 The Shannon number is a lower bound estimate for the number of possible chess games that exist, something around 10 to the 120 possible permutations. However, people have also studied the number of sensible games, that is games that don't have nonsensical or game ending modes, an estimate closer to around 10 to the 40. The gap between the overall state space of the game, and the viable games that exist is something in the range of 80 orders of magnitude. Chess has a wide state space, but that in itself doesn't create depth. It's also the number of viable, non-redundant and meaningful strategies and decisions that emerge from the board configurations that exist within that state space. But is this all that makes chess deep? The thing is, the above story sounds convincing, but it is hardly academic. We still haven't quantified what both depth and complexity are, despite having an intuitive sense that's what makes games unique. Also, should depth be defined independent of us as players, as an objective property of a game's possibility space? This question has been explored by many, with nothing definite. This paper, depth in strategic games, outlines the many elements for this hypothetical D that we are trying to quantify. In addition to state space, we can also say chess is deep because it has lots of viable strategies, a strategy ladder, or a huge skill chain, meaning tiers of players that can be ranked in relation to one another. It's a question that can be confronted in a more empirical sense too. How difficult is it for AI to crack? Chess with deep blue, but Go, a game with an even broader state space, requiring Monte Carlo tree search algorithms with AlphaGo. So this would make Go deeper than chess, right? Except this is far from self-evident. We can also try classifying by complexity classes, which has been applied to genres as varied as Sokoban puzzle games. Go has fewer rules than chess, yet generates a broader state space. This makes Go at the very least more elegant, or efficient. But again, this neither makes it better or worse, just different. Instead of a purely academic or theoretical approach, perhaps instead we can employ a more pragmatic means of assessing for depth. By deconstructing what games we consider to be deep, enabled through the complex interactions of their systems, we might find a way of uniting theory with practice, rendering intuitive what can be hard to define in the abstract. At high levels of chess, most of the opening moves have been mapped. They have been relegated to theory which the GM must memorize. In some sense, this part of the game has been made redundant. You get through this. Theory becomes prerequisite memorization and complexity to get to the tactical part with minor deviations. In the mid-game though, there are many choices, calculations that can be made, where the real depth comes from, decision-making. Sid Meier said games are a series of interesting decisions. We may not know what depth is, but we know that dominant strategies reduce depth. This is why Devil May Cry 2, outside of its poor level design and game feel, is shallow, because the gun is a dominant strategy, allowing you to kill from afar with no decision-making. Conversely, when chess enters the mid-game, countless decisions can be made. You may start with the Italian or Queen's Gambit openings, but this can transpose, transform. Pins, skewers, peace coordination, while culminating in a series of discrete end games. Risk and reward is an eternally interesting decision. It makes it so that there is no clear answer. In Geometry Wars, you can collect pellets from fallen enemies to increase your multiplier, but doing so puts you in harm's way. You have to make a choice, balancing your scoring with your life dynamically. Another way to do this is by using a simple game engine, not a game engine like Unity, but an engine like the book Advanced Game Design Outlines. A system where an action gives you a resource, which you can choose to store or use. Also known as power-ups, boost systems or resource economies. You can more clearly see this in a game like SSX, an arcade snowboarding game. In SSX, you aren't just maneuvering down a track, but the tricks you do fill a boost meter, which can be preserved so long as you maintain a combo chain. The drawback is that you can crash, waste your time doing tricks, and it all requires skill. The track is no longer just an optimization path. Movement systems with granular controls also generate depth, purely through the variables that exist and the dexterity involved in wielding them, like Rocket League, which allows players with sufficient skill to maneuver with freedom in a three-dimensional space. Not only does the speed, angle of approach, and ball's trajectory come into play, micro-positioning of the car in midair empowers players with versatility and directional control. There are innumerable states the ball can be in, and this can be influenced by the variables of the car the player has control over in a dynamic play space. There is also emergence in strategy, with high-level skills like dribbling, flicks, aerial control, and the flip reset being generated by the dynamics of play. Couple this with the resource management of the boost system and the synergies of team play, and you have a game with a practically infinite skill ceiling. Non-redundant interesting decisions. A universal game we know of that has this is Rock, Paper, Scissors. It is a mixed strategy Nash equilibrium game with no dominant solutions in practical play. What games employ this device? Fighting games. In most fighting games, hit beats throw, which beats block, which beats hit. But there are other of these cycles, on Okizemi, between fireballs, anti-airs, and jump-in attacks. But isn't RPS itself very shallow? Sure, a single game is luck, but multiple games of RPS is a game of being able to generate a random sequence and to detect other people's patterns. Fighting games, however, create mixed decisions and strategies around RPS. In Virtua Fighter 5, throw beats block, so if an enemy is turtling, throw them. However, they can also evade, which beats linear attacks, but this loses to throws, and the attacker can use circular moves to catch-stepping opponents too. These circular moves are usually slower though. These option selects can also be combined into higher level strategies called evade throw escape and evade crouch dash canceling. To gain an actual mix-up called Nataku, you have to be between plus six to plus nine frames, earned by blocking certain moves or by getting counter hits, but mix-ups also have counterplay. Virtua Fighter is built around rock-paper-scissors, but it isn't strictly in force. There are always options available to you if you know what the opponent is going to do, which is why the game is a lot about Yomi, or reads. Much like chess though, Virtua Fighter requires you to memorize lots of frame data, moves, to be able to access this high level play, but it is still one of the more elegant fighting games out there. Mixed strategies lead to option selects, metas between characters, and interplay. We often talk about state space and interplay between players, but can individual mechanics be deep? In Steve Swing's book Game Feel, you try to quantify elements of mechanics that can be measured. Mechanics can be sensitive, like how hard you press the jump button influencing the arc, combined, like how move and jump can be combined to create more possible states, and versatile, meaning they have multiple uses, like how a jump can be both a traversal and attack option. On the blog Crit Points, Celia Wagar adds more categories when assessing for depth, including uniqueness, where every element has a niche, nuance, where inputs can be modulated for different outcomes based on the context, and synergies, where elements can be used in conjunction for different outcomes. Swing also introduces a way to measure the feel of mechanics using the ADSR framework, the input frames, the acceleration, how long a move is active. All these measurements relate to how a mechanic actually feels. Using these tools, we can deconstruct a character like Dante in Devil May Cry 5, where you use movement and attacks in conjunction with weapon switches and style switches, enabling expressive and skillful play. There are generic properties of moves, like those that push enemies away, pull towards, launch, or just hit in neutral, but these can be combined to create various sets of options, whether switching between attacks to juggle, or manipulating spacing and enemy positioning. However, simply having lots of versatile character options is what Platinum Games calls functional design, design that doesn't actually have a context where you can use those abilities. Situational design, conversely, uses these skill sets and invokes level design, enemy configurations, and difficulty to craft combat arenas that ask players to make choices. In the context of enemy design, there should be what some call orthogonal unit differentiation, where different enemies have specific uses, exemplified by Doom that has short range and long range enemies, and hit scan and projectile enemies in various combinations to create depth. Level design can add spacing considerations to depth as well, not just traversal, but positional play. Positional play exists in chess, take the center of the board, in Virtua Fighter, stay away from the walls and edges, and in shooters, creating offensive and defensive strategies out of avenues of movement. Now we can fuse some of the previous elements of depth. Devil May Cry 5 has a versatile character with interconnecting mechanics, and advanced techniques like jump cancelling that amplify these systems, increasing the skill ceiling. It also has differentiated enemy types used in combination. Risk reward play, you have to get into cause damage, but this leaves you vulnerable to attack. And a style system that converts functional design into situational design. Shmups are often dichotomized along survival versus scoring design philosophies. Are they designed around needing to survive or score? Survival emphasized games create depth in their own way through bullet patterns and dynamic interactivity and heuristics to deal with combinations of enemies. A score-based system on top of this, though, emphasizes different things, elevating the game's depth. Like how Icaruga asks you to get sequences of the same color and coordinate your polarity to optimize scoring. The best games in the genre are said to have both, depth generated through the dynamics of movement and patterns, as well as scoring systems that encourage new ways of playing. When systems get deeper, more elements can be combined. More variables must be considered. More strategies are viable. Deep systems take in more inputs, have a higher state space of consideration. In F0 GX, there is a mechanic called momentum throttling. Where letting go off the accelerator at certain points actually allows you to maintain speed. When you do this depends on whether you are above the highest speed of your vehicle, if you are mid-air or drifting, turning and boosting. Both the track design and your abilities combine to create more possible states the player has to consider and adapt to. Similarly, in Wipeout, you can turn normally around corners, but you also have an airbrake, a sensitivity modifier to be able to take sharper turns at higher speed. Combine this with having to control the pitch of your craft and side shifts, and suddenly there are thousands of micro variables that can change the state space of the game, all whilst going at blistering speeds. Advanced players are often playing a different game, but this is because they are using mechanics that broaden the possibility space of the game. This creates what many call heuristics, rules of thumb that exist at different levels of a game. In chess, early heuristics are develop your pieces, control the center, castling, but the heuristics change based on where in the game you are. Go has lots of heuristics, about good shapes, alive and dead configurations, but there are always exceptions to the rules. Deep systems seem to allow for an interplay of strategic foresight and improvisation, adhering to rules and breaking them. Tetris is fascinating in this regard. You have to set up blocks in particular configurations to maximize your score. However, you must adapt to semi-random blocks falling at the same time. Modern variants of Tetris have blocks falling bundles of 7, ensuring that set play is possible even amidst the chaos, hence why there are openings like in chess. What's fascinating here is that managed uncertainty is being leveraged to create depth, but a different kind of non-deterministic depth. This framework gives us a jumping off point to understand how rogue likes, randomized terrain and even games involving dice can create depth of their own. The point here is that randomness and uncertainty don't necessarily enhance or minimize depth. It is simply a tool that can be instrumental to depth. The same is true of difficulty and balance. Arbitrary difficulty by increasing a boss's HP doesn't create depth in gameplay. However, in games like Dark Souls, difficulty can also force players to space themselves, manage their stamina, weapons and timing. Early fighting games had symmetrical balance due to characters being identical. However, designers quickly realized relinquishing balance for multiple characters allowed them to create depth through asymmetrical interactions. Again, randomness, difficulty and balance are simply tools to create depth, not depth itself. There are even games that are made deeper because of glitches and exploits. You know, rocket jumping and quake, combos and Street Fighter II. These actually increase the state space through a device called emergence, where the system exhibits properties, the mechanics and sometimes even the designers don't predict. Designing for emergence requires the system you inhabit be interconnected to create a combinatorial explosion. Breath of the Wild's chemistry engine, which links all the elements and abilities of the world together, enables both strategic and mechanical emergence because it facilitates combinations in an open problem-solving space. But like stated, sometimes emergence is unintentional and players play games in ways that push systems beyond their origins, like in the speedrunning community. In Mirror's Edge, there is a glitch called the kick glitch that allows you to kick off a wall jump as if there were ground beneath you. What makes this fascinating is that your speed and the angle of entry all factor into how far you can jump. The mechanics intertwine with this bug, allowing speedrunners to break levels. They can also chain these techniques together to build momentum, as well as use glitches in conjunction with other advanced techniques to traverse geometry they were never intended to. There is input modulation that leads to output variation, which generates emergent strategies that are viable, non-redundant and combinatorial. This is why systems like Roman Canceling and Guilty Gear, which allows you to alter the properties of moves, control time, and experiment with combos, can add depth. In the context of fighting games, this also applies in defense, like Third Strike's Parry system, which effectively allows you to parry any incoming move, altering their frame data, but also changing the risk-reward dynamics of interactions. The mobility of a game like King of Fighters, which gives you jumps, hops, hyper hops, rolls, and a run, enhances both the offensive and defensive options available, allowing them to escape pressure or leap at an opponent from anywhere on the screen. Options in the interplay between offense and defense is what grants fighting games their incredible depth, whilst also expecting fast reactions, frame data memorization, and execution. When we try to start making comparisons between games in a genre, or try to quantify depth between different ones, things become even more difficult though. We can try to compare the depth of a game like Virtua Fighter to Tekken, but this is hard because Virtua Fighter's depth comes from its constant decision-making and reads, whereas Tekken emphasizes micro-positioning and movement in neutral. Action games add new skills like reflexes and reactivity, whereas strategy games have horizons that allow for more intentional planning and play. Is it even possible to compare something like Devil May Cry to Civilization, even though both have risk-reward, engines, and heuristics of viable strategies? In systems-oriented strategic games, engines and resources get built into self-contained economies and ecosystems, where resource acquisition, management, and conversion become relevant skills. These require new metrics beyond simply strategic decisions, but also understanding how the dynamics of a game's economy impacts the interplay between different agents. What of something like a puzzle game, which is defined by the fact that it has a dominant solution, something seemingly antithetical to depth? Depth here I would venture is something more like how the mechanics are used and combined with each other, how the witness takes line drawing and combines it with constraints and rules to expand the idea as far as it can logically go, or how Stephen's sausage roll takes a simple Sokobon premise but increases the variability by allowing you to break free of your skewer and traverse differently. The depth of a puzzle system is more like an explored possibility space, but also the difficulty of the cognitive revelation required, making it more like subjects outside of games. Some puzzles are more deep because of their inherent cognitive requirements, whereas other, more open-ended problem-solving spaces require different systems-oriented metrics. How we quantify this, though, is anyone's guess. But that's why we are still trying to figure it out. The original paper I cited listed many possible avenues of research, from skill chains to strategy ladders to state space to computational complexity, but the scope of that paper was only turn-based strategic games amenable to mathematical scrutiny. Many genres are more fuzzy with their states, not discreet like a Sokobon game, but analog and uncertain. Depth is seemingly what makes games persist, which is why chess and Go have been played for centuries. Depth gives games an aesthetic value that is uniquely their own.