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[petf]

You are playing near end-game and have to make a decision. You are at a point where buying a Province will be a sure win, buying a Duchy will be a probable win, and buying anything else will be a probable loss.

You can either end your actions and buy a Duchy, or play an action by Way of the Mole for a new 3-card hand



You decide to play it safe and buy the Duchy. The next hand you draw is this



Knowing what your next 5 cards were, did you make the right call?

[Wizard_Amul]

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.

[petf]

Well done! You are correct

[GendoIkari]

Does Dominion Online not give you any way of knowing the order cards were in your deck before you drew them?