As a Dungeon Master, you may need to do a lot of rolling. As the group gets bigger, the more rolling the Dungeon Master will find themselves doing. In D&D 5th edition, this is also true as the party levels up (there aren't that many high level enemies so instead larger groups of enemies are needed to challenge the players). In order to help deal with this, I will provide a few ways to reduce the total number of rolls. It will be mostly focused on D&D, though the basic principles can be applied to other tabletop RPGs as well. Most of it will be already known to older players, but I hope it helps.
Don't Go Overboard
If the Dungeon Master goes overboard with reducing the amount of rolls, the game might start to feel too deterministic. It's also important to remember that the goal here is to reduce the rolling in order to keep the game flowing at a pace that is still interesting for the players. The players can handle their own rolls and should be allowed to roll for actions that they take.
Reducing Combat Rolls
D&D 5th edition has the average damage and health provided for their creatures. Simply using these values will allow the Dungeon Master to greatly speed up combat, since they will only need to roll to see if the creature hits (you need to leave some randomness). Combat may feel a bit less dangerous for players, since they will expect certain damage from their enemies (some groups may prefer the reduction in randomness) and the enemies themselves will feel less diverse compared to if health was rolled.
Where it gets a little trickier is initiative. You don't want to completely remove rolling for initiative and take the average because doing so would make combat less tactical. For this kind of situation, I've seen two main ways being used. The first is to break off similar enemies into smaller groups (if there are 8 goblins, you can break them up into 4 groups of 2 or 2 groups of 4) and roll for those groups (this also works for stealth and surprise). Doing so reduces randomness a bit and should really be employed when there starts to be a lot of enemies in a combat encounter. It's also perfectly balanced when the players are also acting as groups (as I outlined here). To make the scene more climactic and to keep things going faster, I've seen Dungeon Masters move multiple characters at once. While this speeds things up, it's also important to try and avoid doing things that couldn't be done if you used turns instead.
Pre-Rolling and Out of Combat
When not in combat, it can be tempting to try and reduce rolls as well. The issue is that often times doing so causes strange results. Stealth, for example, is made against the passive perception of characters. If you remove this roll and use the average values, we end up with the same issues as when we looked at combat (we removed too much randomness). In such a case, it may be beneficial to do rolling before the game and keep a note of it. Doing so has a few advantages. First, it prevents meta-gaming since players don't know the roll has been done. Second, when done during preparation, it makes the actual running of the adventure easier and allows the Dungeon Master to focus more on the role-playing. The down side is that it can sometimes cut down on the suspense and if your players aren't aware of it, may think that the Dungeon Master made the decisions when in reality it was the dice. It can also make some moments less suspenseful, since players won't be waiting in anticipation to see what the dice say. Naturally, it can also only be applied to things that were foreseen or planned. The Dungeon Master should not be too attached to the rolling he did previously to prevent railroading.
Situations where this can be done to great effect are:
- Rolling health (you can keep an array of values for each creature you are going to use for that week)
- Deciding if a creature will be seen by party members (the value will then be used for active checks)
- Deciding if a player will notice a lie (the value will then be used for active checks)
- Deciding if a character will succeed on a skill check (sometimes I find myself making adventures where the bad guys have their own skill checks in order to allow for more outcomes, especially if I like it enough to run with a different group)