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2201

Simulation / Re: Project: Optimizing Big Money X

« on: February 16, 2012, 11:49:22 pm »

Improved scripts for witch and Ill-Gotten Gains:

Code: [Select]

<player name="Witch by WW"
 author="WanderingWinder"
 description="Witch is probably the strongest attack card in the game.">
 <type name="UserCreated"/>
 <type name="Competitive"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="Attacking"/>
 <type name="SingleCard"/>
 <type name="TwoPlayer"/>
   <buy name="Province">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="20.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="5.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="32.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="3.0"/>
      </condition>
   </buy>
   <buy name="Witch">
      <condition>
         <left type="countCardsInDeck" attribute="Witch"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="5.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="30.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Witch">
      <condition>
         <left type="countCardsInSupply" attribute="Witch"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="26.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="5.0"/>
      </condition>
   </buy>
   <buy name="Copper">
      <condition>
         <left type="countCardsInSupply" attribute="Curse"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
</player>


Code: [Select]

<player name="IGG Rush"
 author="WanderingWinder"
 description="Get all the Ill-Gotten Gains and Duchies to empty 3 piles.">
 <type name="UserCreated"/>
 <type name="Competitive"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="TwoPlayer"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Curse"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Ill_Gotten_Gains"/>
   <buy name="Duchy"/>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Copper">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
</player>



I've improved and simplified the IGG bot. It gets a a 57.7/38.7 win-rate vs WW's bot. Some notes first.

I tried deleting the copper-buy-rule and found that it didn't make the bot any worse. Stats (error intervals are with 99% confidence):
  Win: 47.4% +/- 0.4%
  Loss: 47.1% +/- 0.4%
  Tie: 5.4% +/- 0.2%
So it's definitely not worse, and maybe a tiny hair better.

I tried removing the after-silver estate rule, but that made the bot a lot worse. However, moving that estate rule above silver (and deleting the estate rule that was already there and is now redundant) makes the bot significantly better:
  Win: 52.7% +/- 0.4%
  Loss: 42.8% +/- 0.4%
  Tie: 4.5% +/- 0.2%
That's a pretty big difference!

I tried deleting the early-duchy rule, but doing that brings the winrate back down a bit:
  Win: 50.4% +/- 0.4%
  Loss: 44.9% +/- 0.4%
  Tie: 4.7% +/- 0.2%
I tweaked this around a bit and found though that "curse <= 1" performs best, giving a 49.971/45.75 advantage against "curse <= 2".

Finally, I set about tweaking when to start buying estates. Originally this was "#gains <= 4". I found that against this rule, I could get a 51.814/44.415 advantage with "#gains <= 6", and against WW's bot it gets 56.573/39.726, quite good. Unfortunately this causes a slight decrease in performance against BMU, because BMU is going for different piles. So I re-tweaked to "#duchies <= 5" (which should be roughly equivalent in the mirror if early duchies are taken with "curse <= 1"), and this restored performance against BMU and actually does better in the mirror for some reason.

Final bot:

Code: [Select]

<player name="IGG Rush Final"
 author="blueblimp"
 description="Get all the Ill-Gotten Gains and Duchies to empty 3 piles.">
 <type name="BigMoney"/>
 <type name="UserCreated"/>
 <type name="SingleCard"/>
 <type name="TwoPlayer"/>
 <type name="Province"/>
 <type name="Bot"/>
 <type name="Competitive"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Curse"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Ill_Gotten_Gains"/>
   <buy name="Duchy"/>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Duchy"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="5.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>

Performance against WW bot:
  Win: 57.7% +/- 0.4%
  Loss: 38.7% +/- 0.4%
  Tie: 3.6% +/- 0.2%

Performance against BMU:
  Win: 95.3% +/- 0.2%
  Loss: 4.2% +/- 0.2%
  Tie: 0.5% +/- 0.1%

WW bot's performance against BMU, for comparison:
  Win: 95.1% +/- 0.2%
  Loss: 4.5% +/- 0.2%
  Tie: 0.4% +/- 0.1%

2202

Simulation / Re: Improved IGG bot

« on: February 16, 2012, 10:47:40 pm »

WW already did some further optimization:
http://forum.dominionstrategy.com/index.php?topic=625.msg24198#msg24198

Ah thanks, I only checked the second post of that thread, oops.

Edit: I was curious to see how badly WW's bot defeats the dumb bot I posted, so here are the results:

WWIGG vs IGG2 (on ultimate simulation, so the confidence intervals are tighter):
Win: 48.0% +/- 0.4%
Loss: 46.4% +/- 0.4%
Tie: 5.6% +/- 0.2%

So WW's bot has a narrow but measurable edge.

2203

Puzzles and Challenges / Re: 7 copper and 3 estate vs. 50 _____?

« on: February 16, 2012, 09:48:41 pm »

1. 50 hamlets:
a). Any isotropic board; your opponent dies of boredom.
b). Live; ~50 pawns.

This was the first that came to mind to me. A serious winning kingdom would be if peddler is available. First turn, get 6 buys and buy 6 peddlers. Next turn, buy the rest of the peddlers. Now you have $10 guaranteed for several turns and as many buys as you like, definitely enough to win.

On a big money board, it's going to lose horribly.

2204

Simulation / Re: machine learning on Isotropic logs

« on: February 16, 2012, 08:18:17 pm »

I just did something a little like this. My goal was to get some idea of which cards are most skill-intensive, in the sense that when they are in the supply, you see fewer upsets (lesser-skilled player defeating more-skilled player, according to the leaderboard). I don't know much about machine learning though so I just used a least-squares solver.

I don't know if anyone else is interested, but this seems like an appropriate place to post it. =)

Example card ranking, from running on days 20120203 through 20120214, including only players level 25 and up, from most-skill-requiring to least-skill-requiring:

Code: [Select]

0.08516417: Adventurer
0.08456600: Possession
0.08354641: Harem
0.08184241: King's Court
0.08152772: City
0.08026821: Cartographer
0.07940645: Treasure Map
0.07905757: Cutpurse
0.07900007: Torturer
0.07820899: Mountebank
0.07797046: Warehouse
0.07794976: Margrave
0.07706310: Council Room
0.07590907: Apothecary
0.07456282: Trader
0.07446936: Goons
0.07336511: Remodel
0.07328238: Horn of Plenty
0.07298849: Library
0.07270732: Gardens
0.07264993: Tournament
0.07206545: Steward
0.07094222: Border Village
0.07059525: Workshop
0.07033349: Fishing Village
0.06985302: Treasury
0.06904109: Ironworks
0.06859853: Contraband
0.06834661: Nobles
0.06716353: Upgrade
0.06709585: Black Market
0.06592823: Ghost Ship
0.06592215: Ambassador
0.06532851: Farmland
0.06502409: Stash
0.06407454: Apprentice
0.06401693: Haggler
0.06384017: Alchemist
0.06358155: Explorer
0.06356953: Market
0.06328401: Nomad Camp
0.06294425: Throne Room
0.06191573: Quarry
0.06172529: Embargo
0.06152768: Moat
0.06144618: Expand
0.06101341: Baron
0.06098042: Wishing Well
0.06065459: Mint
0.06033086: Bazaar
0.06028343: Conspirator
0.06026394: Highway
0.05953535: Inn
0.05925004: Monument
0.05912377: Spice Merchant
0.05908763: Hoard
0.05908333: Oracle
0.05900228: Native Village
0.05887850: Masquerade
0.05870625: Fairgrounds
0.05862115: Moneylender
0.05860537: Lookout
0.05859416: Forge
0.05852813: Fortune Teller
0.05803387: Transmute
0.05778421: Cellar
0.05764033: Worker's Village
0.05652846: Woodcutter
0.05633609: Embassy
0.05628023: University
0.05592414: Feast
0.05589341: Royal Seal
0.05589257: Village
0.05501166: Wharf
0.05495642: Vault
0.05474288: Scout
0.05458196: Bishop
0.05440966: Smugglers
0.05438207: Mine
0.05427687: Tribute
0.05421006: Tunnel
0.05412809: Mandarin
0.05400339: Chancellor
0.05379845: Crossroads
0.05379040: Venture
0.05372546: Duchess
0.05351463: Scrying Pool
0.05346366: Mining Village
0.05344670: Island
0.05322741: Develop
0.05320709: Courtyard
0.05317686: Secret Chamber
0.05271292: Menagerie
0.05266542: Talisman
0.05254311: Laboratory
0.05229258: Pirate Ship
0.05211550: Horse Traders
0.05177014: Noble Brigand
0.05084035: Golem
0.05080142: Hamlet
0.05060647: Watchtower
0.05057027: Counting House
0.04996165: Loan
0.04979356: Bureaucrat
0.04975353: Minion
0.04949364: Silk Road
0.04931505: Saboteur
0.04885632: Walled Village
0.04876879: Ill-Gotten Gains
0.04820306: Festival
0.04788748: Grand Market
0.04765027: Vineyard
0.04755092: Salvager
0.04715652: Herbalist
0.04682846: Stables
0.04678177: Haven
0.04624035: Witch
0.04609654: Sea Hag
0.04576599: Jester
0.04534426: Philosopher's Stone
0.04526584: Scheme
0.04513696: Bridge
0.04511840: Pearl Diver
0.04487112: Thief
0.04475541: Swindler
0.04429258: Coppersmith
0.04409065: Spy
0.04401970: Trade Route
0.04340535: Farming Village
0.04331577: Jack of All Trades
0.04309553: Militia
0.04306024: Caravan
0.04293130: Pawn
0.04253476: Great Hall
0.04240333: Harvest
0.04205920: Remake
0.04076288: Trading Post
0.04065376: Governor
0.04053754: Outpost
0.04033976: Envoy
0.03950563: Lighthouse
0.03787837: Navigator
0.03695280: Chapel
0.03551853: Oasis
0.03502646: Shanty Town
0.03480394: Hunting Party
0.03213149: Bank
0.03157986: Tactician
0.03077700: Peddler
0.02922237: Cache
0.02914586: Rabble
0.02834067: Fool's Gold
0.02681132: Merchant Ship
0.02346290: Smithy
0.02067544: Familiar
0.02063283: Duke

Some of these things make sense: a lot of cards that are sometimes-traps appear near the top (Possession, King's Court, City, Treasure Map) and there are some strong high-variance cards that appear near the bottom (Familiar, Fool's Gold, various cards good for big money like Smithy, Envoy, Merchant Ship).

Some of the rankings make no sense at all though--apparently Duke requires the least skill of any card? And Adventurer is the most skill-intensive card of all??? Running this on more data might help. =)

2205

Simulation / Re: Geronimoo's Dominion Simulator: the ultimate simulation tool

« on: February 16, 2012, 08:04:26 pm »

Feature request: confidence intervals for simulation results. I've implemented a little Python script that calculates these for me using the formula from http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval. It would be nice to have these in the app itself though.

For what it's worth, the Python code is:

Code: [Select]

import math
from scipy.stats import norm

def binomial_confidence_interval(p, N, conf):
  return norm.ppf(1 - conf/2) * math.sqrt(p*(1-p)/N)
"p" is the observed probability, "N" is the number of trials, and "conf" is the desired probability of the interval being wrong (sorry that the name doesn't make any sense, as I hacked it together pretty quickly).

2206

Simulation / Improved IGG bot

« on: February 16, 2012, 07:56:53 pm »

(Edit: HiveMindEmulator points out in a reply to this that WW already posted an improved IGG bot in the BM+X thread.)

Nothing exciting here: I simply added a rule to buy Province whenever possible. This improves on the IGG bot that is included with Geronimoo's simulator. It is a little stronger against BMU & Smithy and a lot stronger in a mirror.

Edit: I should probably explain why I made a post for such a boring bot. The reason is that I sometimes look at bots to find the "canonical" way to play one-card strategies, and for IGG the current bot seems to suggest that it's better to only buy duchies and not provinces, which is false.

Results are from "Accurate Simulation (10000 games)" and are given with 99% confidence intervals. "IGG" is the original IGG bot, and "IGG2" is the one that buys Province when it can afford it.

IGG vs BMU:
Win: 89.2% +/- 0.8%
Loss: 9.5% +/- 0.8%
Tie: 1.3% +/- 0.3%

IGG2 vs BMU:
Win: 93.6% +/- 0.6%
Loss: 5.9% +/- 0.6%
Tie: 0.5% +/- 0.2%

IGG vs Smithy:
Win: 73.6% +/- 1.1%
Loss: 24.3% +/- 1.1%
Tie: 2.1% +/- 0.4%

IGG2 vs Smithy:
Win: 84.2% +/- 0.9%
Loss: 14.4% +/- 0.9%
Tie: 1.4% +/- 0.3%

IGG2 vs IGG:
Win: 63.6% +/- 1.2%
Loss: 30.1% +/- 1.2%
Tie: 6.3% +/- 0.6%

IGG2 bot:

Code: [Select]

<player name="Ill-Gotten Gains Improved"
 author="blueblimp"
 description="Get all the Ill-Gotten Gains and Duchies to empty 3 piles. Grabbing Province whenever possible improves the bot.">
 <type name="BigMoney"/>
 <type name="UserCreated"/>
 <type name="SingleCard"/>
 <type name="TwoPlayer"/>
 <type name="Province"/>
 <type name="Bot"/>
 <type name="Competitive"/>
   <buy name="Province"/>
   <buy name="Ill_Gotten_Gains"/>
   <buy name="Duchy"/>
   <buy name="Estate">
      <condition>
         <left type="gainsNeededToEndGame"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>


2207

Dominion General Discussion / Re: What is your favorite Dominion Downer?

« on: February 16, 2012, 04:49:38 pm »

I voted for drawing initial buys on turn 5, but another big downer is opening with Baron/Remake/Salvager/Island/etc. and drawing it with 4 coppers the first time.

2208

Dominion General Discussion / Re: What is your favorite Dominion Downer?

« on: February 16, 2012, 04:28:10 am »

Losing the first Tournament to an inferior deck.

That one really pisses me off.

It's even worse when, to add insult to injury, your tournament is parried (so you don't even get the +1 card +$1), and then your opponent's winning tournament is played when you have no province in hand, so they can play the prize on the same turn they get it. So annoying.

2209

Dominion General Discussion / Re: What you think you've done / What you've actually done

« on: February 16, 2012, 04:22:54 am »

Situation: Open Silver / Village
What you think you've done: Given yourself a chance to get some early cards and actions
What you've actually done: Opened Silver / Nothing

I have to confess I've opened Silver/Village before.  Usually on boards where there are a lot of power terminal 5s (esp drawing) and not a lot of note in the 3 and 4 slot.  My reasoning is that I will ultimately need a few villages for my engine and so I may as well pick them up while I can.  Is this legitimate or is it terribad and I should always just open double silver instead?

To add a comment (although I'm not too high level), you actually won't need villages for your engine particularly soon. I find it's way more important to get the drawing components first so that you have enough buying power and deck movement. It's not too bad if you, e.g., buy a couple Torturers with no village and draw one dead, since your deck will be cycling faster on average than if one of those were a village.

2210

Goko Dominion Online / Re: Official(?) Dominion App Available on iTunes

« on: February 16, 2012, 02:25:34 am »

Yeah, this is the same reason Apple avoids announcing products before they're ready to be sold, because they are so bad that if people knew about them ahead of time, they would never buy them.

Or wait, maybe it's that they want to generate interest in the app when it's actually available to buy.

Apple lol. If it would be like Apple someone would have "forgotten" the app half a year ago in some bar...

I gather you use Android. =P

2211

Goko Dominion Online / Re: Official(?) Dominion App Available on iTunes

« on: February 15, 2012, 03:16:24 pm »

Rio Grande Games and Donald V. certainly don't owe us anything, but it is horrible business judgment to refuse to provide us any information about the features and the expected release date of the official iPhone app.  Dominion is one of the most popular and well received games of the last 5 years and has a large customer base.  You would think that RGG would see the wisdom of giving us more details about the app (AI, multiplayer, expansions, etc.) and the anticipated release date.  The only information we have received is a cryptic statement last month that its release is coming in the near future.  No list of features.  No screenshots.  Not even an identification of who the developer is.

The way this has been handled makes me pessimistic about how RGG and the developer will respond to customer feedback once the app is finally released and how forthcoming they will be about future plans to improve the app and release additional expansions.

I once wrote and then deleted a long rant along these lines--I don't remember if it was this thread or another.  You've been a lot more succinct than I was.

I want to add one thing specifically, which is that all indications are that DXV himself is not being allowed to tell us anything.  My entire beef therefore lies with RGG and Jay.  Dominion is basically their flagship product right now--based on the fact that the only RGG game I've seen in non-gaming stores is Dominion (compare with Mayfair having Catan in stores).  Leaving a whole bunch of people hanging like this is terrible business sense, and Jay never struck me as having bad business sense.

It does make good business sense in one scenario....
If they know that the game is gonna suck in many ways that will piss off the isotropic fanbase.
In that case it makes perfect sense to keep it under wraps so the bad mouthing doesn't precede the actual release and dissuade other potential buyers.

Yeah, this is the same reason Apple avoids announcing products before they're ready to be sold, because they are so bad that if people knew about them ahead of time, they would never buy them.

Or wait, maybe it's that they want to generate interest in the app when it's actually available to buy.

2212

Goko Dominion Online / Re: Official(?) Dominion App Available on iTunes

« on: February 14, 2012, 04:56:43 pm »

While I tend to agree that a lot of people here are driven by the urge to sit atop a leaderboard, I could also imagine that there's a potentially large casual fanbase that doesn't care at all that would be perfectly happy to just play the game.

In my opinion, the reason a ranking system is important is to have good match-making, not for a leaderboard. A leaderboard is nice, of course, but I don't care that much since I'm nowhere near the top of it. I do care a lot about not playing matches where one player is way, way better than the other. It's just not fun.

The official app could one-up isotropic by implementing a better auto-match system.

2213

Goko Dominion Online / Re: Official(?) Dominion App Available on iTunes

« on: February 14, 2012, 11:45:27 am »

The Touch Arcade forums are listing the official Dominion Iphone app as being released later this week.  Has anyone seen confirmation of that from Rio Grande Games?

http://forums.toucharcade.com/showthread.php?t=118476

Interesting find. So maybe the isotropocalypse is this week.

2214

Puzzles and Challenges / Re: Gain "infinitely-many" cards in one turn

« on: February 13, 2012, 11:16:37 pm »

The bane of all puzzles: Embargo for arbitrarily many turns under possession, then buy said card (with/without trader per your problems specifications)

While that's clever and the rules are ambiguous enough that maybe it can slip through, it's not really a solution because the more cards you want to gain during the turn, the more pre-turn setup you need to do. The point of the puzzle is to do a fixed amount of pre-turn setup that's the same no matter how many cards you end up gaining during the turn--that was what I was trying to enforce by requiring a "fixed-size deck". That said, if you can find a way to abuse a fixed number of embargo tokens, say by converting the curses to silvers with Trader and then applying a card like Develop, that would be awesome.

The reason I think the puzzle is interesting is that creating this sort of gaining loop without KC is actually pretty tricky. Dominion generally does a pretty good job of preventing gaining loops, by design. I can't think of a substantially different way to do it from the solution I gave in the first post.

Edit: Let me see if I can formalize a bit, if that helps. The puzzle is to find a finite sequence of actions and shuffles Q such that for every specified number G of cards to gain, there is a supply number S such that if the game begins with at least S of every card in the supply, then in the game state resulting from applying the actions and shuffles Q, the player may subsequently gain at least G many cards (of any type) before ending his turn.

I don't know if that made it any clearer, but the point is that the pre-turn setup you do is not allowed to depend on how many cards you plan to gain.

2215

Dominion General Discussion / Re: Simulator help: Trader/Cache

« on: February 13, 2012, 05:47:34 pm »

This Cache-only bot loses about 32-61 to Smithy, so the Trader does not seem to be helping much in the bot above, since this bot is not much optimized. It wins 58-34 against BMU, so Cache by itself is not bad for big money.

Code: [Select]

<player name="Cache+BM"
 author="blueblimp"
 description="Buy Caches with $5.">
 <type name="UserCreated"/>
 <type name="BigMoney"/>
 <type name="SingleCard"/>
 <type name="Optimized"/>
 <type name="Province"/>
 <type name="TwoPlayer"/>
 <type name="Bot"/>
   <buy name="Province">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="18.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="5.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Cache"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>


2216

Puzzles and Challenges / Gain "infinitely-many" cards in one turn

« on: February 13, 2012, 05:38:35 pm »

The puzzle is to gain "infinitely-many" cards in one turn: more precisely, use a finite, fixed-size deck to gain a number of cards in one turn that is limited by the supply only. So if the supply limits were increased by 10x, then the same deck could gain around 10x as many cards in one turn.

This is pretty easy using King's Court, so there are really two puzzles: do it with King's Court and without.

A King's Court solution:
Have 4 Highways or Bridges in play, have your entire deck in your hand, and have King's Court, Ironworks, and Smithy in hand.

KC-Ironworks to gain KC, Ironworks, Smithy. Then play the Smithy to draw the three cards you just gained. Repeat until supplies run out. Each iteration actually also nets you +1 action.

A solution without King's Court:
Have 2 Highways or Bridges in play. Have your entire deck in your hand. Your hand must contain Black Market, 2 Border Villages, Crossroads, 3 Horns of Plenty, and 8 green cards.

Play BV twice, play BM and use it play the horns to gain: Black Market, Border Village+Crossroads, Border Village+Mandarin. (This is possible because BV costs 4 after the Highway effect, and you have BV, BM, Horn, and Highway in play.) The on-gain effect of the Mandarin causes the horns to go on top of your deck. Now, play Crossroads to draw 8 cards from your deck: three horns, a Black Market, two BVs, a Crossroads, and a Mandarin. Repeat until supplies run out.

2217

Puzzles and Challenges / Re: A ____ but not a ____ Riddle

« on: February 12, 2012, 10:29:32 pm »

boardgamegeek.com, but not dominionstrategy.com

2218

Game Reports / Re: Luck is really something I don't understand...

« on: February 10, 2012, 09:46:07 am »

What is the chance of colliding terminals 4 times in a row? I guess it is actually not that low...

I went ahead and simulated this. I don't fully simulate Dominion rules, so I made some assumptions: every turn, some card is bought; on turns 5 and 6, that card is a vault (or moat!); the vaults are always played; there is no interaction with your opponent; if after playing a vault, there is still a vault in hand, that is considered a collision.

Under these assumptions, I simulated to estimate the distribution of number-of-consecutive-collisions-after-buying-the-vaults. (So what "0" means is that they didn't collide the first time you played a vault; they might collide later.) Here it is, with confidence intervals (but don't take them too seriously for the small numbers, as I'm not using the best method):

Code: [Select]

0 -> 43.93% +/- 0.40% with 99.0% confidence
1 -> 31.08% +/- 0.38% with 99.0% confidence
2 -> 16.10% +/- 0.30% with 99.0% confidence
3 ->  6.14% +/- 0.20% with 99.0% confidence
4 ->  2.03% +/- 0.11% with 99.0% confidence
5 ->  0.57% +/- 0.06% with 99.0% confidence
6 ->  0.12% +/- 0.03% with 99.0% confidence
7 ->  0.02% +/- 0.01% with 99.0% confidence
8 ->  0.00% +/- 0.01% with 99.0% confidence
9 ->  0.00% +/- 0.00% with 99.0% confidence
So yeah, it's not impossible to see your vaults collide as much as they did, although it is pretty bad luck. It's around a 2.5% probability. But I didn't check how likely it is to have them miss the shuffle or to have your opponent see them when possessing!

2219

Dominion General Discussion / Re: Crazy luck you've had (or seen)

« on: February 10, 2012, 08:32:17 am »

I just got lucky in a way that completely outclasses my original post. I actually apologized to my opponent at the time because it was so ridiculous, so I posted it to the apology thread:

Dear NinjaBus, I'm sorry for playing literally pure big money and somehow buying my 4th province on my turn 11. That just should not happen (it's a 0.11% chance on a 4/3 split, according to my simulations). I thought my luck was bad when I didn't have $5 to spend on either turns 3 or 4, when I was planning to buy Trading Post to follow my Silver/Silver opening. Instead it ended up as among the luckiest games I've ever played. Log: http://councilroom.com/game?game_id=game-20120209-163506-7ee9bdea.html

2220

Game Reports / Re: Dear My Opponent: I am Sorry

« on: February 10, 2012, 08:28:55 am »

Lots of apology-worthy games for me recently.

Dear NinjaBus, I'm sorry for playing literally pure big money and somehow buying my 4th province on my turn 11. That just should not happen (it's a 0.11% chance on a 4/3 split, according to my simulations). I thought my luck was bad when I didn't have $5 to spend on either turns 3 or 4, when I was planning to buy Trading Post to follow my Silver/Silver opening. Instead it ended up as among the luckiest games I've ever played. Log: http://councilroom.com/game?game_id=game-20120209-163506-7ee9bdea.html

Dear zaubererer, I'm sorry for buying Black Market and pulling out (among others!) King's Court, Saboteur, Torturer, Remake, Salvager, and even a Fairgrounds, when the only attack in the original board was Rabble and the only trasher on the original board was Forge. Also, Village was in the kingdom (and I pulled several Village variants from the Black Market). With my deck reduced to an engine that played multiple Rabbles per turn and King's Courted whichever of Saboteur or Torturer I wanted to abuse that turn, I'm sure play in the late game was horrible, and you had no chance to build a similar engine yourself. The worst is that the points were quite close for a long time so you probably felt you needed to stay in. Log: http://dominion.isotropic.org/gamelog/201202/10/game-20120210-044223-425de153.html

2221

Dominion General Discussion / Re: What you think you've done / What you've actually done

« on: February 10, 2012, 04:38:45 am »

Situation: Trashing Estate into a 4$ with Farmland
What you think you've done: Getting rid of Estate and gaining a great card instead.
What you've actually done: Maikng your Estate worth 1 point more and buying a 4$ instead of 5$ or Gold.

I think MANY people don't get this one...

On a similar theme...

Situation: Have an Estate and Curse in hand, use Salvager on the Curse.
What you think you've done: Completely negated one of your opponent's Witch plays!
What you've actually done: Given up an additional $2 that turn in exchange for +2VP net.

This is not necessarily a bad play, but I definitely feel the urge to trash Curses more than is actually worth it.

2222

Simulation / Re: Challenge: Mint/FG vs Thief/FG

« on: February 09, 2012, 05:34:58 pm »

I would have actually been afraid to open Mint with Thief on the board, but it's really interesting that it's a slight favorite, or at least close.

Yeah, I expected Thief/FG to do even better. And I think that the Mint/FG bot might be pretty bad, since it suffers a lot from dilution that a human player (or smarter bot) might deal with more intelligently.

When I use your bots on Ultimate sim, fixed 5/2 against fixed 4/3, not specifying a starting player, I get thief/FG to win 48.028 - 47.391
So....

I re-ran it a couple times and it seems like there's a bit of variation even on ultimate, around ~1%. Somebody comfortable with statistics should be able to say how much. (Or I might have swapped the results by accident. Hard to say for sure.)

Anyway, I think it's safe to say that they are pretty much even, so I've edited the original post to reflect that.

If you simply change your thief bot to buy two, you get up to about a 5% victory for it. Pretty small, but it ain't nothing.

Thanks, I see that improvement too. When I tried a second Thief before, it didn't help, but I think that's because I bought it after the FG's were all gone, when it was too late to steal much.

2223

Simulation / Re: Challenge: Mint/FG vs Thief/FG

« on: February 09, 2012, 05:21:36 pm »

When I use your bots on Ultimate sim, fixed 5/2 against fixed 4/3, not specifying a starting player, I get thief/FG to win 48.028 - 47.391
So....

I re-ran it a couple times and it seems like there's a bit of variation even on ultimate, around ~1%. Somebody comfortable with statistics should be able to say how much. (Or I might have swapped the results by accident. Hard to say for sure.)

Anyway, I think it's safe to say that they are pretty much even, so I've edited the original post to reflect that.

2224

Simulation / Challenge: Mint/FG vs Thief/FG

« on: February 09, 2012, 03:34:26 pm »

Your opponent opens Mint/Fool's Gold (the 3rd-strongest opening in the game, according to CouncilRoom.com). Sadly, you got a 4/3 split. But wait! Thief is available (voted 2nd-worst card in the game in the poll What is the worst card in Dominion?).

My initial simulations show that the match Mint/FG vs Thief/FG is basically even, with a difference of less than 1% that could be coming from variance alone--see the bottom of this post for detailed results. The challenge is to improve either bot enough to obtain a significant lead. I've included bots in this post, which are simple modifications to BMU and should leave a lot of room for optimization.

(Note: I haven't found a discussion of this elsewhere, although there was a related puzzle thread that assumed perfect shuffle luck: Win the Fool's Gold rush - as second player!.)

For this post, I want to check how all bots I post fare against straight money. I'll use WanderingWinder's Big Money Ultimate bot, which is included with Geronimoo's simulator and is also posted in the thread Project: Optimizing Big Money X. I won't bother comparing against the included Thief bot, because it's computer-generated and only narrowly better than BMU.

The bots:

• Mint/Fool's Gold: This bot is always given a 5/2 opening, and must open Mint/Fool's Gold.
• Thief/Fool's Gold: This bot is always given a 4/3 opening. You're allowed to choose any opening you want, although you probably want to do Thief/Fool's Gold.
• Fool's Gold Rush: The only kingdom card this bot may buy is Fool's Gold. The point of this bot is just to have a baseline for Thief/FG and Mint/FG, so don't worry about it too much. This is NOT the bot included with the simulator because that bot is computer-generated and awful. This bot gets a random opening always (not that it should matter).

If you want and it helps significantly, it's fine if the Mint/FG bot buys a Thief at some point or the Thief/FG bot buys a Mint at some point. That's not really the point of the challenge and I'd be surprised if it helps much, but it'd be unfair to forbid it. I tried adding an opportunistic-Mint rule to Thief/FG, and it didn't make any noticeable difference.

Here are the results with the bots I've posted. Code follows after.

Results vs each other (using Ultimate Simulation for accuracy!):
- Mint/FG vs Thief/FG: 47 : 48
EDIT: WanderingWinder found the opposite of what I initially had here, which was a tiny lead for Mint/FG. I re-ran and found there is some variance even on ultimate, but it seems to hover around this 47:48 split.

Results vs FG:
- Mint/FG vs FG: 72 : 23
- Thief/FG vs FG: 59 : 36

Results vs BMU:
- Mint/FG vs BMU: 97 : 2
- Thief/FG vs BMU: 63 : 31
- FG vs BMU: 66 : 28

Mint/Fool's Gold:

Code: [Select]

<player name="Mint/Fool's Gold"
 author="blueblimp"
 description="The 3rd-strongest opening in the game on CouncilRoom.com. Requires a 5/2 split.XXXXNote: Provinces can't use a money-in-deck condition because that doesn't work well with Fool's Gold.">
 <type name="UserCreated"/>
 <type name="TwoPlayer"/>
 <type name="Combo"/>
 <type name="Bot"/>
 <type name="Province"/>
 <type name="BigMoney"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Mint">
      <condition>
         <left type="countCardsInDeck" attribute="Mint"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Fool$s_Gold"/>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>

Thief/Fool's Gold:

Code: [Select]

<player name="Thief/Fool's Gold"
 author="blueblimp"
 description="Adding a Thief to a Fool's Gold strategy does well and is roughly even against a Mint/Fool's Gold opening.">
 <type name="Attacking"/>
 <type name="UserCreated"/>
 <type name="TwoPlayer"/>
 <type name="Combo"/>
 <type name="Bot"/>
 <type name="Province"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Thief">
      <condition>
         <left type="countCardsInDeck" attribute="Thief"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Fool$s_Gold"/>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>

Fool's Gold Rush:

Code: [Select]

<player name="Fool's Gold Rush"
 author="blueblimp"
 description="Preferring Fool's Gold over Gold does quite well against BMU.">
 <type name="UserCreated"/>
 <type name="Bot"/>
 <type name="TwoPlayer"/>
 <type name="Province"/>
 <type name="SingleCard"/>
 <type name="BigMoney"/>
 <type name="Generated"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Fool$s_Gold"/>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>


2225

Dominion General Discussion / Crazy luck you've had (or seen)

« on: February 08, 2012, 05:12:45 am »

What's some crazy luck you've had in games?

This thread is inspired by a recent game (http://councilroom.com/game?game_id=game-20120207-030103-b8a8d78f.html) where I opened Potion/Courtyard and managed to buy an Alchemist on both turns 3 and 4 (because I played Courtyard on turn 4 and it pulled a potion into my hand). My opponent pointed out to me how ridiculously lucky this is, so I simulated afterward and found that this opening only has a 2.1% chance of getting alchemists on both turns 3 and 4.