Huh, so it basically comes down to whether there is an odd or even number of things to buy left. Still complicated to work out the math on the fly, and actually on this particular board we could have disrupted each others decks by buying Embassies as attacks, hoping the opponent will whiff on their Province buy, pretty risky, but it at least gives you a slight chance if you are in the losing position. This could also be done with a slightly higher likelihood of success with IGGs or Noble Brigands.