I have had to leave more than one game, due to emergiencies, but because I do not know any other players, end up simply deadbeating. Also, even those who know people may not want to give out their personal password (even if it can be changed later). What about settiing up a button/system whereby someone can punch in a button and more or less advertise for someone else to play the game.
Here's how I see it working. The botton is on the active board, perhaps near the bottom or off to the far right so on cannot accidentally mix it up with the regular turn button. Once you push it, a special access code would generate for that game only (this might mean adding a tag to everyone already in the game, though I suspect you already do something of the sort to keep games limited). Then either anyone at all can joing the game or anyone with a certain rank range (say a rank or two to either side of the one leaving). Points would either go solely to the new person or would be split equally. Splitting would help defray the problem some new people might swoop in on an experienced person's game and gain a bunch of points or losing a bunch of points, but might be too complicated to program. In either case, I think folks would prefer these options to the current "let's sit and wait". Also, it would not solve unexpected issues like power outages, etc. However, I think a good many non-newbie misses are predictable. Also, if folks had options, it would be easier to tell if someone is repeatedly deadbeating/missing or really having outside problems.
SORRY, goofed on setting up poll -- no positive response allowed. This pretty much negates poll. OOPS.