combined onslaught, but then I would have had to face the fully armed and operational battle stations that the other two were assembling, and that would have been worse for me than keeping Dan alive and slowly whittling down all three of them.

To put things a little differently, Brent, Brian and I all shared an understanding of what the right play was, but because that allowed me to predict what they would do, I was then able to determine a better play. That is strategic complexity.[d]

I followed that strategy all the way to the win. It was a reasonably long game with a lot of twists and turns, and I got a little bit lucky with some of the randomness that ensued (Brian’s Warp World gave me Asceticism, Lurking Predators and Chameleon Colossus – one of the best Slivers in Magic! – and I was able to get five creatures from the Lurking Predators before Dan waxed it). At one point, I almost had to use Moment’s Peace to save Brent in order to keep the others focused on each other. However, by the time everyone realized I was on 50 life, they were all in the low teens or single digits, and I had more creatures than anyone except Dan. They couldn’t focus all of their attention on me because they’d done so much damage to each other that the risk of getting stabbed in the back was too high. Eventually I was able to finish off Brian and Brent with plenty of mana left over to prevent the damage from Dan’s alpha strike and trample back for the win.

What is Politics, Anyway?

Someone who watched the game without understanding the strategy might assume the action was driven by politics – as if I’d made an alliance with Dan, or Brent and Brian had “ganged up” on him – but that is very clearly not what’s happening here. Each person in that game was making the best decisions they could with the resources at their disposal to achieve their goals, just like a rational decision maker is supposed to. Everyone was active enough to make the game very entertaining, and there was no Quiet Guy waiting silently to finish off their weakened opponents at the end of it; I was as active as anyone else, casting critters and attacking every turn, and my Chameleon Colossus was the biggest creature on the table. In short, the things that are commonly derided as “politics” did not play a central role in the outcome of this game. In fact, only a handful of people have ever tried to define exactly what politics means in multiplayer, and none of them really succeeded, so when someone says “It’s all about politics,” they literally don’t know what they are talking about!

In this game, there was a little bit of table talk, but nothing in the way of bribery, horse-trading or “I promise not to attack you for three turns if you use Ashling to blow up his Slivers,” which might be legitimately defined as politics. Instead, in the language of game theory, most table talk would be classified as signaling. For example, when I told Brent that I was only attacking him to kill Koth, it was a signal to let him know that my intentions were not fundamentally hostile to him. Some might call that politics, but at most it’s in a grey area, because in the absence of table talk anything else you do can also send signals. Attack me? I interpret that as a signal that you want to kill me! Don’t attack? You must be building up to an alpha strike! Play a fattie? That’s a signal that you are a threat to me.[e]

In other words, you can’t avoid sending signals to the other players, because ultimately anything that allows your opponents to infer what your intentions are is a signal – even if you aren’t trying to send signals, they’ll still be receiving them. If table talk such as “Don’t worry about the Kaervek I just cast, because I want to kill Dan” is politics, because it tells you that I’m not a threat, then so is playing Kaervek in the first place! After all, playing a powerful card sends a signal to the table that you have the capability to hurt them, and most people assume that in a free-for-all,[f] capabilities are the same as intentions. It doesn’t make sense if sending a signal that I’m not a threat counts as politics, but sending a signal that I am a threat doesn’t. That’s why table talk is sometimes necessary to make sure you’re sending the right signal.

On top of that, what happens if someone plays a card and I make a comment like “Wow,” “That’s a great creature,” or “Third turn Akroma? Nice play”? Is that just normal conversation, or is that politics, trying to get other players to deal with the card? Consider the alternative: if someone plays a really strong card – like Ulamog with Lightning Greaves – and I don’t react, is that a signal that I’m holding an answer, so I’m not worried about it? When you stop to think about it, a lot of the things that are normally thought of as politics – such as sending signals to other players – are merely extra layers of the strategic complexity of multiplayer.

What, Me Worry?

All of this is lost in a duel, because the intentions don’t matter, only capabilities. In a duel, if I can do something nasty to my opponent then I’m going to do it to them, because there’s no one else to do it to; if there’s only one person to direct my attacks against, then I’m going to attack them; if I’m the only one who can kill my opponent, then I have to deal all the damage to them myself; if I have creatures on the board, then the only decision is “will I attack them?” not “who will I attack?”

Once you add more players, the decisions become much more complex, as you have to answer a host of new questions, such as:

• Who should I attack first?
• Will they attack me or someone else?
• Will they use their removal on my creature or someone else’s?
• Should I destroy that permanent or wait for someone else to do it?
• Does it hurt me more or less than it hurts my other opponents?
• How much damage will my opponents deal to each other and how much damage do I have to do myself?

Most of these are questions of intentions as well as capabilities: sure they have the capability to hurt me, but will they? Not necessarily.

At the same time that you’re making all of these decisions, each of your opponents is asking similar questions, and what answers you all come up with depend in part on how you assess each other’s intentions, interests and priorities. If you can correctly identify what your opponents are worried about, who they think is the biggest threat and how they intend to use their capabilities, then you have a big advantage – not because of politics, deal-making or playing favorites, but because of an understanding of the rich strategic complexity of multiplayer Magic.

Keep it casual – and complex,

D

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[a] He’s also a clear threat to all three of us, which makes a big difference. Sometimes everyone has a different idea about who the biggest threat is, because each deck has unique answers and paths to victory, and in those cases there’s usually much less “coordination.” For example, if Dan had a Moat effect, then that would almost completely eliminate my ability to deal damage, but the other guys wouldn’t have to worry about that because both their generals can go straight for the face.

[b] There’s a huge question of exactly how rational is ‘rational’; saying that someone is rational does not mean that they have the same goals as you, or can see the same set of options for achieving them that you can, or that emotions, preferences, etc, won’t affect their decision making, it just means that if you understand their goals you have a good chance to predict and control their actions. The homeless person in the tinfoil hat may be rational; given the belief that aliens are broadcasting mind control rays from satellites orbiting the fifth dimension, a reflective hat is a legitimate strategy for achieving their goal of not becoming an alien puppet. It doesn’t mean that they’re right about the aliens, but it does mean that, if you want them to leave you alone, you can control their actions by telling them there’s a hole in their hat and they’d better go and patch it up before they get zapped.

[c] Also, from Dan’s point of view, I was less of a threat to him than the other two. If he was getting ready to take someone out, the most reasonable target for him would not be me. Again, I wasn’t making alliances, I was just aware of how my opponents saw their threat environment.

[d] In a complex environment, things can tip to a different game state very easily. For example, if Brent had got mad when I destroyed the Grafted Exoskeleton that Kaervek was wearing and dedicated himself to killing me, then Dan probably would have gotten out of control very quickly. Maybe Brian wouldn’t want to attack him on his own, or maybe I would have had to waste my Moment’s Peace fending off Brent’s attacks while I joined Brian in trying to finish Dan before he got out of control. I honestly don’t know what would have happened in that situation – that’s a big part of what makes multiplayer so much fun!

[e] There’s a fine line between expert multiplayer strategy and paranoia; I tend to spend an equal amount of time on each side of that line.

[f] That’s “anarchy,” for all you International Relations majors out there!