I read somewhere (forget exactly where) that it isn't completely random, its based more on ratio's and percentages.
Lets say you play a card with that ends up with 24 attack power, and your opponent plays a card that ends up with 16 attack power (both in any denomination of pillz and power).
In this case, you would have a 24/40 (60%) chance of winning, and your opponent would have a 16/40 (40%) chance of winning. The number 40 is gained by adding the two attack power totals together.
In this way, even though it is possible for someone with a 5% chance to win, you can increase your chances to win based on some simple math.
Memento Mori -Wednesday 06/06, 14:22
6 power 6 pillz = 42 attack
3 power 3 pillz = 12 attack
the opponent has a 20% chance of winning, not too high but a nice chance (1 to 5)
The opponent has NO chance of winning. If your attack is double the opponent's you have a guaranteed win. It's important to keep that in mind when playing random.