Similar to a lot of other games, the numbers will combine if there's a clear path.
If you cannot make a match, then 2 new numbers will randomly appear. This is bad.
The game ends when you have no more room and cannot make a match.
After every 24 moves, all of your tiles will be rearranged in a new location. Also when that happens, you don't get a new tile. This is critically important.
The highest tile that can be achieved is 12.
The game Threes! has a formula: whatever your current high tile is, divide that by 8, and that's the highest random tile that can pop up. My suggestion to Cetin: make the random tiles rise up to 3 less than the highest tile.
My high score is 6539 which places me at #22 out of 29,000 players. That particular game took more than an hour. Not because I took my time. Getting the first 11 can take about 30 minutes.
Addendum: I just found out that this game was updated. I've been playing the 'aggressive' version. There is now a 'normal' and 'hard' option. I'm not sure how they are different.
Housecleaning: The List of Best Puzzle Apps of 2014 will be published on December 30 & 31. Get your party hats ready.