I would have liked for this to be handled via the `OnRoomChanged` event
flow, but this isn't present in RealtimeMatchSubScreen due to
inheritence woes.
`RNG.Next(int, int)` is max-exclusive, so the random state choice would
actually never pick `MultiplayerUserState.Results` on its own. The only
reason why that state ever did show up was by a freak accident of sorts
(the logic in `TestRealtimeMultiplayerClient` would automatically
convert every `FinishedPlay` state to `Results`, up until seeing the
first player that was in the `Playing` state).