Profile photo of Justin Shearer By Justin Shearer On March 13, 2012 Posted In Game of Thrones LCG

Expected Value and AGOT Uniques

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March 13, 2012

One of the biggest debates around TC has been related to the optimal number of copies of a given card to include in a deck. With the competition running, I thought I’d put my two cents in – hopefully I can convince even stalwarts like Steven that 3-of-everything is not the optimal strategy for AGOT. This is going to be a fairly lengthy discussion, so I suggest you get some snacks.

A good starting place is to begin by explaining why you might want to include 3-of-a-kind in AGOT. The main reason is that consistency is far better than flexibility. Sometimes including 1-2 copies of a given card can be worthwhile in TCGs generally, but having potential options isn’t worth very much if you can’t access them reliably. With that in mind, unless you have lots of card draw or the ability to search out specific answers as you need them, you need to include multiple copies. This tends to result in, for most builds, streamlining your build so that you may have fewer options, but you will have access to them more consistently.

The next concern is that not all cards are equal. If you have three choices for a generic early-game beater, one will be better than the others. Rather than include one of each, you’ll be better served by including three of the best choice, even if the difference is only slight. Sometimes the most marginal differences can be all important.

Related to this, is the notion that by including too many cornercase cards you dilute the deck. A focused deck tends to do better – it is better if you’re playing aggro, in magic for example, to close a game out reliably in four turns than have a few more options but take a little longer to win. Here’s where I’d like to introduce a concept that I like to call “expected value”.

Expected Value is the idea that each draw you make, sight unseen, has a value. That value can be estimated to be an average of what is left in the deck – modified by context. With the diluting problem above, expected value of cards is overall lower by including lots of cornercase cards that might be dead in any given matchup. Additionally, expected value changes based upon what you need – you have 30 cards left in the deck, you really need to draw into characters post-Valar… but you’ve already chewed through 20 of them…

The nature of uniques in AGOT makes expected value interact with deck building a little differently. Unique characters in AGOT die. Not only do they die, they die all the time between military challenges, Valar, Wildfire, removal… in the Game of Thrones, you win or you die… and sometimes you die anyway. Over and over.

All men must die (Women too).

In most games, that’s no biggie – you just play down another. In AGOT, when your characters die, that’s it – barring a very small number of effects they’re not coming back. This means that each additional copy of a unique is a dead draw – to draw on a concept I introduced earlier, after you lose a unique, if you have multiple copies, you reduce the expected value of *every draw thereafter*.

That is huge! But, just like a TV salesman, I’m going to tell you ‘that’s not all’… this also means that the first unique you draw is a lot less valuable than it should be. That might seem odd, but by including lots of uniques, you constrain your ability to play single-copies… to get any value from your uniques, you need to hold them until you can play a duplicate – or you risk suffering big efficiency losses from deaths.

But wait! There’s more! Your second copy is less valuable than another, similar card. A duplicate isn’t as valuable as another body. There’s plenty of ways to beat duplicates and saves more generally – Search and Detain is an example that you will see in almost every deck.

I told you to get snacks...

Faced with the choice between having a single character with a duplicate and two characters on the board, it is a no-brainer. A generic character with a duplicate is making one challenge, where two generic characters are making two.

It gets worse. Lots of uniques also hurts your setups. You can’t play duplicates during setup – and this largely means that you can’t play key uniques into setup for fear of a crippling first turn Valar/Marched to the Wall. The end result? You are stuck with bad opening hands and you see far fewer cards than your opponent before the game begins.

I’d like to now take an opportunity to introduce the concept of “functional equivalents”. If you recall the beginning of this post, I made mention of why you don’t include 1 of each of three similar beaters in other games – those three cards are “functionally equivalent”. That is, they all do the same job roughly equally well.

In AGOT, it is important to make use of functional equivalents. The reasoning is that the marginal difference between cards that normally exists is eliminated in AGOT because of the drawbacks to unique characters and the expected value of draws. To highlight what I’m talking about, let’s consider an example from my Baratheon deck…

Functional equivalents allow us to retain consistency in the face of Expected Value – in this instance, Ser Jon is a little better than Brienne, but at the end of the day, they’re both 3 cost Renown weenies. I need more sources of renown, so I’ll take one of each… I’ll also take a Knight of the Flowers (who is easily the best of the three), a Lady Stoneheart and a Renly. Each of these cards has advantages/disadvantages over the others… but all are fundamentally 3 drop renown characters to support the power rush.

So, how does this help us be more consistent? Well, let’s say we want to include 3 renown weenies with military icons for Baratheon. We *could* take 3 copies of Knight of the Flowers – but unless we want to build around him as our key personality, we run into problems with Expected Value. Instead, we take 1 Loras, 1 Ser Jon and 1 Brienne – our chances of drawing each of these is the exact same as drawing each copy of Loras if we took three. Loras is better, sure, but the advantages are more than eliminated by Expected Value. In this way, we maintain consistency in the deck but improve the expected value of each of our draws throughout the game.

This calculation changes dramatically by the differential between the base value of cards. Once we consider Stannis or Ser Eldon in the above comparison, the difference isn’t just a small margin – these characters represent the key of the deck. We are willing to take the expected value hits because the base expected value of those cards is so much higher than anything else – we want to draw these guys each and every game and there’s no real functional equivalents available. These characters are key to the deck’s functioning.

Which brings us to exactly when we’d want 3 copies of a given card. High base value – no functional equivalents – key to the success of the build. For my Lannister Intrigue deck, that’s Cersei – she’s an incredible card that serves a role that isn’t easily filled by anyone else. She’s also critical to the deck – she can make use of the agenda on her own and, in addition, she’s got a noble crest and her ability virtually gives her renown and stealth (sometimes deadly too!). For my Baratheon power rushes, I take 3 of a few different key fatties – their vulnerability to death is diminished by Power of Blood, so the expected value hit is less, but additionally, I need to draw into at least two different ones in the first turn or I risk being unable to close a game fast enough. There’s also only a couple characters that combine power grabbing with an ability to land challenges, so functional equivalents are few and far between.

Where it gets a little murkier is when to include 2 copies of a given unique character. In my own decks, this situation occurs with Jhogo, the Blackfish and Jumpin’ Catelyn Stark. In each case, these characters bring something desirable to the deck, there are no functional equivalents, they are all powerful cards with a high base value… but in each case, the deck’s success doesn’t hinge on their presence. I want to see one copy throughout a game, but I generally don’t want to see a second one.

This outlines my thinking on the topic. I’m fairly new to AGOT myself and I’ve often seen this argument played out. Too often, it appears to me, it is taken for granted that the reasoning revolves around characters getting murdered and then being unplayable – what I have attempted to do is develop the underlying logic more explicitly. This is certainly how I view deckbuilding – the result of which is, in some decks, I have no 3-of uniques. My burn deck, for example, doesn’t centre around anyone in particular and so, I want to increase the expected value of my draws as much as possible. No dead cards!

Does anyone else think the same way? Is this really intuitive and everyone is well aware? Were you aware of this, but hadn’t really thought about it explicitly? Do you think about this differently?

Very interested to get more thoughts on this!




  1. I wouldn’t say the answer to the 3-vs-(2-vs-)1 debate is at all intuitive — at least not for most people. If a card is both easily played (low cost) and good you want more of it… that’s a rule of thumb, and most card-game players instinctively abide by that rule almost on instinct. And while the potential drawback of adding more than a single stares everyone right in the face there in the GoT rules on uniques, it’s hard to deliberately include a worse card over a better card because of something that might not even happen.

    I like the way you framed things here. It’s helpful, and reasonably straightforward as well. I do think rather differently than you though — but how I think will either be my own contest article or commentary after the contest is over.

    1. The point, largely, is that it isn’t a case of “something that might not even happen”. This applies to every draw that hasn’t happened yet – to a large extent, you’re disadvantaging yourself at the deckbuilding stage each and every game. The effect merely worsens as the game progresses and the value of some cards becomes zero.

      1. By “might not even happen”, I refer to the fact the game can end before you draw the dead card. The difference in value between the better card (the unique) being drawn/played early vs an alternate card (generally weaker) drawn/played early instead is important — that power drop “out of the gate” can lose games just as often if not MORE often than a late-game dead draw. 3-of is sprinter mentality, and 1-of means you aren’t running at full strength in the opening turns.

      2. @Theorist; the point is not so much that cards can be dead, more that by their mere inclusion, you decrease the value, overall, of each card you draw. The extra power differential between functional equivalents is eliminated by this phenomenon – given the number of cards you see before plot 2, you are likely to have “drawn” 1 less card in setup and also be holding one less valuable card in hand… and it could be a lot worse too.

        But the sprinter/marathon type thing isn’t such a good characterisation – as the original post outlines, it doesn’t apply to the characters that are winning you the game, just their support staff. For the most part, this represents merely a third of your character choices.

  2. Justin,

    This is an excellently stated case. Argument is outlined well, with some good support. Top-notch.

    Expected Value + Functional Equivalence is a great way to lay out the case. There’s a lot wrapped up in those concepts that lead to a lot of different conclusions.

    1) Can my deck save characters? (Power of Blood, Wendamyr, etc) If yes, does expected value go up or down? Initial value of a character is much higher given that it’s “safer”. However, if you can adequately save throughout the game, does the expected value actually go down because duplicates are even less desirable?

    2) How long do games last? This is an interesting one. Number of rounds in the average game drastically affects initial value v. expected value. Most games going 2-4 rounds? Initial value from dupes becomes proportionally higher than the loss in expected value for the rest of the game. Games going 8-10 rounds? Expected value becomes a huge factor.

    3) Intrigue defense. It’s not a strong argument, but even if dupes are dead in your hand, they’re less dead than they would be in other games because they defend your better cards against Intrigue challenges. Your “good” cards also act as screens, so you’d still never *want* a dead card, but dead here can still be a bit useful.

    4) Dominance gold. While normally when you draw into dead cards it means you have a wasted turn, in AGoT those unspent resources contribute to your winning dominance. Again, dead cards are slightly lessened.

    There’s certainly more, but I’d like to see what other blogs go up before really diving in.

    Also, Justin, I guess we inadvertently discussed this article a little bit on 2G1T last night. It was you whose name I couldn’t remember for which I apologize. My mind just totally went blank!

    1. As to your points:

      1 – This is a little tricky. I’m not sure it has a terribly great effect on your decisions here – ultimately, you need to consider the degree to which you can replace certain effects/roles within a deck. I will need to think on this one more – I rarely play Greyjoy myself.

      2 – The game length thing is important. But it is important to recognize that a large hit from expected value is occuring very early because of setup and the sheer number of cards you’ll see pre-game. The effect just worsens as cards die and the game progresses. I estimate that it could be robbing you of as many as two cards pre-game – one fewer in setup and one poor card in hand.

      On this, I expect that this effect does loom larger in melee, purely because there’s even more murder and games go for longer (in my experience).

      3-4 – although true, these factors are pretty negligible. They really say “these cards help you lose slowly”.

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