Cognitive load describes how much information the working memory can hold at any given time. A higher cognitive load overwhelms working memory and can make running a game stressful when it doesn't need to be. You can start to forget things, like whose turn it is or features in a room you just deacribed. Simplifying any complexity in your games can reduce cognitive load and even speed up your game. For example, do you ever need to know a goblin's charisma score? Don't put it your notes! I want an intuitive game; Intuitive means something is so simple you can do it without thinking about it. There are many designs to simplify games.
Target Number, Easy, and Hard
Take as a modern example, in Index Card RPG (ICRPG), there are no Armor Classes or Defense ratings for monsters. Instead, a single Target number is assigned to all actions in the scene. That's it! If ever a circumstance is present that would make a creature more difficult to hit, let's say one monster in a group is particularly better armored, then you would rule that attacking that monster is Hard, and the Target number to hit that monster goes up by 3. If a monster was blinded, then he would be worse at dodging, so he would be Easy to hit, and the Target goes down by 3. There are no prescriptions in the rules, just apply logic. Enemy in partial cover? Hard. The target also represents saving throws for the players. I love this idea so much.
Hit Die (HD) of Monsters
In classic D&D, the number of hit die of a monster was a measure of its overall difficulty. It was the equivalent of the monster's level. The monsters to-hit bonus was equal to its number of hit die. 2 hit die means +2 to hit. It also had the save saving throws as a fighter of equivalent level. A 3HD monster saved just like a 3rd level fighter. As another design rule, the floors of the dungeon were called levels. As an assumption, the number of hit die a monster had was equal to the floor it would appear on. You could write the fighter's saving throws right on your dungeon map. All monsters had a d8 for hit die. I love these design ideas.
One Saving Throw
White Box is based on the classic D&D games. It creates a single Save for all monsters. That number changes based on character level or monster HD. Some creatures get a bonus or penalties to specific saves, but all saves use one number. For example, a fighter gets a +2 to saves against poison because they're tough. I love this rule.
Experience Points
Dungeon Crawl Classics says every encounter is worth between 1 to 4 EXP where the difficult of the encounter relative to the players represents the EXP value of the encounter. A 2 EXP encounter is an average encounter. Characters need 10 exp to level from 0 to 1st level. To get from 1st to 2nd level, they need 40 EXP. The game then uses a simple formula where the amount of EXP needed increases by 20 every level. So, it goes 40, 60, 80, 100, 120, etc. You'll never have to calculate monster EXP and then divide it, which isn't even hard. The hard part is pacing how quickly your players level up. I am looking forward to using this idea some day.
Initiative
Turns order is clockwise around the table is a rule that comes from ICRPG. It means no tracking initiative, and no rolling for initiative and recording everyone's rolls. I would change the rule about rolling dice to a coin flip to determine which side goes first. For example, on a d20; lower numbers (1 to 10) mean the NPCs go first, and higher numbers (11 to 20) mean the PCs go first. I would also waive the initiative roll when it makes sense that one side is obviously ready to act before the other. You will never lost track of turn order either.
One Action Per Turn
Older games keep it simple. On your turn, you can do one dedicated thing (an action). You can move up to your movement as part of your action. Basic Fantasy RPG and other games based on D&D B/X describes this. There is no double move (thank goodness!). This also makes your game go faster. You will never have to ask "is that it for your turn?" or "is your turn over?" You will know when someone's turn is over.
Close, Near, Far, Distant
Do not use precise, literal measurements for distances or ranges. Just use categories for distances and ranges. Close means you're so close you don't need to move; you can reach out and touch it. Near means something can be reached within one turn, so up to 6 squares or the length of a pencil. Far means something is further away than that, and you could impose a penalty for ranged attacks at this distance. Distant means something is out of sight or too far to clearly see, and so is effectively out of range.
Minions
D&D 4e had a minions class of enemy who only had 1 hit point. Use minions, or track number of hits instead of damage for disposable NPCs.
Inventory Slots
Inventory management is unimportant unless survival mechanics are important to you, in which case having a limited capacity for carrying equipment forces players to prepare and to plan, and to set priorities. It keeps them from looting and hoarding even thing. Using slots rather than tracking weight and volume of equipment is a great idea for getting the experience of management without the more laborious bookkeeping. Different games do it differently. In ICRPG, 10 items are worn or carried, or stored in pockets, 10 items are in your backpack. If PCs recruit an NPC follower to carry their junk, this makes it easier.
Point Crawl
Hex Crawling is perfectly fine, but Point Crawling simplifies the process. Traveling somewhere is simplified into a number of turns where each turn represents a day or a portion of a day. For example, Location A and Location B have two routes in between them. Route 1 is 4 turns and dangerous, but Route 2 is 7 turns but safer. If the the party gets lost, add additional turns. That's it. Players can make choices. They have thr option to use turns to explore, search for resources, rest, they can skip a rest and force themselves to march, etc. Random encounters can threaten them.
Flow Charts, Not Maps
Maps in TTRPGs often represent a location and provide its scale using precise or literal measurement. This conditions you to think you need to track and present locations with literal, precise space. GMs simply do not need to literal space. Abstract space is easier. Instead, use flow charts where blocks represent rooms in a dungeon and the lines connecting them represent the hallways or corridors. Annotate your flow charts with the notes you need such as "entrace, 3 goblins, 1 guard dog". Entire towns can be represented as a grid where the different cells represent different districts or other subdivisions, and you would list the major locations such as shops or NPC homes, in each grid along with names of each.
Adventures, Not Campaigns
Why do GMs offer to run a campaign with a payoff in 6 months or longer? I was in a campaign for over a year that I joined a year after it began. What madness! It's more complicated to do all this, and it's a big ask of your participants. Just prepare your setting and NPCs as the players explore it. Prepare for this session, not six sessions from now. Make this session kick ass. Does no one realize 5e Curse of Strahd is side content for 7 levels, then you get to the good part which is Castle Ravenloft and Stradh. Eff that. Stop thinking so far ahead. That's overthinking. A series of adventures IS a campaign.
