3/10 probable loss: estate, curse, gold

1/10 win: gold, gold, gold

6/10 probable win: gold, gold, estate or curse

We can assign win an expected value of 1, a loss an expected value of 0, and a "probable win" an expected value of x (also assuming "probable loss" has expected value of 1 - x).

Just buy duchy means expected value of x. Use way of the mole means expected value of (0.3)*(1-x) + (0.1)*1 + (0.6)*x = 0.3x + 0.4. For the way of the mole to be good, we need the following: 0.3x + 0.4 > x --> .4 > 0.7x --> x < 4/7. So, if a "probable win" means something between 50% and 4/7 (~57%) win, then using way of the mole was the right play. If "probable win" means more than 4/7 change of winning, then just buying the duchy was the right play.