You can only play the game at 12 AM-1 AM NST, unfortunately (when trying to get the avatar, I had to stay up until 3 AM every night, as I live on the East Coast, which is three hours ahead of Neopets, argh!).
The game itself is rather simple: you and Count VonRoo each role dice. Whoever gets the highest number on their roll, wins. If you win, your active pet gains a level. If you lose, their level drops by one. If you tie with the Count, you roll again, and this time, if you lose, he takes away two levels. If you win, you get an avatar and your pet's level goes up by two. If you tie, same, just with another level at stake (because it's three rolls, so three rolls, three levels at stake, and so on).