I've been running D&D Encounters for the last several seasons. One of the areas I would like to improve is keeping players involved and interacting with the scene when it's not their turn. When you have 6 players at a table, which I often do for Encounters, it can take a long time to get back around to a particular player's turn. What are some ways to keep the players engaged with the encounter while they are waiting for their turn to start?
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Here's a few ideas that may help...
Sadly, thinking about stuff that doesn't have to do with the player's next turn adds to the time that they will spend on their turn. A great indicator of this is when someone begins their turn, looks around and begins flipping through their powers with a ponderous look. The best thing you can train players to do when it is not their turn is to build their one-turn buffer. They should always have the next minor, move and standard action that they wish to perform ready to go.
When their turn comes up, they can instantly crank through their turn and hand the reins over to the next player. This way, when it's not a player's turn they are constantly engaging with the combat as it changes, trying to ensure that their buffer is appropriate and ready when their turn comes around.
Use Free Actions to Flavor
When monsters are acting (or even when it's not their turn) you can engage non-active players with threats, growls and overall foreshadowing. This does not have an effect on game mechanics, but it involves a non-active player and gets their wheels turning on what they should do next. It also encourages players to get excited and interested in what is going on around them. Plus it never hurts to give monsters/NPCs personality.
Sometimes when things are getting really stale, you can throw in a random occurrence. It doesn't have to be a drastic or overly contrived event, but just something to allow all players to have an immediate reaction allowing them to roll something. A little skill check to stabilize when the floor shakes, Endurance to withstand a powerful wind or Acrobatics to dodge a sudden landslide are all good examples. Remember to inflict monsters as well so the players can cheer when the goblin shaman face plants while the heroes persevere.
The best thing to focus on is building GREAT turn velocity across all players and then use in-game flavor to keep people interested in what's going on. This way, the game is as efficient as possible and players are always in the game.
This is a tricky one.
Your situation involves an unkonwn number of players every week.
Involve other players in recordkeeping
Ask for volunteers. Have one person be responsible for initiative (especially if you don't use a visible means of tracking initiative.)
Have another person be responsible for conditions. It's their job to make sure that every condition is accurately tracked on everyone, so anyone can ask them what their current buffs and debuffs are.
Have a third person track monster hitpoints. All they track is how much damage the party has done, not how much is remaining.
This frees the load from you and keeps people invested. In return, you can increase the narrative richness of combat.
Some of the lack of investment may come significantly different levels of expertise. Ask for some players to serve as mentors, available to answer questions about the game and powers outside of players turns. It's important, here, that they are directed to only answer questions, rather than to volunteer advice.
In 4e, I make them track their own bonuses and effects. If they don't call out that they had mark on an enemy, that mark doesn't take effect. If they made an enemy grant CA for the turn, they get to remind everyone who hits the enemy that that happens.
I also have them roll dice for me. I have one player who is always encouraging me to kill the party. He gets to roll a lot of my important monster attacks. I think he likes hitting players more than monsters.
Appoint a rules lawyer. There are a lot of rules that can be answered with a rules lookup. Maybe the rules lawyer doesn't know a random feat off the top of his head, but he usually knows what book it's in. Not only does this keep the players busy, but it keeps their basic questions from reaching you. You should still judge ambiguous rules though.