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[shark_bait]

In a standard BM game, the game is often decided by the Duchies.  Most people probably think of Duchies as things to buy when there are 4 Provinces remaining.  I'm not discrediting that philosophy, I just would like to propose an additional way to think about Duchy buying.  Instead of thinking of the Provinces remaining in the supply, think the future number of Provinces in the supply. 

There are times in a BM game where you have just reshuffled your deck and let's say that there are 6-7 Provinces left.  Let's assume a 20 card deck with no draw giving you 4 hands during this deck.  My sake of clarity, the amount of money in each hand will be 2x$5 and 2x$8.  If you get your 2x$8 hands first, standard Duchy buying means you will take the Duchies with your 2x$5 hands.  But let's assume you get your 2x$5 hands first.  You still should buy the Duchies.  Even though there are 6-7 Provinces left, it is more important to correctly assess what the game state will be at the end of this draw deck.  If you know that your current deck will have the power to get the game into full scale green mode by the time you reshuffle, you want to start greening immediately even if the current game state doesn't seem to imply greening.

In short, sometimes you should green based upon the future game state rather than the current game state by assessing will happen to the Province pile in your future hands.

***I do not claim this to be empirical truth regarding the best way to Duchy buy.  Conventional Duchy buying is conventional because it's very easy to understand.  I merely am suggesting a different way to think about Duchy that may be applicable every once in a while.***

[WanderingWinder]

In a standard BM game, the game is often decided by the Duchies.  Most people probably think of Duchies as things to buy when there are 4 Provinces remaining.  I'm not discrediting that philosophy, I just would like to propose an additional way to think about Duchy buying.  Instead of thinking of the Provinces remaining in the supply, think the future number of Provinces in the supply. 

There are times in a BM game where you have just reshuffled your deck and let's say that there are 6-7 Provinces left.  Let's assume a 20 card deck with no draw giving you 4 hands during this deck.  My sake of clarity, the amount of money in each hand will be 2x$5 and 2x$8.  If you get your 2x$8 hands first, standard Duchy buying means you will take the Duchies with your 2x$5 hands.  But let's assume you get your 2x$5 hands first.  You still should buy the Duchies.  Even though there are 6-7 Provinces left, it is more important to correctly assess what the game state will be at the end of this draw deck.  If you know that your current deck will have the power to get the game into full scale green mode by the time you reshuffle, you want to start greening immediately even if the current game state doesn't seem to imply greening.

In short, sometimes you should green based upon the future game state rather than the current game state by assessing will happen to the Province pile in your future hands.

***I do not claim this to be empirical truth regarding the best way to Duchy buy.  Conventional Duchy buying is conventional because it's very easy to understand.  I merely am suggesting a different way to think about Duchy that may be applicable every once in a while.***

You should ALWAYS buy the duchies based on future game state. The whole point of the conventional wisdom is that it approximates the guessing of what the future game state is pretty well.
But it shouldn't be used as a hard-and-fast rule, more of a rule-of-thumb. There are lots of ways that it breaks down, and you always want to take into account the actual game at hand, along with what your opponent is doing, points and point differential, and what other options you have (i.e. generally you buy duchy on 5 before you do on 6, because there's gold on 6; but also if there's a good 5, you can hold off on the duchies more).

[shark_bait]

You should ALWAYS buy the duchies based on future game state. The whole point of the conventional wisdom is that it approximates the guessing of what the future game state is pretty well.
But it shouldn't be used as a hard-and-fast rule, more of a rule-of-thumb. There are lots of ways that it breaks down, and you always want to take into account the actual game at hand, along with what your opponent is doing, points and point differential, and what other options you have (i.e. generally you buy duchy on 5 before you do on 6, because there's gold on 6; but also if there's a good 5, you can hold off on the duchies more).

I agree on all your points, Duchy buying is not something that can be broken down into an exact formula and that Gold with $6/Power $5 actions need to be considered.  This isn't meant to be the Holy Grail of Duchy buying.  I merely wanted to put out the idea of future game state.  Although this "future game state" idea doesn't really teach you anything new, I figured that there are many players who wouldn't intuitively make that conclusion themselves and this would get the ball rolling in their minds.

[cherdano]

Here is a very simplistic rule that tells you whether to buy a duchy instead of a gold:

Buy a duchy if you expect to see the card you are buying at most once in your hand before the game ends. Consider buying gold over duchy if you expect to see the card at least once more in your hand before the game ends.

Rationale: Say you buy a duchy instead of a gold. You have 3VP more. But hey, what if in the next reshuffle, this will make you unable to buy a province? Oh wait, you can buy a duchy instead! 2 duchies = 6VP = one province!

Why is it too simplistic:
- If you have properly studied Borinion, you know that you should only buy the duchy if there is a reasonable chance that the 3 VP will put you over the top. Maybe you will likely lose the duchy race anyway, and your only chance is to get 5 provinces. Etc.
- Obviously the decision whether to buy a gold or a duchy has a small impact on the length of the game - so it may well be right to spend one $6 buy on a gold and another on a duchy within the same reshuffle.
- Maybe you weren't getting a province buy anyway when the gold you wanted to buy next comes up in your hand, and it's the type of game where you rather buy a duchy now and an estate next shuffle instead of a gold now and a duchy next shuffle. Or maybe you expect to get a province only when you see your mega-counting house, in which case you won't need the gold.

[DG]

This simulator script for a pure treasure game is highly effective considering how simplistic it is. It does beat the default big money ultimate script in the simulator. This certainly demonstrates that a purchasing strategy related to shuffling can have merit.

Code: [Select]

<player name="4/3 Big Money Ultimate ( 6-9-12)"
 author="DG"
 description="Buy provinces after the second reshuffle (turn 6)XXXXBuy duchies ahead of silver after the third reshuffle (turn 9)XXXXBuy duchies and estates after the fourth reshuffle (turn 12)XXXX">
 <type name="Optimized"/>
 <type name="SingleCard"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
 <type name="Province"/>
 <type name="TwoPlayer"/>
 <type name="Bot"/>
   <buy name="Province">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="12.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="12.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="9.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>

[WanderingWinder]

This simulator script for a pure treasure game is highly effective considering how simplistic it is. It does beat the default big money ultimate script in the simulator. This certainly demonstrates that a purchasing strategy related to shuffling can have merit.

Code: [Select]

<player name="4/3 Big Money Ultimate ( 6-9-12)"
 author="DG"
 description="Buy provinces after the second reshuffle (turn 6)XXXXBuy duchies ahead of silver after the third reshuffle (turn 9)XXXXBuy duchies and estates after the fourth reshuffle (turn 12)XXXX">
 <type name="Optimized"/>
 <type name="SingleCard"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
 <type name="Province"/>
 <type name="TwoPlayer"/>
 <type name="Bot"/>
   <buy name="Province">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="12.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="12.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countTurns"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="9.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>

Well, the thing there is that you are also getting a lot of information as to how strong your deck is, which also tends to happen pretty programmatically in straight big money.

[Geronimoo]

DG's script basically does this (for the many among you who can't read simulator buy rules):

Start to buy Provinces after turn 6
Start to green entirely after turn 12 (Duchies and Estates over Gold)
Start to buy Duchies over Silver (but not over Gold) after turn 9

This greening strategy is closely linked to when the reshuffles happen.

[HiveMindEmulator]

This simulator script for a pure treasure game is highly effective considering how simplistic it is. It does beat the default big money ultimate script in the simulator. This certainly demonstrates that a purchasing strategy related to shuffling can have merit.

Code: [Select]

Well, the thing there is that you are also getting a lot of information as to how strong your deck is, which also tends to happen pretty programmatically in straight big money.

I think that's the point. 6/9/12 is no the right answer for every (any?) deck, but the point is that thresholds for this bot are based on shuffle count rather than Provinces remaining, causing them to not be affected by the  randomness described in the OP. Of course, if you put it against anything other than BM, the thresholds are going to be wrong, so it's a demonstration of the concept more than an actually strategy.

[Davio]

Simulators can be handy to show some general tips, but they don't reflect a real game.

I tend to green earlier when I think that I have enough money and me or my opponent is going to buy Provinces.
I assess my situation at the beginning of every shuffle. How much money do I have? Are we both going to drain Provinces fast?
Then I make a plan for that reshuffle. Either go mad green or buy some extra money.

I reassess at the end of my shuffle. Do I want an extra Gold for my next reshuffle or is there simply no time?

[jonts26]

1. Sometimes people think that once you start greening, you have to keep greening. This is sometimes true, but sometimes you have to switch back into income generating. This can happen in situations where you green too early or have a few unfortunate hands and you find yourself in need of provinces, but are too clogged with duchies/estates to expect to draw $8 again.

2. Whenever you take a green card over something else, you have to ask yourself how likely it is that you'll see that card again. Or how many times you might see it again and how much benefit you expect from say, drawing a Gold/Silver instead of a duchy. Every time you buy a duchy/estate, you make it less likely to buy a province later, or at the very least, you can't improve your odds (except for maybe baron or crossroads or something). If you are unlikely to see that card again, buy the green. I've started getting estates with 4-5 provinces left before and it can be the difference every once in a while.

[WanderingWinder]

1. Sometimes people think that once you start greening, you have to keep greening. This is sometimes true, but sometimes you have to switch back into income generating. This can happen in situations where you green too early or have a few unfortunate hands and you find yourself in need of provinces, but are too clogged with duchies/estates to expect to draw $8 again.

Indeed. This comes u most often for me when you rush duchies hard, but then estates just don't matter much. Means very often you should grab for money again to get the last province or two, rather than estates. Especially if you're reasonably likely to reshuffle again.
Also, if you grab some green to try to block your opponent early, you can somewhat reasonably swap back to engine-building following that, in certain cases (like with upgrade) especially.

[Davio]

1. Sometimes people think that once you start greening, you have to keep greening. This is sometimes true, but sometimes you have to switch back into income generating. This can happen in situations where you green too early or have a few unfortunate hands and you find yourself in need of provinces, but are too clogged with duchies/estates to expect to draw $8 again.

Indeed. This comes u most often for me when you rush duchies hard, but then estates just don't matter much. Means very often you should grab for money again to get the last province or two, rather than estates. Especially if you're reasonably likely to reshuffle again.
Also, if you grab some green to try to block your opponent early, you can somewhat reasonably swap back to engine-building following that, in certain cases (like with upgrade) especially.

I find that Estates hardly ever matter in practice. Most games are decided by a 5-3 Province or a 5-3 Duchy split.
Sometimes I only buy an Estate if it increases my lead from 5 to 6 or 6 to 7 with one Province left.

[jonts26]

Estates usually dont matter. But especially as player 1, that extra 1 point can change the endgame quite a bit.

[WanderingWinder]

Multitudes of estates are GENERALLY insignificant, except: as a 3rd pile; in a rush scenario, where grabbing all of them quickly may overcome some other deficit (though this is hard to do), baron, silk road; most importantly, the first estate over is really important, because it turns a tie into a win (or a loss into a win as p1); but then, given that your opponent has the same opportunity, that makes the second estate important in several cases. And by then, hey, one more estate equalizes out a duchy.
Indeed, I disagree with the statement that most games are decided by a 5-3 province split or a  5-3 duchy split. Most games don't see all the duchies bought out. And probably only a plurality are so dependent on the split of provinces - alternate VP sources become very important, as well as 3-pile or colony endings.