so we get an alert 4 hours before the game starts... How about another alert when the game actually starts?

you should get one like that too. check your log, you should see it in there.

There is a game start alert in the log on my iPad where the alerts are turned off, but not on my iPhone where the alerts are turned on.

I also didn't receive a game-start notification for the same game, on neither my iPhone nor iPad.

Odd. Obviously there's supposed to be an alert when the game starts. I'll look into it.
Thanks.

Great. Thanks to this I was able to track down some problems with the starting push notifications and fixed them. They should work as expected in the next build.