I have not tried joining with Hamachi or under a lan yet so I'm not sure if joining in-progress is established at all.. also I feel bad if this is already posted but I did an honest effort looking around at the 3 pages of suggestion topics.
I would like game hosters/leaders the option to allow new players to jump in their game within whatever timespan they choose. Think of it as jumping into a match of Team Fotress 2 when its already in progress and joining the action right away. Before you go in you can download any necessary mods the game creator put in.
If a player drops, they can jump back in within a few minutes, otherwise:
Option 1: A player looking for a random match can choose: (pick a random new game starting up) or (pick a random game already in progress).
Option 2:A player looking for a specific game type can browse in-progress games that have the join-in feature unlocked. They can see how many minutes are left and jump in if they like brand new games or really late games.
The player will pick up the Demigod of the player that left. This demigod could have disappeared when the player left or was under AI control (does not matter to me).
If 2 players left making the game even (3v3 to 3v2 then to 2v2) then two people would have to que up to join. I suggest this because the big reason is to fix imbalanced games. Theres no huge advantage to joining in-game at all, but I would enjoy a record of how many games I randomly picked up and finished, just for some fun prestige of helping out folks.
I would not know what games to prioritize first for a random game, nor do I know the coding problems with jumping into a game someone is hosting.