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[GendoIkari]

I'm not completely sure if this counts as a puzzle, because I have no idea what the answer is, but would like to get people's thoughts... based on the last post in this thread, it seems that taking a free Colony every turn could still lose to an awesome strategy + awesome luck. So...

New house rule: at the start of the game, you are allowed to add between 0 and 4 Provinces to your deck before you start playing (before you shuffle and draw for turn 1 even). Your opponent does not also get this same choice; he is playing by normal rules. What is the optimal play?

My instinct is to say that grabbing 4 Provinces is the right move more often then not. You will lose the equivalent of a few turns, but I think you would make up for it. On the other hand, your opponent could build a strong engine that grabs 4 Provinces + a few Duchies before you've had a chance to build up enough to do much of anything.

Surely it is a board-dependent question. A weak board where BM is better will probably mean you want more Provinces. But maybe only take 2 or 3 instead of 4. A board with mega-turn possibilities, take less. A board with Crossroads, Scout, Island, or Bishop, take all 4!

Does the answer change if your option is for taking Colonies instead?

[jonts26]

In the absence of a strong alt VP strategy, I can't think of any reason not to take the 4 provinces. basically, if you want the provinces anyway, go ahead and take them. If your strategy would have you avoid them, like a tactician/goons deal, you'd be better off leaving them alone I think.

[Anon79]

Your deck is going to be incredibly slow with 4 Provinces though. You now have 7 coin, all in coppers, spread among 14 cards (i.e. your first 3 turns). If there are no $2 cards in the kingdom, you're in for a long game of doing nothing for most of your turns (is Copper a good buy in this situation? I suspect so.) until you get some of your treasure together.

[jonts26]

Copper is a great buy. And really, you dont need any more provinces so don't worry about getting up to 8, just grab duchies. Really you just need to grab 4-5 duchies before the other player can get 4 provinces and 4 duchies himself. So a typical game that's what, 17-18 turns? Very doable. i'd reconsider it if there is a super fast engine on the board but most of the time take the provinces.

[DStu]

I was working on modified of Dominiate to change starting conditions, and while it does not what it should at the moment it does exactly what it needs to answer this question (i.e. you can change the starting state of the players deck, but when adding cards to the player it does not change the supply [If you also want to change the supply, Geronimoo's simulator does exactly this]).
So when you take the built-in BigMoney bots (reduced to the Province version), and let one of it start with 4 extra Provinces, it wins 3:1 against the original bot. Letting it buy Copper does not change much. So probably both bots could be optimized for the new situation, but I don't think that you can (with BigMoney) take this into a win for the standard bot. Kingdom cards of course change this, but they (Warehouse, Vault, SC, ...) might also further buff the guy with the 4 Provinces.

[DStu]

Copper is a great buy. And really, you dont need any more provinces so don't worry about getting up to 8, just grab duchies. Really you just need to grab 4-5 duchies before the other player can get 4 provinces and 4 duchies himself. So a typical game that's what, 17-18 turns? Very doable. i'd reconsider it if there is a super fast engine on the board but most of the time take the provinces.

When you take the 4 extra Provinces from the supply, this is really enough, if you take them from the box and have 8 Provinces in the supply you also need to get some Provinces.

[WanderingWinder]

I think a far more interesting question is what the WORST number of provinces to start with is. I'm guessing it's usually 1 or 2.

[GendoIkari]

Copper is a great buy. And really, you dont need any more provinces so don't worry about getting up to 8, just grab duchies. Really you just need to grab 4-5 duchies before the other player can get 4 provinces and 4 duchies himself. So a typical game that's what, 17-18 turns? Very doable. i'd reconsider it if there is a super fast engine on the board but most of the time take the provinces.

When you take the 4 extra Provinces from the supply, this is really enough, if you take them from the box and have 8 Provinces in the supply you also need to get some Provinces.

I intended it to be from the supply. But from the box is another interesting question!

[GendoIkari]

I think a far more interesting question is what the WORST number of provinces to start with is. I'm guessing it's usually 1 or 2.

That's funny... I was thinking that 1 free Province would be a beat 0 free Provinces in almost every situation; more often than 4 free Provinces would beat 0 free Provinces. I thought the 1 card wouldn't slow you down nearly as much as the 4 cards.

[DStu]

Copper is a great buy. And really, you dont need any more provinces so don't worry about getting up to 8, just grab duchies. Really you just need to grab 4-5 duchies before the other player can get 4 provinces and 4 duchies himself. So a typical game that's what, 17-18 turns? Very doable. i'd reconsider it if there is a super fast engine on the board but most of the time take the provinces.

When you take the 4 extra Provinces from the supply, this is really enough, if you take them from the box and have 8 Provinces in the supply you also need to get some Provinces.

I intended it to be from the supply. But from the box is another interesting question!

From the supply 1 Province beats 0 Province 54:37

:e both BMU

[WanderingWinder]

Interesting... simulations show that the worst number to start with for big money is... 0. And that every province helps.
Duchies unsurprisingly hurt.

[GendoIkari]

Interesting... simulations show that the worst number to start with for big money is... 0. And that every province helps.
Duchies unsurprisingly hurt.

Thanks for running the sims. This is in line with my initial instinct on it... BM would favor each extra Province. It's when a massive engine is possible that you really don't want to start with 4. Also, if it's a deck where you can buy all Provinces in a mega-turn, even 1 Province at the start probably hurts, because your opponent will still have his mega-turn with 7 Provinces and a bunch of Duchies before you can build the same.

[Jorbles]

If there's something like a Remodel or Salvager on the board, you'd obviously want to take max Provinces in the hopes of just Remodelling or Salvaging your Provinces so you could eat up the existing ones.

[Ferrouswheel]

If there were trash for benefit cards out, I'm thinking salvager, remodel, expand, and bishop, I doubt even a crazy engine could pull it off.

edit: and I look at the post above me 2 hours ago and realize I must have skipped over it.

[GendoIkari]

Ok, similar question. Your starting deck is now 7 Provinces; no other cards. Your opponent's starting deck is 1 Monument. Who has the advantage?

Again, board is going to matter. If there's an Embargo, Province player probably has no chance. (Turn 1, play Monument, buy Embargo. Turn 2, Embargo Copper.) Any good 2's are going to be great for the Monument player of course.

My guess is that most boards will lead to a Monument victory. If there's any Village at all, it will be easy to get to the point where you are playing 2-3 Monuments every turn (assuming Monument is in the Kingdom as well).

[WanderingWinder]

Ok, similar question. Your starting deck is now 7 Provinces; no other cards. Your opponent's starting deck is 1 Monument. Who has the advantage?

Again, board is going to matter. If there's an Embargo, Province player probably has no chance. (Turn 1, play Monument, buy Embargo. Turn 2, Embargo Copper.) Any good 2's are going to be great for the Monument player of course.

My guess is that most boards will lead to a Monument victory. If there's any Village at all, it will be easy to get to the point where you are playing 2-3 Monuments every turn (assuming Monument is in the Kingdom as well).

My guess is that most boards will lead to a province victory. Think about it, how many duchies can the monument player safely buy while still being able to assuredly get the last province before his opponent? He needs the game to last 36 turns, -3 times the number of duchies he can nab, plus the number of turns he's going to miss playing a monument. In kingdoms with a village, it'll be close, maybe. And in a few cases, monument has it cold. But usually, I don't think so.
Edit: and with remodel or salvager or something along those lines, forget it.

[GendoIkari]

Ok, similar question. Your starting deck is now 7 Provinces; no other cards. Your opponent's starting deck is 1 Monument. Who has the advantage?

Again, board is going to matter. If there's an Embargo, Province player probably has no chance. (Turn 1, play Monument, buy Embargo. Turn 2, Embargo Copper.) Any good 2's are going to be great for the Monument player of course.

My guess is that most boards will lead to a Monument victory. If there's any Village at all, it will be easy to get to the point where you are playing 2-3 Monuments every turn (assuming Monument is in the Kingdom as well).

My guess is that most boards will lead to a province victory. Think about it, how many duchies can the monument player safely buy while still being able to assuredly get the last province before his opponent? He needs the game to last 36 turns, -3 times the number of duchies he can nab, plus the number of turns he's going to miss playing a monument. In kingdoms with a village, it'll be close, maybe. And in a few cases, monument has it cold. But usually, I don't think so.
Edit: and with remodel or salvager or something along those lines, forget it.

Definitely wasn't thinking about Remodel or Salvager. But without those cards, Monument player can do something like this:

1. Buy Pawn
2. Buy Silver
3. Buy Duchy
4. Buy Duchy
5. Buy Duchy (at this point, he has 6 cards in deck, but 1 cantrip so still playing Monument every turn)
6. Buy Hunting Party (Lab could work too, but not as well).
7. Buy Duchy (now, she has a very slight chance of drawing 4 Duchies and a silver)

She can alternate HP/Lab and Duchy; with average draw luck, after about 13 turns she will have 7 Duchies, and 13 VP tokens.

Next 3 turns, purchase Silver, Silver, Province.

Only 16 turns...
(7 * 3) + 16 + 6 = 43 points.

What can Province guy do in 16 turns? Hard to say... but his first 5 or more turns will probably be buying nothing but Copper, or Pawn if he's lucky.

[WanderingWinder]

Ok, similar question. Your starting deck is now 7 Provinces; no other cards. Your opponent's starting deck is 1 Monument. Who has the advantage?

Again, board is going to matter. If there's an Embargo, Province player probably has no chance. (Turn 1, play Monument, buy Embargo. Turn 2, Embargo Copper.) Any good 2's are going to be great for the Monument player of course.

My guess is that most boards will lead to a Monument victory. If there's any Village at all, it will be easy to get to the point where you are playing 2-3 Monuments every turn (assuming Monument is in the Kingdom as well).

My guess is that most boards will lead to a province victory. Think about it, how many duchies can the monument player safely buy while still being able to assuredly get the last province before his opponent? He needs the game to last 36 turns, -3 times the number of duchies he can nab, plus the number of turns he's going to miss playing a monument. In kingdoms with a village, it'll be close, maybe. And in a few cases, monument has it cold. But usually, I don't think so.
Edit: and with remodel or salvager or something along those lines, forget it.

Definitely wasn't thinking about Remodel or Salvager. But without those cards, Monument player can do something like this:

1. Buy Pawn
2. Buy Silver
3. Buy Duchy
4. Buy Duchy
5. Buy Duchy (at this point, he has 6 cards in deck, but 1 cantrip so still playing Monument every turn)
6. Buy Hunting Party (Lab could work too, but not as well).
7. Buy Duchy (now, she has a very slight chance of drawing 4 Duchies and a silver)

She can alternate HP/Lab and Duchy; with average draw luck, after about 13 turns she will have 7 Duchies, and 13 VP tokens.

Next 3 turns, purchase Silver, Silver, Province.

Only 16 turns...
(7 * 3) + 16 + 6 = 43 points.

What can Province guy do in 16 turns? Hard to say... but his first 5 or more turns will probably be buying nothing but Copper, or Pawn if he's lucky.

That is quite a contrived kingdom, and... there's quite a decent chance province guy can get to the province by turn 16, especially with pawn on board (helps a LOT).

[GendoIkari]

Ok, similar question. Your starting deck is now 7 Provinces; no other cards. Your opponent's starting deck is 1 Monument. Who has the advantage?

Again, board is going to matter. If there's an Embargo, Province player probably has no chance. (Turn 1, play Monument, buy Embargo. Turn 2, Embargo Copper.) Any good 2's are going to be great for the Monument player of course.

My guess is that most boards will lead to a Monument victory. If there's any Village at all, it will be easy to get to the point where you are playing 2-3 Monuments every turn (assuming Monument is in the Kingdom as well).

My guess is that most boards will lead to a province victory. Think about it, how many duchies can the monument player safely buy while still being able to assuredly get the last province before his opponent? He needs the game to last 36 turns, -3 times the number of duchies he can nab, plus the number of turns he's going to miss playing a monument. In kingdoms with a village, it'll be close, maybe. And in a few cases, monument has it cold. But usually, I don't think so.
Edit: and with remodel or salvager or something along those lines, forget it.

Definitely wasn't thinking about Remodel or Salvager. But without those cards, Monument player can do something like this:

1. Buy Pawn
2. Buy Silver
3. Buy Duchy
4. Buy Duchy
5. Buy Duchy (at this point, he has 6 cards in deck, but 1 cantrip so still playing Monument every turn)
6. Buy Hunting Party (Lab could work too, but not as well).
7. Buy Duchy (now, she has a very slight chance of drawing 4 Duchies and a silver)

She can alternate HP/Lab and Duchy; with average draw luck, after about 13 turns she will have 7 Duchies, and 13 VP tokens.

Next 3 turns, purchase Silver, Silver, Province.

Only 16 turns...
(7 * 3) + 16 + 6 = 43 points.

What can Province guy do in 16 turns? Hard to say... but his first 5 or more turns will probably be buying nothing but Copper, or Pawn if he's lucky.

That is quite a contrived kingdom, and... there's quite a decent chance province guy can get to the province by turn 16, especially with pawn on board (helps a LOT).

I didn't mean to contrive it that much. I only specified 2 cards being present, and both are replaceable. Even without Pawn, Monuments just has to buy a Copper instead of that Pawn. And HP isn't necessary, it was just meant to be 1 such card that could help keep the Duchy-buying going. Cartographer, Warehouse, Stables, Minion, etc, all would work. Celler and Crossroads too, but those would be more helpful to Province guy.

But, if Province guy can buy the last Province within 16-17 turns, then I guess that discussion is moot. I didn't think he'd be able to... I might play around with that when I get a chance.

[WanderingWinder]

Okay, some very quick sims:

Code: [Select]

<player name="JustAMonument"
 author="WanderingWinder"
 description="The optimized Monument strategy that buys no other actions.">
 <type name="Optimized"/>
 <type name="BigMoney"/>
 <type name="TwoPlayer"/>
 <type name="SingleCard"/>
 <type name="UserCreated"/>
 <type name="Bot"/>
 <type name="Province"/>
  <start_state>
    <hand contents=""/>
    <discard contents=""/>
    <drawdeck contents="Monument" shuffle="true"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterOrEqualThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="divideBy" attribute="2.0" />
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="divideBy" attribute="1.0" />
      </condition>
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Monument">
      <condition>
         <left type="countCardsInDeck" attribute="Monument"/>
         <operator type="smallerThan" />
         <right type="countCardTypeInDeck" attribute="Treasure"/>
         <extra_operation type="divideBy" attribute="5.0" />
      </condition>
   </buy>
   <buy name="Silver"/>
   <buy name="Copper">
      <condition>
         <left type="countCardsInDeck" attribute="Copper"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
</player>


Code: [Select]

<player name="7 Province guy"
 author="WanderingWinder"
 description="The optimized Monument strategy that buys no other actions.">
 <type name="Optimized"/>
 <type name="BigMoney"/>
 <type name="TwoPlayer"/>
 <type name="SingleCard"/>
 <type name="UserCreated"/>
 <type name="Bot"/>
 <type name="Province"/>
  <start_state>
    <hand contents=""/>
    <discard contents=""/>
    <drawdeck contents="7 Province" shuffle="true"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Monument">
      <condition>
         <left type="countCardsInDeck" attribute="Monument"/>
         <operator type="smallerOrEqualThan" />
         <right type="countCardTypeInDeck" attribute="Treasure"/>
         <extra_operation type="divideBy" attribute="5.0" />
      </condition>
   </buy>
   <buy name="Monument">
      <condition>
         <left type="countCardsInDeck" attribute="Monument"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
   <buy name="Copper"/>
</player>

7 Province dude wins something like 98.5-0.5 with nothing but monument and basics (not optimized)
What else do you want to test?

[GendoIkari]

Wow. Do the sims tell you how many turns the games lasted? Anyway, thanks for running it.

[WanderingWinder]

Wow. Do the sims tell you how many turns the games lasted? Anyway, thanks for running it.

About 21 and a half turns.

[GendoIkari]

Wow. Do the sims tell you how many turns the games lasted? Anyway, thanks for running it.

About 21 and a half turns.

That's surprising... I would think that if Province took 21 turns to end it, that Monument would have enough time to get more points. 

[WanderingWinder]

Just spent a little time optimizing guy who starts with a monument:

Code: [Select]

<player name="JustAMonument"
 author="WanderingWinder"
 description="The optimized Monument strategy that buys no other actions.">
 <type name="BigMoney"/>
 <type name="Optimized"/>
 <type name="TwoPlayer"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="Bot"/>
 <type name="UserCreated"/>
  <start_state>
    <hand contents=""/>
    <discard contents=""/>
    <drawdeck contents="Monument" shuffle="true"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="plus" attribute="2.0" />
      </condition>
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="plus" attribute="2.0" />
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="plus" attribute="7.0" />
      </condition>
      <condition>
         <left type="countCardsInDeck" attribute="Gold"/>
         <operator type="greaterOrEqualThan" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Monument">
      <condition>
         <left type="countCardsInDeck" attribute="Monument"/>
         <operator type="smallerThan" />
         <right type="countCardTypeInDeck" attribute="Treasure"/>
         <extra_operation type="divideBy" attribute="3.0" />
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="countAllCardsInDeck"/>
         <extra_operation type="minus" attribute="6.0" />
      </condition>
   </buy>
   <buy name="Silver"/>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Copper">
      <condition>
         <left type="countCardsInDeck" attribute="Copper"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
</player>

He now wins over 17% of the time, though I imagine that'll go down if I similarly optimize the other dude. Also shaved about half a turn off.
You also have to realize that province dude is picking up his share of monuments, which slows monument guy's comeback.