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[rrenaud]

I'd love to see the duke game against Blooki.  Was it today?  I can't find it on councilroom.

[WanderingWinder]

Yes, just played it right before posting here. I will try to post it tomorrow.

[Geronimoo]

In a pure money game I simulated a Duchy/Duke player against a Province player and after many iterations found these optimal:

Here's the Duchy/Duke player's game plan:
-when I have 1 Gold I start buying Duchies, I don't care for Provinces
-when all the Duchies are gone I go for Dukes (but will buy a Province if I have $8)
-when the Dukes are almost gone (3 left) I'll start buying Estates

Here's the Province player's game plan:
-when I have 1 Gold I start buying Provinces unless I see my opponent going for the Duchy/Duke plan in which case I'll turn to the dark side as well and buy Duchies over Provinces
-when all the Duchies are gone I go for Dukes (but will buy a Province if I have $8)
-when the Dukes are almost gone (3 left) I'll start buying Estates

>99% of these games end in piles and last 23 turns on average. The Duchy/Duke player wins 51% and the Province player wins 41%. If we delay the Province's player switch from Provinces to Duchies his win rate drops dramatically. If I let either player buy Dukes before the Duchy pile is depleted their win rate drops.

Quite a surprising result, no?

U can try these out yourselves if you paste these in my Simulator (VXML-button):
The Duchy/Duke player

Code: [Select]

<player name="BM - Duchy/Duke">
   <buy name="Duchy">
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Province">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Duke">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duke"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="3.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Silver"/>
</player>
The Province player (who will turn into a Duchy/Duke player out of necessity)

Code: [Select]

<player name="BM - Province">
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="8.0"/>
      </condition>
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Province">
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Duke">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duke"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="3.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Silver"/>
</player>

[rrenaud]

Did you try to make a more long term province player?  EG, what if you find a solitaire bot that minimizes time to 8 provinces and play that against the duke/duchy player?

[Geronimoo]

Long term Province players will indeed be better at continuing to buy Provinces, but at the cost of letting the Duchy player get a lot of Duchies which makes his Duke buys huge.

[WanderingWinder]

I don't buy that the Duke strategy is that good. It'll be interesting to see what the flaws in your bot are that make this happen. Here are a few things it seems it's missing:
1) The duchy player shouldn't grab all the duchies before turning to dukes IF her opponent is rushing only provinces. Exactly when, you have to gauge based on the speed of the opponent's deck, but 6 duchies is a decent rule of thumb (sometimes 5, sometimes 7).
2) The provincing player has some interesting decisions on when to turn for duchies. I'm not sure that ignoring province buys for them is good. Maybe not even Gold buys is very good, depending on the circumstance. On exactly $5, definitely duchy.
3) I really doubt that going for Dukes is going to be very good at all, unless somehow they were heavily invested in the duchies, or it guarantees a win, or there's no way to run a 3rd pile.
4) If there's no way to run a 3rd pile, this is good for the province player. This hardly ever comes up.
5) Province player probably wants to buy estates only when it basically guarantees a win.
6) Duchy player shouldn't pass up dukes for provinces if she has 6+duchies in most cases. Essentially never if it is 7+.

Beyond this, probably the big thing is that almost any set of kingdom cards is going to provide good acceleration that's going to be of significantly more help to a Province player than a Duke player.

[HiveMindEmulator]

Horse Traders is pretty darn good for Duchy/Duke, as it lets you get to five quite often.

It sounds appealing, but is not really that good, because to make a duke/duchy strategy work, you need to do more than "get to five quite often". You need to get *multiple* duchies per turn, or your opponent will just respond by buying half the duchies and be just fine.
The most likely card to make duke/duchy work, imo, is horn of plenty. Get a bunch of horns (using them to gain each other), and then turn them all into duchies, not giving your opponent a chance to block your duchies. Since you haven't committed to the duchies early, he can't really do it pre-emptively, or you can just switch into something else.

I think the focus on duke vs duke strategies is mostly red herring.  I am not sure I've ever seen a duke vs duke game, it's almost always a province vs duke game when at least one player goes for duke/duchy.  So presumably as a duke player, you should be able to handily beat your opponent in the duchy race (opp went from provs, after all).  As the duke player, you want to be able to consistently churn out 5s for a long while.  While most province decks are optimized to churn out 8s for a short period (just enough to hit 4 provs and change).

I didn't say anything about duke vs duke. Playing any normal province strategy, when you know dukes are around, and see your opponent buying duchies, you start buying duchies as well to keep them to 4-5 duchies instead of 8. If, as a duke player, you can't get duchies faster than this province player who has made an emergency duchy switch, you're not going to be at an advantage.

[ImperialStout]

I feel like a discussion of duchy/duke vs. province is difficult to have productively without taking into account the board in question.  Some cards will favor duchy/duke over province strategies (bridge, hoard, lots of +buys, cursing cards with no trashers in play) whereas others will favor provinces (embargo, bank with no +buys, no +2 or more cards). 

[Geronimoo]

@WanderingWinder
All your arguments are valid of course and my initial bots did all the things you mention, but many iterations later trying to improve both bots against each other their behavior changed dramatically and the Province player slowly morphed into a Duchy/Duke player and the game becomes a race for the Duchies which the Duchy/Duke player will win because he starts off with the correct strategy while the Province bot adjusts only when he sees the strategy of the other bot.
When I add a Smithy in the mix the Province player gets closer, but is still unable to win (it's still a 3-pile ending). When I use the Chancellor/Stash shell the Province player suddenly wins (and big!) because this strategy is really geared towards getting $8 consistently and doesn't die out when it gets swamped with green cards.

[DG]

Playing any normal province strategy, when you know dukes are around, and see your opponent buying duchies, you start buying duchies as well to keep them to 4-5 duchies instead of 8. If, as a duke player, you can't get duchies faster than this province player who has made an emergency duchy switch, you're not going to be at an advantage.

From a situation where player (a) has 2 provinces and 3 duchies and player (b) has 5 duchies, player (b) is the favourite. Player (b) has already spent less, has as many green cards clogging the deck, and will take a lead by splitting the duke pile 4/4. If player (a) can empty the provinces while player (b) struggles buying dukes then it's not the dukes that are losing the game.

[rrenaud]

Interesting.  What about big money smithy/province vs duke/duchy/horse traders?

[Geronimoo]

Interesting.  What about big money smithy/province vs duke/duchy/horse traders?

big money smithy/province (37%) vs duke/duchy/horse traders (57%)

Identical buy rules as the ones I posted earlier, except Province bot buys 1 Smithy and Duchy/Duke bot buys 2 Horse Traders.

Horse Traders really seems like the perfect companion for the Duchy/Duke strategy. If you let both bots buy Smithy:

big money smithy/province (43%) vs duke/duchy/Smithy (49%)

[CMAR2P2]

University chain anyone?

[randomdragoon]

Universities can't gain Dukes or Duchies.

[WallyNate]

Universities can't gain Dukes or Duchies.

University + Transmute?   

[WanderingWinder]

I assume that was in jest, but for anyone who thinks it was serious, this (transmute) is way too slow like 99% of the time.
Also University can't gain transmutes, so they don't combo AT ALL

[WanderingWinder]

I'm unable to come anywhere near beating Geronimoo's Duke bot with only BM cards (unless you can go for colonies ) But the vast majority of improvements to the kingdom swing it the other way. Interestingly, if you throw Horse Traders in, it starts beating Big Money with colonies more often than it loses (though it's very close).
Edit: And the Colony-seeking bot isn't paying any attention to her opponent.