Theorem 1: The proabilitythat you will go first is positiely correlated with the amount of attention you are giving to the game as you wait for it to fill up.

Theorem 2: The probability of winning a dice battle is negatively correlated with the need to win that territory to create a connection.

Theorem 3: Your new dice are more likely to be placed where they cannot do you any good. Your opponent's dice are more likely to be placed placed on the states bordering you. (kdice Impossibility Theorem)

I'm sure there are plenty more.Please add.