The D&D 5e Dungeon Master's Guide's "Know Your Players" section gives GMs a starting point for tuning they game experience for their players, but I think the approach detailed here supplements that guidance, and will lead to a better gaming experience. Thinking about these options as tune-able parameters will help that -- instead of trying to pigeonhole players into an archetype, figure out what are the parameters that matter most to the individuals and the group, and tune the game towards them.
What are "game parameters"?Your game has a number of dials or controls. They are the theme or tone of the game, what rules are firmly adhered to and which can be bent, the amount of humor, the gritty realism, the level of fantasy, and the ceiling for impossible actions. They can include binary options like whether there is PvP combat, or they can exist as some point in a range between two extremes, like serious vs. silly. They can cover how the group divides its time between combat or RP-based encounters. Some are controlled by the players and only loosely defined or steered by the GM, and others the GM exclusively controls.
The game system itself might define some of the parameters, or at least set baselines for them. Others are set by the players and/or GM. Some emerge dynamically as a campaigns plays out, and will fluidly change from session to session. Others will be constant, perhaps for the system, the campaign, or the group.
It would be impossible to list them all, but let's look at some common and/or important ones for a game like D&D 5e (with some other games mentioned for comparison):
Combat vs. role-play
The division between combat encounters and role-playing is probably one of the easier things to tailor to your group, and one that players can feel diversely about.
Combat styleTactical grid-based combat or theater-of-the-mind? Or maybe something in-between, like zone-based combat. Not every encounter needs to be the same, sometimes the encounter can lend itself to one style over another, but it's good to know your players' preferences.
PvPWhether PvP is allowed (and if so, under what circumstances), or even things like allowing intentional friendly-fire for area-of-effect spells.
Inclusion of sensitive topics (rape, torture, gore, etc.)
Especially important when playing with people who don't know each other well, make sure everyone knows where the line is for sensitive topics, and what is allowed and what is not.
A D&D game might hardly be a D&D game without a Monty Python or Adventure Time reference somewhere, but sometimes you need to disallow a familiar being named Dickbutt or a character named Tronald Dump when you know it will only break immersion after the initial chuckle is gone.
My Gamma World games are inherently more silly than my D&D games, and that's part of the appeal for when we run it. For some parameters, like this, the system can set the baseline in very different spots.
Single character spotlight vs. the group
This might come under splitting the party, or even just players talking about how their characters spend their downtime. Know what the threshold is for you and the players is for focusing on activities that aren't including the whole group. Some activities like this can be dealt with between regular sessions with just the individuals in question.
Whether you the GM rolls their dice in the open or not, and how hard you play the monsters to take down the characters. I feel, that when I GM, if I'm not rolling dice in the open, there's no point in rolling -- but I'll tweak less visible aspects (like monster HP or tactics) if I've misjudged an encounter's intended difficulty. My goal is to make the players have fun, but rolling the dice in the open is a way to keep risk in the minds of the players.
Some players are more attached to their characters than others, and will be more upset by character death. It's a good idea to know how the players feel, as well as to set their expectations of the game you intend to run.
Along the lines of PvP, but you might want to include discussion about non-combat actions, like stealing from the party (I'm looking at you, stereotypical rogue player) or conflicting alignments/goals.
Is the basis in reality in your game more akin to Crouching Tiger, Hidden Dragon or Heat? The system will often have its own anchor on the reality scale, but you can always push that up or down. Some character concepts may hinge on a being able to operate on the envelope of what is allowed, so it is important for players and the GM alike to be in accord.
How (or who) makes decisions for the group
This is one dynamic that the GM doesn't really control, but would be wise to pay attention to. Does the group vote on decisions, to work until they have consensus? Does a single player (or character) dominate the decision making, or is there anyone that routinely is excluded from getting what they want? Some players may not care so much, but make sure the ones that do are getting what they want.
Can the players freely contribute their additions to the world's history, events, places, and people? Or, as the GM, do your prefer to keep narrative control to yourself? You'll have to weigh your comfort with being able to assimilate new ideas with the players' desire to collaborate in world-building. Games like Dungeon World rely on player contribution, but not all players want that responsibility.
Are you playing strict rules-as-written? Following guidelines like Adventure League when it comes to supplements? What homebrew and houserules do you have? Are you including Unearthed Arcana or DM's Guild material? Extra rules options can tax the GM, but give the players more options. How flexible are you with "the rule of cool" and letting the characters pull off stunts beyond what the rules allow?
Rewards and pacing
How much treasure and how many magical items do you reward the party with? Do you follow by-the-book XP rewards, or use milestones, or something in-between? The feeling of character progression in terms of gear and level is important. Does the system have a "sweet-spot" where you want to slow progression a bit to spend more time there? Does the player have a specific item in mind that is part of their character concept and goal?
Puzzles and problem solving
Some players thrive on solving puzzles or coming up with creative solutions, while others will be easily frustrated and quickly become disinterested when they feel "stuck" for any length of time.
Will characters get away with breaking laws or violating customs? Sometime the players just want to play murder-hobos, but sometimes they want a world that reacts to their transgressions.
Expectation, importance, and experienceMost of the time that there is unhappiness or dissatisfaction at the table, it likely stems from someone's expectation of one of these parameters not meeting what they are experiencing. Certainly, people can be pleasantly surprised when the is a disconnect between expectation and experience, but it can also lead to disappointment. If the person has attached importance to that expectation, that disappointment will mean a greater level of dissatisfaction.
Ideally, for each parameter you, you should ask each player what their desired level is and how important that parameter is to them. In an ongoing game (or in retrospective), you should also ask what they perceive the value to be or ask if it needs to be dialled up or down, relatively.
Not everyone in the group will have identical desires for every parameter, but hopefully your group's range of desires falls within a close range of values. Depending on what it is, though, it can be okay for there to be wildly different values.
Group vs. individual parametersEven if your players have some wildly inconsistent expectations, that is not always a problem. Some parameters are easy to fine-tune or have different settings for that player. For example, if only one player gets a lot of enjoyment out of creative contributions, then don't force prompts for that on the other players. If one player wants extra solo spotlight time or to be able to do stuff on their own, then see if you can handle that between regular sessions.
Values changeIt is important to remember that any of these parameter can change. Players may evolve different tastes, and the focus of a campaign my drift over many months. Game systems that lend themselves to one play-style in the beginning may be more rewarding played differently at higher levels.
After each session, evaluate where the game hit the mark and where it missed, and make yourself a note of what to adjust for the next session. It's not hard to fine-tune towards your marks this way.
Periodic re-calibration is a good idea. Give your game a tune-up by checking in with the players every now and again to see where things stand.
For game mastersThe first step is to find out what is important to your players, and to yourself. Explore and set expectations at the beginning of a campaign for yourself, and find out what the players are expecting and wanting.
Recheck periodically, and make sure you are checking the right things. You can do it more formally with something like a survey, or just check-in with players pre/post or between sessions.
For playersMake sure you are clear about your expectations, as your GM can't fix/adjust what they don't know. If there is a gap between your expectations and experience, bring it up sooner rather than later. Keep in mind that other players have their own expectations, and GM may be trying to find a happy medium. Contribute to that effort.
These days, with Critical Role and Acquisitions Incorporated, Twitch and YouTube, simply watching RPGs is a lot more common than it used to be. It is important to remember, that as audience or viewer, you may have different expectations and desires than the players and the GMs of the games you watch. Moreover, viewers are less likely to be privy to discussion about the parameters. Before you get upset about how someone else is playing their game differently, remember that even in the most rigid of rule sets, there will be variation in how different groups play.
By thinking of the game system and sessions as something that has qualities you can tweak and adjust, it's easier to identify what the GM and the players want out of the game, and whether the sessions are hitting or missing those targets.
The targets can (and will) change over time, so it is important to continually adjust with them. The good news is that all of this is easy, and doing so will make for a more fun game for everyone.