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Subject: Researching Depth rss

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Oliver Kiley
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All, I'm working on another lengthier blog post tentatively titled “Searching the Depths: Strategy, Tactics, and the Deception of Complexity.”

Principally, I’m interesting in understanding what we mean by depth, how different kinds of depth might exist, and what the relationship is between complexity (or perhaps "complicatedness") and depth.

I’m hoping to gather input from the Cult of the Critical on how you all perceive depth in games. So velow are some questions to prompt your thinking!

(1) Does the intensity or balance of tactical vs. strategic decisions translate into a difference in depth?

(2) How does depth becomes revealed or discovered through more repeat plays?

(3) What types of games create the sense of having greater depth (for your or in general)?

(4) What is the time horizon for strategic choices and is there a connection to depth?

(5) Are complicated games deeper games? What’s the connection? Is complexity the same as complicatedness?

(6) How might we measure or gauge depth?

Have at it, I’d love to hear your input.
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Russ Williams
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Mezmorki wrote:
(1) Does the intensity or balance of tactical vs. strategic decisions translate into a difference in depth?

I think a really deep game needs interesting tactics and strategies.

(And clearly defining the difference between those two common labels "strategy" and "tactics" is another topic...)

By which I mean there should be interesting non-obvious long-term planning as well as short-term problem-solving. E.g. in Go you need to have a strategic sense of territory / influence / direction of play as well as tactical skills like life and death.

Quote:
(2) How does depth becomes revealed or discovered through more repeat plays?

I often recognize them by experiencing an aha-effect. "Oh cool, I didn't think about this possibility before." The more you play, the more you realize how much you still don't know.

Getting wiped out by a stronger player is another indicator that a game has some kind of depth.

Quote:
(3) What types of games create the sense of having greater depth (for your or in general)?

Games where there are clear skill differences between beginners and experienced players. If a newbie can win as often as an experienced player on average, the game doesn't seem deep.

Quote:
(4) What is the time horizon for strategic choices and is there a connection to depth?

Not sure what you mean; I'm guessing you mean how far ahead can you plan in a game...? I think in a deep game you should at least tentatively have some rough idea of how the game will play out, but of course no plan survives contact with the enemy and all that, so you continually revise your prognosis.

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(5) Are complicated games deeper games? What’s the connection? Is complexity the same as complicatedness?

Assuming you mean "complicated rules", my answer is no. A complicated game can be deep, but certainly complication in no way guarantees depth. A lot of complicated games (e.g. some wargames or ameritrash) are fairly straightforward to play strategically competently.

For me, the ideal is strategic depth arising from simple elegant rules, not complicated rules.

Some people enjoy complicated rules for their own sake, either for their detailed simulation value, or for the puzzle pleasure of working out how all the parts of the game work together. That's a valid intellectual challenge, but a different thing than depth, I think.


Quote:
(6) How might we measure or gauge depth?

The most practical traditional way I know is to see how wide the gap is between a newbie and a top player, e.g. by ELO ratings or something similar. For tic-tac-toe this is a very narrow gap. For Go it is very wide.

The main disadvantage is that this requires an established player community, so it doesn't work for new games.


Edited to add: sometimes one sees more directly mathematical / objective measures like average number of options per turn, average number of turns, total possible game positions, and the like. I think these can shed a bit of light (a game with a brute-forcibly small game tree is not going to be deep), but they ignore important factors like how easily people can pick out good choices, whether there are often many good choices or just one, etc. I.e. in some sense "depth" includes a subjective component, I think.
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Ben Draper
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When I speak of game depth, I refer to the number of levels of good play which can be uncovered over time. This definition informs the following answers to your questions.

Quote:
(1) Does the intensity or balance of tactical vs. strategic decisions translate into a difference in depth?


Not necessarily. Stereotypically, games with a large strategic space are considered deep, while primarily tactical games are considered shallow. But even some of the most tactical games (El Grande, etc.) can be quite deep if there are successive levels of tactics to discover.

Quote:
(2) How does depth becomes revealed or discovered through more repeat plays?


I find it to reveal itself to me through a series of 'breakthrough' plays, where I come to understand the game in a deeper way than in previous plays. This is my primary understanding of the difference between a deep and a shallow game.

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(3) What types of games create the sense of having greater depth (for your or in general)?


I'm not sure I understand the question. Do you mean to ask what types of games do have the most depth, or what types of games seem to have the most depth upon first glance/play?

Quote:
(4) What is the time horizon for strategic choices and is there a connection to depth?


Can you define 'time horizon'?

Quote:
(5) Are complicated games deeper games? What’s the connection? Is complexity the same as complicatedness?


Deeper games often have more complicated interactions between game mechanisms compared to shallow games. However, complicated rules and gameplay themselves are not necessarily indicative of a deep game.

Quote:
(6) How might we measure or gauge depth?


Objectively, it would be very difficult, if not impossible. Here are two subjective ideas that come to mind, though:

1. Some measure of the number of data points that have a meaningful effect upon individual decisions. The more data points that affect a decision, the deeper that decision is. The downside to this approach is that it looks primarily at tactical depth, and only includes strategy insofar as it affects that tactical depth.

2. Some measure of the number of levels of good play one can reach in the game. This has the obvious downsides of being a) difficult to define; and b) difficult to account for uneven levels (i.e. the drop from level 3 to level 4 may be less deep than the drop from level 5 to level 6).
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Tim Seitz
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One aspect: I differentiate between depth and breadth. Some games have depth, and some games have breadth, while very few have both. I define depth as having a lot of room for analysis and learning for a given setup. Whereas breadth would involve having a lot of different setups.

Applied to Dominion: For an initial set of 10 kingdom cards, you probably don't need a tremendous amount of analysis or repeat plays to identify an optimal strategy. An expert player good probably pick out what to do with out even playing it. A new player might require a couple of plays to decide what is best, but that's not much of an experience gap, at least for a given set of cards.

However, where Dominion shines is in its massive breadth. There are a gajillion different combinations of cards that makes every layout an interesting strategic puzzle, even for an expert player. When playing each game with a different setup, an expert will have an advantage over a new player because they can more likely hit on the best strategy at the start. So there is the potential for a large skill gap, but it's breadth-driven, rather than depth-driven.

I see strategic space as a like the volume of water in a lake. Some lakes are very deep; some lakes are very shallow. But a shallow lake can still have as much water in it as a deep lake. If that makes any sense.
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Dave C
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I would say depth is a game’s sum reflection of all player motivation, player choice, and player proficiencies. Each game is one little mirror of this triangulation. Some reflect much, some little.
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Quote:
(1) Does the intensity or balance of tactical vs. strategic decisions translate into a difference in depth?
 

Yeah, Russ beat me to the "strategy vs. tactics" debate. Some BGGers use the two to refer to timeline differences in the lifespan of a player's move, i.e., long-term and short-term, respectively. Other users use the term "strategy" to mean that a decision "requires thought" and there's no real attention to the lifespan of the move or for how long it takes for the ripple effect of the move to die down. "Strategy" is the meal for me, and "Tactics" is how you have to pay attention to how the oven heats differently and affects stated cooking time, or how/when all the ingredients need to be prepped ahead of time, or how a shortage of ingredient X means you have to improvise, but the meal still needs to be finished all at the same time, so find a way to make it work.

Quote:
(2) How does depth becomes revealed or discovered through more repeat plays?
 

I forget which baseball player (a hitter) said this, but he was referring to Mariano Rivera's cut fastball. He said something like "it's a great pitch; even when you know he's going to throw it, you still can't hit it." That's close to what I take depth to mean, I think. That hitter was among the top few hundred players in the world. And there existed a facet to the game he more or less mastered that was still beyond his grasp; even when he knew it was coming, he couldn't hit the pitch. Rivera was able to change the game; no one had a cut fastball that good before, and that wasn't even an established career path (Rivera was a failed starter, remember).

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(3) What types of games create the sense of having greater depth (for your or in general)?
 

It's tempting to interpret this question as "what kinds of games do you prefer," and I want to avoid that. For me, abstracts and economic games offer the most sense of "play," and tend to avoid pre-baked paths into the game (i.e., the Starvation strategy, the Nobles strategy, the Shipping Strategy, the Purple Building strategy, etc). It might be semantic, but I have a hard time accepting games that have been balanced to death as being deep. Related to the above, it's very hard to "change the game" if the game resists being altered, no ripple effects, no changing values, no creative play.

Quote:
(4) What is the time horizon for strategic choices and is there a connection to depth?


I'm not sure I follow. Do you mean "how many moves in advance do I need to think before I call my move "strategic" over "tactical"? I'll answer that question with an I'm not sure. "Tactical" moves are closely related to "reactive" in my mind, and "strategic" is closer to "opportunity creation." So I guess if the goal is to create opportunity (i.e., set a trap, create a diversion, start a new way of getting points), that can take anywhere from 2 moves to a lot. But again, this kind of gets back to what Russ said about having a standard definition.

Quote:
(5) Are complicated games deeper games? What’s the connection? Is complexity the same as complicatedness?


Complicated games are not necessarily deeper games. A game that features a huge amount of choices that don't appreciably differ from one another is not "deep." It might be closer to Tim's "breadth."

Quote:
(6) How might we measure or gauge depth?


It's defeatist, but I'm not sure we do. This kind of thing (depth in games, greatness in art, longevity in music, etc) tends to be community-defined by standards that don't necessarily exist at the time of creation. One of the biggest hurdles in addressing this, too, is that games don't tend to get played that frequently; most BGGers move on to new things before any experiment in depth can run its course.
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J C Lawrence
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I define depth as a combination of long look-aheads (ideally game-long), and nuanced & reasonable trade-offs among short, medium and long-term (dis)advantages in player decisions.

Mezmorki wrote:
(1) Does the intensity or balance of tactical vs. strategic decisions translate into a difference in depth?


Only to the extent that tactical quality is irrelevant to depth. The focus in depth is on the interplay between early and late implications of decision, not their current-time complexity.

Quote:
(2) How does depth becomes revealed or discovered through more repeat plays?


It often is but need not be.

Quote:
(3) What types of games create the sense of having greater depth (for your or in general)?


High information, long look-ahead, high butterfly games such as the 18xx.

Quote:
(4) What is the time horizon for strategic choices and is there a connection to depth?


I generally view strategic choices range from game-long (made before the game started and pertaining to the end of the game), to a minimum of 3.5 turns into the future from the current state.

Quote:
(5) Are complicated games deeper games? What’s the connection? Is complexity the same as complicatedness?


No. Complicated games are just...complicated. It is orthogonal.

Quote:
(6) How might we measure or gauge depth?


With difficulty. I'd start out with something like the square of a measure of the tractability of the implications of long-term look-ahead decisions, by the degree of interplay among decisions targeting variously near, medium and long-term.
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Oliver Kiley
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Oh my goodness, so many great responses!

russ wrote:
I think a really deep game needs interesting tactics and strategies.

(And clearly defining the difference between those two common labels "strategy" and "tactics" is another topic...)


This distinction merits some attention for the blog post; and I’d like to get some working definitions for both to aid the conversation. I see it roughly as this:

Tactical Decisions:
- Tend to focus more on immediate and short-term opportunities
- Tend to emphasize the execution of actions to support broader strategic goals.
- Tend to relate more to actual changes in the board state

Strategic Decisions
- Tend to focus on long-term or game winning opportunities and the pathway to get there.
- Informs the “look ahead” and deals more with uncertainty and the planning of actions
- Tends to be decoupled from boardstate, the strategic disposition of players “is in their head.”

In my professional life we deal with a lot of cross-scale design/planning issues, and hierarchy theory has a significant bearing on the thought process. At a basic level, hierarchy states that at the scale of focus, higher levels of scale impose goals and constraints on the focal scale, while lower (smaller) levels of scale/order explain the effects, operations, and impacts.

So when it’s your turn to make your next move – ultimately this is at “tactical” level of focus – yet the choice of which move to make is constrained and/or driven by higher level objectives at a strategic level (i.e. how am I going to win?). At the smaller scale, how the move is taken and resolved is explained by the game’s mechanics.

In a certain way, I wonder whether an argument can be made that all actual “actions” taken in game are ultimately a tactical choice as suggested by hierarchy theory. Obviously the factors that go into that tactical decision can have long-term, strategic consequences that must be considered.

I wonder, are there pure games of strategy and pure games of tactics?

Out4Blood wrote:
I see strategic space as a like the volume of water in a lake. Some lakes are very deep; some lakes are very shallow. But a shallow lake can still have as much water in it as a deep lake. If that makes any sense.


Consider yourself quoted for the blog post! This is a great conceptualization of what I can “Decision Space” (your strategic space). I’ve been hunting for a good analogy and this works brilliantly. And of course, games with lakes of greater volume have relatively more breadth and/or depth, other factors being equal.

BennyD wrote:
I'm not sure I understand the question. Do you mean to ask what types of games do have the most depth, or what types of games [seem] to have the most depth upon first glance/play?


What types of games “do” have the most depth is more pertinent, although perception plays a role.

It’s easy to look at Chess or Go and say these are really “deep” games because so much has been written about them. But I wonder – is that a consequence of the games really being significantly deeper than other games? Or is it they are such universally played games for so long that time has afforded the discovery of their depth (plus combined with competitive play environments). I often question whether most games could achieve a similar level of perceived depth given 100’s of years of play.

The influence of luck or randomness is also an important consideration here. Chess and Go are zero luck (beyond start player) and are perceived to have great depth. But what about Poker (also played competitively) that has a relatively high level of randomness. Clearly more skilled players are able to navigate the probability fields and work the meta-game better and can more often win. I think luck often has to do with the potential for depth, but is not automatically a limiter of it.

BennyD wrote:
Can you define 'time horizon'?


I think of time horizon as how far down the road do you need to plan for victory. It’s similar to, but different from look ahead. Look ahead, to me, is more about how far down the road you plan and conceptualize a series of tactical moves and counter-moves. I.E., in chess, “if I go here, my opponent might do this, and then I could do that, and then he’s likely to do this other thing, etc…” That’s look ahead to me.

Time or Strategic Horizon is more about how far out in terms of the overall arc or length of the game and I planning my strategic objectives that lead to a win. So I might say, I want to strengthen my position on this part of the board and try to capture my opponent’s Rook – how far down the road is that? Ultimately, Chess has a strategic horizon that’s synonymous with the end game condition – capture the opponent’s king, you win and the game is over.

So how does this compare to a game like El Grade where every few (3?) turns is a scoring round? Your strategic horizon is primarily oriented towards a series of milestone points throughout the game, with players trying to maximize their score at each point while maintaining the opportunity for success in subsequent scoring rounds. Carcassonne has a very short strategic horizon, as most of the scoring is driven by immediate tile placement – but there are some elements that tie into game-end bonus scoring that merits consideration during play.

russ wrote:
Some people enjoy complicated rules for their own sake, either for their detailed simulation value, or for the puzzle pleasure of working out how all the parts of the game work together. That's a valid intellectual challenge, but a different thing than depth, I think.


Yes. I’m currently trying to learn + play Le Havre on the iOS. The rules aren’t necessarily complicated – but there is a great deal of complexity/intricacy in all the cards and their effects and interactions. I want to struggle through so I can gain a better understanding of the game’s (potential?) depth – but I wonder whether all these card interactions + conversions are going to lead towards this being a deep strategic game versus a game of informational + logistical optimization; in other words, of puzzle solving.

To a certain extent – I wonder whether there is a tie in between depth and the “modes of thinking” concept, which suggests that games are a mixture of logistical, spatial, and intuitional thinking. I’d argue that pure games of any of those three types can have significant depth – but it depends on what the players are looking for. A very complex puzzle can provide a deep experience; but that experience is different from a pure negotiation game where the depth originates from the players, or a spatial game where the depth comes from the intricacies of spatial interactions.

raveros wrote:
It's tempting to interpret this question as "what kinds of games do you prefer," and I want to avoid that. For me, abstracts and economic games offer the most sense of "play," and tend to avoid pre-baked paths into the game (i.e., the Starvation strategy, the Nobles strategy, the Shipping Strategy, the Purple Building strategy, etc). It might be semantic, but I have a hard time accepting games that have been balanced to death as being deep. Related to the above, it's very hard to "change the game" if the game resists being altered, no ripple effects, no changing values, no creative play.


On a personal note, I’m right with you. I think the balance between “perscriptive play” versus “creative play” is of enormous significance.

Stone Age is my poster child for perscriptive play – although this is not a well-grounded conclusion as I’ve only played it a handful of times. But the existence of these “discrete” strategies or pre-baked paths, in my mind, makes the gameplay all about tactical execution; of who can pick a path and execute it more effectively at the expense of others.

Tigris + Euphrates is an awesome game of “creative play” in my mind. The decision space/volume is large creating the opportunity for all kinds of novel or unexpected moves. There are no clear pathways to victory – the board state is constantly in flux and changing and it takes genuine creativity and imagination to conceptual future moves that can place you in the lead.

BennyD wrote:
Objectively, it would be very difficult, if not impossible. Here are two subjective ideas that come to mind, though:

1. Some measure of the number of data points that have a meaningful effect upon individual decisions. The more data points that affect a decision, the deeper that decision is. The downside to this approach is that it looks primarily at tactical depth, and only includes strategy insofar as it affects that tactical depth.

2. Some measure of the number of levels of good play one can reach in the game. This has the obvious downsides of being a) difficult to define; and b) difficult to account for uneven levels (i.e. the drop from level 3 to level 4 may be less deep than the drop from level 5 to level 6).


The concern with #2, as others have eluded too, is that it is only relevant for “institutionalized” games that track ELO or other skill rankings. But the online implementations of many games might offer opportunities for better aggregating and understanding rankings for newer games.

I’m personally interested in digging through ideas along the lines of #1. My older blog post Towards a Science of Boardgames (Part I) explored the idea of “goal trees” in games. Goal trees are a way to measure how many decision points do you need to navigate through in order to reach a strategic goal AND how many factors need to be weighed at each decision point. The idea isn’t fully developed, but I find it pretty interesting.

Below is a Goal Tree I made for Race for the Galaxy.



This doesn’t incorporate the “factors to weigh” at each decision point, or for that matter really map the decisions themselves. Instead, it’s the structural/mechanical process of how to go from cards in your hand to Victory Points.

I wonder whether more elaborate goal trees increase the “complexity” of a game, and potentially the depth; but it is really the “factors that must be considered” that accounts for the depth in a game. If there are no external factors that must be considered – is it just then a puzzle, with the size of the goal tree creating a more or less complex puzzle?
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clearclaw wrote:
I define depth as a combination of long look-aheads (ideally game-long), and nuanced & reasonable trade-offs among short, medium and long-term (dis)advantages in player decisions.


Although long look-aheads are an indicator of depth, they aren't sufficient in and of themselves. Take chess for example, players do not look ahead from the beginning. There is look-ahead but it isn't exhaustive. Positional analysis is also important. There was the famous quote from Capablanca (I think) "I only see one move ahead, the right one". In reality good chess players mix both positional analysis and look-ahead and mix the amount of each they rely on at different times of the game.

There are also the games, such as Arimaa, which have such a high branching factor resulting in such a bushy tree that look-ahead is too problematic. I think Arimaa almost demands an entire positional analysis approach. Although I haven't played it enough to develop anything more than gut feel.
 
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About 'pure tactics' vs 'pure strategy' games. I think that Innovation is about as close to a pure tactical game as you are likely to get. If you omit the special wonder cards, where you might decide for strategic reasons that you would like to play a certain number of cards to win the special domination, which does cause for strategic play, there is very little scope for strategic thought. Take a look at the cards you have. See which one can do the most damage to your opponents. Activate it. That's pretty much it. There is no point in having a long range strategy -- even if you have all the cards memorised -- because what's best for you to do is entirely dependent on what the other players have played, which can change every turn. The more people that play, the less useful a strategy is. Can you thrive amidst chaos? Can you live without a plan?

The howls of anguish from those BBGers who think the game is 'broken' and 'too chaotic' -- either all of the time, or with 3 or 4 players indicate that there are many people who cannot -- or who at least find it very unpleasant. Myself, I just have deepest admiration for Carl Chudyk for coming up with such a game. And I prefer to play it with 4.

I'd call this game very broad but as shallow as it gets - where deep means 'strategic depth'. It's tactically-deep, but maybe we need to use a different term to describe that.



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lacreighton wrote:
About 'pure tactics' vs 'pure strategy' games. I think that Innovation is about as close to a pure tactical game as you are likely to get. If you omit the special wonder cards, where you might decide for strategic reasons that you would like to play a certain number of cards to win the special domination, which does cause for strategic play, there is very little scope for strategic thought. Take a look at the cards you have. See which one can do the most damage to your opponents. Activate it. That's pretty much it.

While I agree (and love) that Innovation is mostly a tactical, improvisational, game, I don't think that's quite right. There are a few broad long-term strategies to follow. For example, a 'teching-ahead' strategy looks quite different from an 'early achieving' strategy or a 'focus on splaying' strategy.
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Inexperienced Innovation players tend to play the game more tactically, but that doesn't make it a solely tactical game. With two experienced players, the game is made up of tactical responses to shifts in long-term strategy.

The long-term strategies are often unclear to new players, because they are contingent upon a solid understanding of the game's internal timer (i.e. the ways in which the game can end) and/or specific cards or groups of cards. Without this understanding, the game has to be played primarily tactically.
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BennyD wrote:
Inexperienced Innovation players tend to play the game more tactically, but that doesn't make it a solely tactical game. With two experienced players, the game is made up of tactical responses to shifts in long-term strategy.

The long-term strategies are often unclear to new players, because they are contingent upon a solid understanding of the game's internal timer (i.e. the ways in which the game can end) and/or specific cards or groups of cards. Without this understanding, the game has to be played primarily tactically.


Go is a great example. Typically, new players play close to each other, in one corner or another, before switching to another corner, and race along lines. I played this way for almost a year. And then I played someone who knew a little about what they were doing; while I captured one corner, he seemed to be placing stones randomly around the board; only later did I discover that whenever we raced along a line or battled somewhere on the board, he always had one piece already placed to gain the advantage. Ultimately, I won the corner, he won the board. His solid understanding led to opening tactics that spoke of a long-term strategy that I just couldn't grasp at the time. I did a lot of reading after that game.
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