Locking In a Riskless Dollar

Shares of Helios Robotics will do exactly one of two things by tomorrow's open: double, or fall by half. Separately, a colleague is happy to take either side of an even-money (1:1) wager on which direction the stock moves. Suppose you put $A$ whole dollars into the stock and stake $B$ whole dollars on the wager, choosing sides so that your total profit comes out identical whether the stock jumps or drops. What are the smallest whole-dollar values of $A$ and $B$ that lock in a positive profit either way?