Prologue
A while ago I was reading the piece Jacob Clements wrote on ‘Value’ and I had the thought: does he actually think this way? The article is well written, and I found many of the concepts useful, however, the theory does not resemble my in-game thought process at all. Is Clements really suggesting I…. *Gasp* DO MATHS??? Surely not. I thought again, am I ever counting value to compare different lines in-game? No. It’s a useful way to communicate strategy and to reduce the complexity of the game to a framework you can talk through. Not a literal guide for how to think through a turn cycle. Right, guys?
After some reflection I concluded that perhaps different players use different thought processes to parse game states. This interested me. What 'strategic language' do I use to make sense of the game turn to turn? What language do other players use? And, most importantly, what can we learn from the different approaches? To answer these questions, I enlisted the help of my friends and competitors: Sam, Michael, and Brodie. My conversations with them were instrumental to writing this piece and I would like to thank them for their wisdom and insight.
To Count Or Not To Count
So, what ‘strategic language’ do I think in? Usually when I parse a turn cycle my thoughts are something like this: “I could attack with CnC, he still has armour... it’s an easy defence... Do I just preserve life and set up?” and so on. I consider things like who’s winning, and how to maximise future agency. I think about my plan in the matchup and what my goals are. My thoughts are a set of questions I use to guide myself towards the correct play. I am not doing maths. My thoughts are what I will call ‘conceptual’. They seek to maximise win percentage through adhering to strategic concepts like efficiency, risk/reward and line up theory. The Value Framework that Clements discusses I will call ‘concrete’. It seeks to maximise win percentage through the proxy of ‘Value’ as a reliable mathematical equivalent. Since these approaches are trying to reach the same end goal, the core difference is the methodology of your own thoughts.
I asked Michael Feng how he navigates game states and whether he is calculating Value on each turn cycle:
“I think for Gravy and Lexi I was always trying to do that as much as I can. I know Hamilton literally does the math every time he considers blocking or attacking, then tries to assign value to things that are subjective.”
Michael explained that when playing more defensive heroes, like Guardians, he spends more time thinking about things like; 'are they going to end the chain early?' 'How will I handle an on-hit later in the turn?' So, Michael shifts his approach to match the hero he’s playing. Michael finds concrete thinking useful when parsing a game state, especially in heroes who want to utilise a 4-5 card hand. Doing the math is a part of his game, however, he also mentioned that:
“There is a weakness in sometimes not seeing the big macro plan.”
I felt that there was wisdom in his choice to lean into different styles as not every hero has the same goal. Is this why I suck at playing aggro decks? Perhaps I gravitate to heroes that leverage my thinking style to the greatest effect. With Assassins, you always need to think about the cards in your opponents’ hand, and how they might block. I remember my friends telling me Uzuri just defends for 6 and attacks for 6. We were clearly thinking about the game in different ways. Perhaps if I calculated Value on each turn cycle, other playstyles might come more naturally.
Counting in Numbers Vs Counting in Concepts
Next, I reached out to Brodie Spurlock. We ended up discussing the mental efficiency of different approaches, he said:
“I think everything comes down to math, but it’s often easier for us to think of it as concepts.”
This made a lot of sense to me. In most game states I don’t have time to math it out. Concepts can help you navigate the game quickly. Brodie uses maths to add clarity to his thinking.
“I do count the actual math of lines when two are close, to identify the factors besides Value and articulate a question in my head– this line is 2 points worse to upgrade a Loot the Hold to a Portside in arsenal, is that worth 2 points?”
He presents a different theory to Michael, where concepts are shorthand for a full Value Framework. They help us reach similar conclusions to a concrete thinking style without needing to do as much work.
“Words & concepts are more digestible/zoomed out.”
Perhaps the reason I don’t do math when I play is the instinct to think efficiently. Everyone takes mental shortcuts; it is an important part of a healthy mind. Why put in effort to ‘check my working’ when I have already decided from pure vibes? The reason is clear to Brodie.
“Everything can be broken down to math and sometimes attempting to do so reveals the answer in a close spot.”
I think he makes a great argument for balancing the practicality of how we think with the benefits of a more structured process.
I do not believe that conceptual thinking is a proxy for value calculations, since strategy concepts and value maths are both a proxy for raw win percentage. However, blending them together seamlessly like this makes a lot of sense. On some turns, we make the choice that we must prioritize setting up a power turn to not get fatigued. On others, we can use a Value Framework to clean up our play when we lack a strong idea for the current goal. The fact that value maths is less mentally efficient than some of these more zoomed-out concepts is a point that resonates with me. The Value Framework that often gets discussed always seemed a little impractical to me. Perhaps that is because I am not practiced in applying it. Using it to help refine the conceptual side of your thinking into something more specific is the most appealing description of it I have heard.
Conscious & Unconscious Calculation
Sam Sutherland said he is always working with Value, but usually this was done unconsciously.
“Most turn cycles I’m intuitively comparing Value. It’s not really a conscious; this line is worth X, this line is worth Y, X > Y. Fundamentally that IS what I’m doing, just… I’d say my brain rushes through it.”
This is closer to how I experience the game. I am unaware of doing any 'counting' on a given turn cycle, however, clearly I am still processing the numbers on the cards somehow. Sam said although he sometimes does the math directly, it isn’t a core part of his thoughts each turn.
“When a game state gets very complex, or I’m not super familiar with the two heroes yet, I do the manual comparing of lines.”
This touches on a nice point: that we learn what efficient play looks like overtime. I don't need to count to 8 to work out that Felling of the Crown is impactful, playing with the card a few times is enough. If I do spend time counting the value differential of defending a Command and Conquer or letting it hit, I quickly pick up a feel for when it is wise to do so. Sam's idea of intuitive Value suggests that I do in fact 'do the math', I just do it via pattern recognition rather than manual calculation.
I asked him if he thought there was a difference between the way we talk strategy and the way we process it in game, he said this:
“How your conscious mind perceives and thinks about things and how your unconscious does, in this case, are fundamentally the same. Just your experience is different. In terms of strategy it doesn’t matter which one takes over, if you do things consciously, you eliminate chances for edge case mistakes but also open up chances for overthinking mistakes. Generally, that’s a good trade-off."
When we spoke about this, I realized how much of my thinking in-game is not conscious. Most of my processing is something I cannot see. When I pivot in draft is not something I am making conscious arguments for. I might articulate the reasons clearly and convincingly afterward, however, that is a communication technique, not the way I made the decision. Interestingly, he attributes a different mistake to each way of processing. I know exactly how these feel. Sometimes your instinct tells you a line that, in hindsight, was just forgetting an important piece of the game state. Other times the first line you think of was perfect, but you talk yourself into a nonsense block. Sam argues that risking overthinking is preferable to relying on your unconscious processing. So, if we can only control the conscious thinking process, should we always use a Value Framework? Or rely on conceptual strategies? Sam says:
“You need to understand both to play optimally because your standard FAB math only applies to tempo. ‘My value this turn cycle is X’ and ‘choosing the highest X’ doesn’t take into account a potential longer game plan.”
Many of these macro considerations are working their way into the Value Framework as great players like Clements develop it more and account for things like who wants to accelerate the game. What Sam is saying and what Clements is exploring in his piece on Value are essentially the same thing: That you must understand both the maths and the shape of the game. The difference then between my approach and something more concrete is if you are converting concepts into maths or vice versa.
Instinct Vs Logic
My chat with Sam made me think of the ways that we use both unconscious processing and active thoughts to make our choices in game. Is your pattern recognition of the game state a better guide than trying to play towards some strategy? These instincts are built up from the hundreds or thousands of hours spent playing, seeing the outcomes of different choices. If your gut tells you to make one choice, and your thoughts tell you to make another, which do you go with? Sam said when they clashed, he would pick his conscious thought process every time. I am not so sure myself. I’ve had the instinct to block with Scowling Flesh Bag at the perfect time more than once and not done it because logically I couldn’t see the reason. Despite that, my instincts were screaming at me to send it. Perhaps they were picking up on the body language of my opponent, or ‘feeling’ the shape of the hands more accurately than my logic could follow. I asked Michael Feng what he did when his instincts and conscious understanding of a game clashed:
“The real answer is I’ve gone with one or the other with no set heuristic. It’s more painful when ‘your feeling’ was right and you went with some type of logic. My instincts have won me many games. Sometimes it’s a soft tell from an opponent, sometimes it’s a sudden thought in my head ‘Play around this’. It's complex. I want to base my play on things that can be backed up with math and logic but lately I’m going by instincts more because I find myself in new situations.”
I would like to trust my instincts more in these moments, however, like Michael, I want to play towards some strategy or reasoning. Sam Sutherland on the other hand regularly uses his instincts turn to turn (to parse Value) but didn’t seem interested in listening to them when conflicted.
“The only reason it happens is because the conscious found a specific issue with the unconscious line, so I’m always going with my conscious thought.”
In some ways this response from Sam implies he is always trusting his instincts. He only stops when he has a clear reason not to. In other ways, it suggests he highly values logical reasons to take lines. From my own experience, the 'specific issue' he talks about is not always so clear cut. As Michael mentioned, sometimes your opponents’ body language makes you want to commit harder to a specific 'read' than would make sense given pure probabilities.
Stockfish
"What I describe (in my article) is probably best expressed as my attempt to formalize fab decision making. I’m essentially attempting to give an early draft/rough sketch of what would happen inside the Stockfish of FAB."
Holy shit how did Jacob Clements get in my article???
"I actually think about the Value Framework stuff the most when deciding macro game plans, both in testing and also at the start of a game. During game I’m naturally very instinctual and often force myself to slow down and either confirm what I’m doing is best Value or attempt to specifically articulate to myself why I’m deviating."
So, Jacob says he also has to work to apply the framework to his natural thought process. However, he uses the theories he put forward in his article to critically analyze his approach when not directly in game and refine his macro plans. This is something I can see myself trying. Outside of the game is a great opportunity to apply different thinking/evaluation styles. You might discover a new way to view a matchup and, at the very least, you can practice applying different perspectives. He also applies these ideas in game and calculates Value to make sure he knows when and why he is deviating. It seems very few players are 'Value native' thinkers. However, the process of formalizing this thought and considering how to apply it to your play is a useful exercise for growth. Developing either a sense or a formula for efficiency is an important process for every player.
Jacob's idea of Value as the beginnings of a Stockfish-like algorithm interested me a lot. For those who are unaware, Stockfish is a very powerful Chess engine. I find myself more excited to delve into an exploration of Value when I frame it in this context. What other systems would I try to add to a formalized thinking process, so it could always find the correct play? Despite my focus on subjective experience during this piece, I do think formalizing these processes into something more concrete is immensely valuable. However, I think that people mistake 'Value' for 'the way you should play the game' too often. We are not chess algorithms and trying to think like one is not a good approach to developing as a player. However, you can learn a lot from something like Stockfish and I think the same is true of the Value Framework in flesh and blood.
"I think the more one understands about what’s going on ‘under the hood’ the better chance one has to come to the right plays in game. One of the best pieces of advice I got when I was learning, was whenever I make a play I should imagine someone is watching over my shoulder to whom I must explain why I made the play I did. The Value Framework is good as you can either answer ‘it was Value maximising’ or ‘this other factor I believe to be worth the x points of value my play was worse by’."
I love the 'why did you make this play' test. I think regardless of your approach to the game it is one of the most powerful tools to examine your own lines. At the end of the day, if you don't know why you are making these choices, it is hard to learn from them.
Finding Lines
After talking with all these great players, I realized something. None of the Value Framework is focused on how to find or think of lines. It is, rather, a method for evaluating them. This sounds obvious but the distinction between coming up with and evaluating a line is not always clear, even in our own headspace. As Clements explained, Value is a way of talking through his choices and exploring his decision making. It is a very effective method of comparing two approaches to a turn cycle. However, at its core, it doesn't help you think of those turn cycles in the first place. This puts into words something I have always felt, that the idea of Value was somehow 'missing the point'. I could never quite explain why, as clearly it is an effective framework and a good approximation of win percentage in a lot of game states. So what's the problem? The problem is, regardless of if you calculate the value of different lines or not, you have to think of them first. Comparing two or more approaches is only useful once you have created several ways of navigating a hand. When I say 'I don't really do maths' what I mean is 'I spend most of my time thinking of different ways I could play my hand and then I pick which one seems stronger'. If you were trying to optimize my approach you could change it to 'I spend most of my time thinking of different ways I could play my hand, and then I use a Value Framework to check my instinct for which one is stronger'. This is a fair improvement. However, I think for most players the initial step is the most impactful one. Finding plays in the first place. When I make a mistake and someone says "Why didn't you defend with this here?" the answer is usually "I didn't see the line" rather than "I thought the other line was stronger". When I'm coaching players, one of the main things we work on is developing many ways to play the same turn cycle. If you come up with one line and do it, you have not made any decisions. If you come up with two lines then you start having to apply strategy to which of those you prefer. This second step is where the Value Framework is useful, as a ruler to measure your lines. So what pen are we using to draw them?
The 'macro' plans that people talk about– like fatiguing Dio or developing a potion combo with Verdance– can help you to find lines in the first place. They give you ideas for how to play a turn cycle. Macro strategy can give a direction or inspiration for how to play, however, you still need a way to parse novel situations. An exercise I like to use is: find the first line that comes to your head, and then work out the best way to achieve the opposite. For instance, I might quickly realise I could defend out a Felling of the Crown and arsenal a threat for a later turn. Then I ask how could I pressure my opponent instead? What is the most effective way to attack rather than defend this turn? I can return to the original line with two different ways of navigating the turn cycle and pick which one suits the game state more, or I could apply the Value Framework to see how they compare. If you imagine you are a boat trying to move towards the deepest part of a lake (the highest win percent play) and the Value Framework is a depth finder, it tells you roughly how deep your current location is (if you put in the effort to use it), you still need a smart captain to drive around the lake and decide what spots to test. Perhaps driving to the center of the lake is wiser than testing the shores.
Your Approach
As Sam Sutherland has shown us, you can play cleanly and efficiently by honing your instincts, and knowing when to apply a specific framework. Michael Feng likes to manually math out his turns, but still questions the efficacy of 'Value' in certain game states. Brodie uses those calculations to add clarity and rigor to the more zoomed-out concepts that help him come up with lines in the first place. Jacob likes to apply these concepts to his macro plans and formalize his thought processes, but still has a natural instinct that guides him. These players all seem to play with a mind towards Value, but in their own way, with other thoughts and goals mixed in. For different players, different approaches will help them to develop and compare plays more accurately. Perhaps 'doing the math' directly doesn't work for you. This is not a free pass to ignore the way you approach the game. You can still practice coming up with efficient lines and use the Value Framework as a guide to check your answers. There is always room to grow. However, you have to tailor what works for other people to your own context and environment. Try to steal great ideas from all the players you meet, and work them into your own understanding of the game. That could be the way you compare lines, or how you come up with them in the first place. I am aware that all this 'thoughts and feelings' stuff that I have a tendency to talk about can feel very far away from what the correct play is, or how to win the Kano vs Briar matchup in Silver Age. You might ask, 'Isn't it more efficient to focus on FAB fundamentals?' the way I see it, how you think and feel are the fundamentals. For many players, they interact with the fundamentals of how they approach the game instinctually. I am arguing that it can have a huge impact to consciously process and examine these elements of your game. What is your approach? Did you choose it? And what other approaches are out there?
Epilogue
Value is a powerful framework for examining the game. Understanding the theory is an important step in developing your instincts and your reasoning in flesh and blood. It is hard to find a successful player who doesn't have a mind for Value in some way, shape, or form. However, the way we process information is very complex. What may seem like a simple calculation often involves many mental processes being integrated together: The conscious and the unconscious, the conceptual and the concrete, our pattern recognition and past experiences. Not to mention the emotional side of our decision making. Different players rely on different elements of this process. On top of this, we think differently to the way we communicate our thoughts. So try as I might to shed some light on the topic, we are left peering into each other's minds from a distance. I hope despite all the pitfalls that you enjoyed this piece, and found something of use to take out of it. Good luck on your journey.
I would like to thank everyone involved with this article for their contributions to the game and to my life. Their perspectives have given me a lot to think about.
GG, Much love!
-Ben
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Ben Dodd
The puzzle guy! I also play the game sometimes. Have fun solving and good luck at your next tournament!