During my monthly game, at the Gold Star Anime, I have an open game with varying numbers of players. In the past year I sometimes deal with groups larger than five players which is something I haven't dealt with for a long time. April's session was one with one such large group.
Normally my style is for each player to roll individual imitative. I always disliked the caller system and my style is to speak directly to each players as to what they want to do. But I admit this doesn't scale too well. For the large group sessions I been a bit erratic on how I handle things as I try to relearn old techniques after a gap of 30 years.
In April session I think I finally feel that I got a grip on two aspects of managing a large group. First retaining individual initiative, and wandering around a town or dungeon as separate individuals.
For initiative, I am going to a count down system. Basically start at the top with the highest number calling out for anybody who has that initiative and working my way down to 1. This way I don't have to fiddle with my initiative board. I think this works great with large groups and allows for the individual bonuses to come into play.
For town or when the party splits, I use a strict round robin policy. I start on my left and referee that player or group for two or three minutes and go onto the next person or group. The key element is timing, looking at the roleplaying/action and getting a feel for the right moment to cut them off. Combat is rather easy due to the round structure. For roleplaying to go around town I generally use one complete exchange between a player and a NPCs. For example going to a shop and ordering magic items. The danger of not doing this right means you have players sitting around twiddling their thumbs. But on other the other hand the individual players get some center stage time like in a smaller game.
It a compromise and I am always juggling things around keeping the game moving forward, the players having fun and retaining interest. One thing is that I need to look at the seating arrangement as the long table means that the players seated farthest away are least engaged. I am thinking of turning the table longwise so everybody is sitting in front of me like a panel. That should cut the distance between me and the furthest player down considerably as well as make the game board more accessible. The other method is to make a T with me sitting at the top and the players sitting in the L section on both sides.