On the other hand, if you're in the end game and want to scrape as much points as possible, you should buy 3 Duchies first and then alternate between buying Dukes and Duchies.
Technically, you should probably buy 4 Duchies first, then alternate.
It doesn't really matter points-wise.
Going for 3 Duchies first gets you 3-6-9-12-16 points.
Going for 4 Duchies first gets you 3-6-9-12-16 points.
Although I could understand the importance of denying your opponents them in which case getting 4 is better than getting 3.
Have I missed something? If you have 4 duchies, and then buy Dukes, wouldn't it go 4-8-12 etc?
Your Duchies are worth points too.
Respectfully, I submit that Dukes are worthless without Duchies. The card text reads: Worth 1 VP per duchy you have. So if your have trashed your opening 3 estates, and buy a Duchy as your first "new" victory card, you have no VP.
Given that, why would you not accrue as many Duchies as possible before buying any Dukes? Here's why I would, and I'm open to counterarguments (I acknowledge that later in the game, opportunity costs come in to play, but assume the basic circumstances exist to make a Duke/Duchy strategy viable):
1) If contested for the duchies, I'll want as many as possible.
2) If duchies are uncontested, each Duke is then (obviously) more valuable
3) My opponent, having lost the race for the duchies, may decide to buy Dukes to keep them from me. This will only magnify my edge, because if he's buying Dukes, he's not buying Provinces, he's helping empty the 2nd pile, he's wasting turns/buys, he's clogging his deck, and receiving fewer (or no) VPs for the trouble. All his later turns will be limping with less money, and if he buys estates, he's helping me with a third pile ending.
I acknowledge that racing for the Dukes with fewer (or none) of the duchies is suboptimal, and may not be likely for an opponent with average or better skills, but if it does happen it would likely be because I've created the possibility. It's another example of doing whatever I can to increase the possibility of my win, even if that increase is slight. In poker, EV x volume = profit. That is, the Expected Value of a given play, even when small, becomes significant when multiplied by many iterations.
The math (if I've not messed up) is as follows. The first set of 3 columns is for an all duchy procurement. Second set of 3 columns represents the strategy of alternating duchies with dukes, beginning immediately after the firsty Duchy. Third set of columns represents getting to 4 duchies, then alternating. (Let Dy = duchy, Dk = Duke. GC = Green Card)
Holding VP/GC VP/$ Spent Holding VP/GC VP/$ Holding VP/GC VP/$
Dy 3 0.6
2 Dy 3 0.6 Dy, Dk 4/2=2 4/10 = 0.4
3 Dy 3 0.6 2Dy, Dk 8/3=2.66 8/15 = 0.533
4 Dy 3 0.6 2Dy, 2Dk 10/4=2.5 10/20 = 0.5 3Dy, Dk 12/4=3 0.6
5 Dy 3 0.6 3Dy, 2Dk 15/5=3 15/25 = 0.6 4Dy, Dk 16/5=3.2 0.64
6 Dy 3 0.6 3Dy, 3Dk 18/6=3 18/30 = 0.6 5Dy, Dk(=4Dy,2Dk) 20/6=3.33 0.667
7 Dy 3 0.6 4Dy, 3Dk 24/7=3.43 24/35 = 0.686 5Dy, 2Dk(>4Dy,3Dk) 25/7=3.57 0.714
8 Dy 3 0.6 4Dy, 4Dk 28/8=3.5 28/40= 0.7 5Dy, 3Dk(>4Dy,4Dk) 30/8=3.75 0.857
I leave it to each of you to draw your own conclusions. (As Disraeli said, there are three kinds of lies: lies, damn lies, and statistics.) As a newer player, I would appreciate some feedback on whether the value for "VP per card" can be used analogously to "average $ per card" to evaluate/describe/compare degrees of deck clogging.
Is there any decision-making use of the value for VP/$ spent?
