In the standard rules of the board game Risk, players take turns selecting or "drafting" the 42 territories on the board until all territories are owned. We present a technique for drafting territories in Risk that combines the Monte Carlo tree search algorithm UCT with an automated evaluation function. Created through supervised machine learning, this function scores outcomes of drafts in order to shorten the length of a UCT simulation. Using this approach, we augment an existing bot for the computer game Lux Delux, a clone of Risk. Our drafting technique is shown to greatly improve performance against the strongest opponents supplied with Lux Delux. The evidence provided indicates that territory drafting is important to overall success in Risk.