These are terms that are thrown around a lot, but are not well defined. So, here’s an attempt at a definition.
Complexity is a measure of the possible choices a player has at any given moment, as well as the number of factors the player must consider.
Depth is a measure of the number of choices a player can make at any moment that are not dominated strategies.
Example: Tic-Tac-Toe
Tic-tac-toe is a great example of a game with no depth. At each turn, there is a single move that is definably the best move to make. Some moves seem to have more than one “best” move, but that is because the moves are functionally equivalent - picking any corner on move 2 is essentially the same move.
Tic-tac-toe is boring. The reason tic-tac-toe is boring is that it has no depth - at any given move, the player’s response is dictated.
Interestingly, game theory states that any sequential game with perfect information can be “solved.” So chess, for instance, is solvable. There is, theoretically, a single best opening move, if you have full and perfect knowledge of every possible move after that.
Depth Isn’t Necessary
Many games are successful without much depth. Almost all puzzles fall in this category - there is a single solution. By extension, most adventure games fall into this category as well. The challenge and enjoyment of these games comes from analyzing the puzzle and determining the correct solution.
If you’re going for a game that is not based on depth, there are two ways of approaching it. You can either increase the complexity of the rules, or you can present different configurations of the puzzle to the player.
Sudoku, for instance, has very simple rules. The reason Sudoku is fun is that players can play different puzzles, giving them new challenges within the same ruleset. Crossword puzzles are similar.
On the other hand, most computer games that don’t increase depth increase the complexity - once players have mastered making the correct decision between A, B, and C while considering factors 1,2, and 3, games will either increase the options available, or increase the factors the player must consider. Either of these increase complexity, but not necessarily depth.
Increasing complexity has the side effect of eventually becoming a barrier to entry for new players. By the time our hypothetical game has choices A-Z, and factors 1-100, new players will find themselves unable to grasp the game sufficiently to play.
Another way to make a game fun without depth is to focus not on the gameplay aspects, but rather on the entertainment aspects - the graphics, sound, writing, plot, etc. This is completely valid, but a bit beyond the scope of this blog in general.
Increasing Depth
How, then, do we increase depth?
Simple. Make more valid options at each decision point, and make sure we don’t fall into any pure strategy equilibrium.
A pure strategy equilibrium is an equilibrium where the players do the same move every time, compared to a mixed strategy equilibrium where the players choose different choices with a certain probability - humans are very poor randomizers, so actually properly executing a mixed strategy, for a human, is very nearly impossible. In RPS, choosing each symbol 1/3 of the time for both players is a mixed strategy equilibrium, however people are almost incapable of doing so, which is why things like Roshambot can beat humans.
If dealing with a single player game, one thing to look at is AI. As discussed here, if the AI always chooses the “best” option, it is predictable and therefore defeatable. One option is to have the AI randomly choose between a certain number of the best strategies (or between strategies that are within n% of the best, or…). This will prevent the game from having a single, best strategy due to AI predictability.
Another thing that can be done is to hide information. If not all information is known, the player will have to make choices to take into account a number of possible scenarios.
Randomization is a form of information hiding - if the results of an action are unknown, then devising a single, best strategy will be hard to do, if not impossible.
Complexity can also be increased by adding choices. However, be careful when doing this, and do it slowly, as adding a choice can often invalidate others, leaving your game with less depth, but more complexity, than it previously had.
In some cases, you can increase complexity by removing choices. If a particular strategy dominates two others, then removing that one strategy can increase depth while simultaneously reducing complexity! In most cases, that’s a win-win.
Adding a skill requirement is another possible way to increase depth - requiring a certain level of skill to execute a given strategy effectively will essentially randomize the outcome. For instance, in Street Fighter, a player may not be able to execute a Shoryuken 100% of the time. This introduces a decision point for him - weighing the benefits of executing properly against the drawbacks of a failure. Be careful with this, however, as it can lead to a situation where the game has less depth at the high end if everyone can eventually perform the skill 100% of the time (or at least close enough as to be functionally the same). While I don’t like making general proclamations, I think a good general rule is that games should have more depth at the high end of ability, not less.
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