How do I get the third daily card from the Steam Monster game?

Per the Steam monster minigame's FAQ:

If you’re Steam Level 8 and above, you’ll get a Summer Sale trading card at random intervals while playing, up to three per 24-hour period.

Today is the 7th day of the sale, and I've gotten 14 cards from the game - two each day, and always right when I load up the game for the first time that day. I've tried leaving the game actively running in the background all day, but I have never gotten a third card for playing the game. What do I need to do to get that third daily card to drop?

Solution 1:

1st card: for joining a game.
2nd card: if you joined a friend's game.
3rd card: actively be there when level 10 gets beaten.

Source