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Subject: A note on dukes rss

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Yanni Cooper
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I've noticed a lot of people suggesting that 6/4 is a "proper" split for duchy/dukes. 7/3 is just as good. I've done a little math and the breakdown is thus:
When you have an odd total, you want to have 3 more duchy then dukes. Then you want to buy one of each, but it doesn't matter which order you buy them in, they both yield the same amount of points.

So if you have 3 Duchy buying either will get you 3 more points.
If you buy a 4th Duchy then Duke is worth 4 for your next buy.
If you buy a Duke then Duchy is worth 4 (It'll increase the value of your Duke) for your next buy.
That will leave you with 4 Duchy and 1 Duke. And again you will want to buy one more of each, but you can do so in either order.
 
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Ben Bateson
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I would imagine that 7 duchies are harder to buy due to deck exhaustion. It depends how highly your game-mates value them.
 
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Yanni Cooper
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Yeah, that is definitely something I didn't factor in...
 
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Travis Cooper
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Usually you will have to buy the duchys earlier. If somebody else is going for that strategy, or if they see you are then the duchys become more valuable. Somebody trying to stop you will buy a duchy long before they will buy a duke. With competition you won't get as high. I typically try to get at least 4, possibly 5 duchys before going for the dukes because of this.
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Grzegorz Kobiela
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I've found this is the most optimal play:

4 Duchies, 2 Dukes, 1 Duchy, 1 Duke, 1 Duchy, 1 Duke,...
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Ian Kelly
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Ponton wrote:
I've found this is the most optimal play:

4 Duchies, 2 Dukes, 1 Duchy, 1 Duke, 1 Duchy, 1 Duke,...


Why?
 
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Grzegorz Kobiela
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1st Duchy 3vps vs Duke = 0vps
2nd Duchy 3vps vs Duke = 1vp
3rd Duchy 3vps vs Duke = 2vp
4th Duchy 3vps
1st Duke 4vps vs Duchy = 3vps
2nd Duke 4vps
5th Duchy 5vps* vs Duke = 4vps
3rd Duke 5vps
6th Duchy 6vps
4th Duke 6vps
etc.

* Duchy is worth 3, but you've got 2 Dukes already, that are now worth another 1vp each.
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Ian Kelly
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Ponton wrote:
1st Duchy 3vps vs Duke = 0vps
2nd Duchy 3vps vs Duke = 1vp
3rd Duchy 3vps vs Duke = 2vp
4th Duchy 3vps
1st Duke 4vps vs Duchy = 3vps
2nd Duke 4vps
5th Duchy 5vps* vs Duke = 4vps
3rd Duke 5vps
6th Duchy 6vps
4th Duke 6vps
etc.

* Duchy is worth 3, but you've got 2 Dukes already, that are now worth another 1vp each.


I realize that. I was wondering why you find that buying the Duchy fourth and the Duke sixth is optimal. Points-wise, it doesn't make any difference which card you buy in these positions.
 
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Grzegorz Kobiela
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It does make in the long run:

1st Dy 3 vs Dk 0
2nd Dy 3 vs Dk 1
3rd Dy 3 vs Dk 2

1st Dk 3

4th Dy 3 OR 2nd Dk 3 <-- here I've got 4 with above strat

rest irrelevant, cos inferior to above strat
 
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Ian Kelly
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No, the 4th Duchy is worth 4 in this case, not 3. 3 base VP + 1 Duke = 4.
 
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Grzegorz Kobiela
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Peristarkawan wrote:
No, the 4th Duchy is worth 4 in this case, not 3. 3 base VP + 1 Duke = 4.


Yeah, you're right. Doesn't matter. So, both ways are equally good:

4/2/1/1/...

3/1/2/1/...

So, my initial pattern is optimal (along with a variant, still optimal) and easier to remember.
 
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Ian Kelly
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Ponton wrote:
Yeah, you're right. Doesn't matter. So, both ways are equally good:

4/2/1/1/...

3/1/2/1/...

So, my initial pattern is optimal (along with a variant, still optimal) and easier to remember.


Or any other variant that starts with 2 Duchies and then always buys so as to maintain the inequality Dukes + 2 <= Duchies <= Dukes + 4.
 
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Timothy Hunt
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The thing with Dukes is they not only have a variable value to you, but a variable value to your opponents.

Taking a 4 player game as an example:
If I can get half the Duchies (6), then Dukes are worth 6 to me, same as Provinces. if the other 3 players aren't working on Duchies that much, and evenly split them 2/2/2, then Dukes are only worth 2 to them. It's much less of an incentive for them to buy the Dukes.

I think a better acquisition strategy is to try and buy Duchies as fast as possible until they run out, making Dukes (close to) worthless for other players. You can then pick up the Dukes at your leisure.


 
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Jeff Wolfe
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Timotheous wrote:
The thing with Dukes is they not only have a variable value to you, but a variable value to your opponents.

Taking a 4 player game as an example:
If I can get half the Duchies (6), then Dukes are worth 6 to me, same as Provinces. if the other 3 players aren't working on Duchies that much, and evenly split them 2/2/2, then Dukes are only worth 2 to them. It's much less of an incentive for them to buy the Dukes.

I think a better acquisition strategy is to try and buy Duchies as fast as possible until they run out, making Dukes (close to) worthless for other players. You can then pick up the Dukes at your leisure.




In that scenario, you give your opponents a big incentive to buy Dukes. Since they are (relatively) worthless to your opponents, that's not a bad thing.

 
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Timothy Hunt
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jeffwolfe wrote:


In that scenario, you give your opponents a big incentive to buy Dukes. Since they are (relatively) worthless to your opponents, that's not a bad thing.



Right. Either they don't get them, thus allowing me to, or they do in order to prevent me, which hurts them as they are spending 5 coin on just a few points, and clogging their deck

 
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