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You're a Dungeon Master with a party of adventures around 8. Some of the magic used by the players' characters included summoning 10 more to aide the party. On top of that the party stumbled on a small patrol of 20 monsters with maybe a dragon or something big in the background. My question is how do very big battles like this get handled with play by post without having weeks and weeks go by?
With play by post big battles may takes weeks to get through as you allow the other players a chance to get their actions in or special actions in. Even in a group setting a large battle like this can take a few hours. With all the questions and clarifications a large battle is usually a big deal so having it take a bit of time where in person or play by post you have to allow the players to go at their pace sometimes.
I'm not a Dungeon Master but this is what I've seen. One of the best ways is to have people post four or five rounds of actions at a time. If something changes in the meantime they can change their actions such as needing to heal. If you have frequent posters it doesn't take too long.
Yes, I agree with Kyrroeth here on posting multiple turns and allowing changes as the battle ebbs and flows. That said, the length of time still very much depends on the players themselves staying actively engaged. If just one or two players don't keep up their posting a battle can fall way behind. That is why for any games I Dungeon Master I make sure players understand I won't wait around. If I get X% of player posting and one or two are lagging, I'll pick for them. As a Dungeon Master I won't make the vast majority wait for one or two players.
The best thing to do is to collect as many rolls as possible and the general actions of each character from the start that way most of the battle can be calculated within 1 or 2 posts rather than round by round.