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26

Game Reports / Tactician / Remodel / Treasure Map

« on: October 10, 2012, 11:08:50 pm »

http://dominion.isotropic.org/gamelog/201210/10/game-20121010-195800-aee086dd.html

cards in supply: Bazaar, Explorer, Native Village, Outpost, Pearl Diver, Remodel, Tactician, Treasure Map, Walled Village, and Warehouse

Nearly every card can be relevant here. I open Tactician/Native Village with some vague intent for double Tactician, while my opponent goes for Warehouse/Treasure Map. The WH/TMap goes nearly perfectly, with a hit on turn 5, and suddenly the heat is on--I don't have as much time to fashion my engine as I'd like!

I get a couple Remodels on turn 4/5, then convert two Estates to Treasure Maps on turn 7. On turn 10, I cash them in for 4 Golds, drawing 3 of those on the same turn, and remodeling two to Provinces. I think I'm in okay shape then, but on turn 11 I don't draw my 2nd Tactician, putting me in great danger as my opponent takes the 2nd-last province on his turn 11, putting me 9 points down.

I'm lucky in that he can only afford an Estate on turn 12, making the gap 10 points--and then on turn 13, I barely cross it, remodeling a gold to a Province, a Tactician to a Duchy, and buying 2 Estates with $4.

All-in-all: in my 13 turns, I gained 4 Provinces, 2 Duchies, and 2 Estates; while he bought 4 Provinces, a Duchy and an Estate. Very fast game!

On reflection, Outpost could have helped me a lot, and I should have been in less of a hurry to take Provinces, since (with Warehouse aid) the engine should be strong enough to take a bunch of Duchies too. Thank goodness for first player advantage!

27

Dominion General Discussion / What's a reasonable time control for Dominion?

« on: September 08, 2012, 01:57:41 am »

Wikipedia:

A time control is a mechanism in the tournament play of almost all two-player board games so that each round of the match can finish in a timely way and the tournament can proceed.

Either online or in real life (edit: although I'm more interested in how it could be done online). A maximum time for the whole game seems bad, because different kingdoms can last drastically different numbers of turns. Allocating a certain amount of time per turn also seems bad, because different strategies can take different amounts of time per turn, so a per-turn time restriction would favour treasure-oriented strategies over engine strategies.

One could allocate bonus time per click on isotropic, but that doesn't seem very fair to players who use click-light strategies. Would it be better if the bonus-time-per-click were given to both players?

28

Variants and Fan Cards / Adapting Dominion to asynchronous play

« on: August 20, 2012, 12:35:06 am »

One interesting topic to come up in Goko-related discussions (on BGG mainly, not here) is asynchronous play. The usual answer is "it wouldn't work", which is of course correct with the current rules, because Minion-Moat-type games would be a nightmare. But maybe varying the rules could make async play work.

I think that async play ideally wants each player's turn to require no decisions from his opponent. You could ask for more maybe, like being able to specify multiple turns at once (especially in the opening), but this is good for a start.

So, I made a list of cards that currently have a player make a decision when it's not their turn. These fall into two categories: reactions and opponent-choice. First the list, then a discussion of how they might be changed.

Reactions
Base: Moat
Intrigue: Secret Chamber
Prosperity: Watchtower
Cornucopia: Horse Traders
Hinterlands: Fool's Gold, Trader, Tunnel

Opponent Choice
Base: Bureaucrat, Militia
Intrigue: Masquerade, Saboteur, Torturer
Seaside: Ghost Ship
Prosperity: Contraband, Mountebank, Rabble, Vault, Goons
Cornucopia: Tournament, Young Witch, Followers
Hinterlands: Duchess, Oracle, Margrave
Promo: Envoy, Governor

Overview of Discussion

There are two main ways to adapt cards: one is to make the decision automatic, and the other is to delay the decision to the beginning of next turn. Making a decision automatic loses some flexibility compared to the current rules, but otherwise is faithful.

Delaying the decision can make a pretty big difference compared to current rules, although it often gets played this way IRL in situations where it doesn't matter. Sometimes it matters a lot, e.g. playing a discard attack to help your Tournaments, which is an interaction that would be lost.

If you're playing asynchronously online, the server could choose to report delayed effects one-by-one, to help preserve the frustration of not knowing how many times you'll get hit by Torturer.

Discussion of Reactions

Moat and Horse Traders are easy: just force them to always be revealed to attacks. Although you don't always want to do this, usually you do. IRL, it's difficult to make this accountable (because your opponent can't tell the difference between you failing to reveal Moat and simply not having one in hand), but that's not a problem on a computer.

Fool's Gold's reaction is fine to delay.

Secret Chamber, Watchtower, and Trader are difficult to deal with. Trader could perhaps be auto-revealed to anything your opponent gives you, because almost never will they give you something better than a Silver. Watchtower is tough, because sometimes you really want to trash (Curse, Copper) and sometimes you really want to top-deck (Silver from Governor or from revealed Trader)--maybe it's best to delay the decision, so that in the meantime, the card is set aside. Secret Chamber seems almost impossible to adapt, because delaying the decision would make it useless against deck attacks, so the card would need a redesign.

Tunnel is obvious. Reveal it always. Has anybody ever not revealed Tunnel when they can? There are some problems with accountability here again, since in principle you can discard in a way that hides the Tunnel from your opponent.

An example of an interesting card interaction lost by these changes: not revealing Moat to a Mountebank so that you can reveal Trader instead.

Discussion of Opponent Choice

Some of these are no-brainers: for Tournament and Young Witch, auto-reveal always. Like with reactions, there would be accountability problems IRL. Mountebank is less clear-cut, but it's usually good to reveal against it, so auto-reveal for that card too.

Oracle and Rabble sometimes require re-ordering cards that go on your deck, but it rarely matters, so they could be put back in original order. (Remember that the reason re-ordering is usually allowed is that, IRL, it's hard to keep track of the original order. This isn't a problem on a computer.)

Discarding and put-back-on-deck effects (Bureaucrat, Militia, Torturer, Ghost Ship, Goons, Followers, Margrave, maybe Vault) can be delayed.

(Then there's a question of whether opponent-draws-a-card effects should also be moved to the beginning of opponent turn. I think they should, because the interaction of opponent-draws-a-card effects and discard attacks is important pretty often.)

Saboteur's gain, Governor's opponent-remodel, and Duchess's self-spy can all be delayed. For Governor and Saboteur, your opponent should get to resolve these effects even if the game end condition is fulfilled before their turn starts. (Note that moving Governor's effect can hurt a lot if you are defensively remodeling $7's into Provinces, so this loses some interesting situations.)

Masquerade, Contraband, and Envoy all seem impossible to adapt. With Masquerade, the pass could be removed, which makes the card much less interesting but at least preserves part of it. I don't see any way to deal with Contraband and Envoy.

Conclusion

Using the changes suggested above, nearly every card can be adapted somewhat reasonably to asynchronous play, with the loss of some interesting interactions. The exceptions are Masquerade, which needs its pass removed, and Contraband, Envoy, and Secret Chamber, which seem impossible to adapt.

Compiling this list made me realize how much worse Dominion would be without interaction on opponent turns. Sure, in most games it doesn't make any difference, but the games where it does matter are some of the most interesting games.

That said, the core of Dominion would still be there. It'd still be a fun game, albeit a little less so than normal.

29

Goko Dominion Online / Which existing card do you predict will be implemented last?

« on: August 17, 2012, 01:10:56 am »

Which existing (i.e. non-Guilds) card do you think will be implemented last in Goko? I'm expecting it's one of the two remaining promos, which both have unique implementation challenges (Black Market deck, special Stash back).

30

Dominion: Dark Ages Previews / Best knight?

« on: August 16, 2012, 03:25:55 pm »

Which knight do you think will be the best (i.e. strongest)?

Full descriptions: https://dl.dropbox.com/u/20240121/dark_ages/3.jpg. I put the non-jousting effects along with the poll options.

31

Goko Dominion Online / Anyone else looking forward to the campaign/adventure mode?

« on: August 14, 2012, 02:29:37 pm »

My first reaction was "that sounds stupid", but after reading some comment from Donald X about designing kingdoms for it, I think it could be pretty fun. Sort of like solo challenges, except from the designer.

32

Dominion: Dark Ages Previews / If the Dark Ages cards were submissions to the mini-set design contest...

« on: August 09, 2012, 09:21:00 pm »

...what would you say? Would you vote for them?

33

Council Room Feedback / Feature request: conditioned best/worst openings

« on: July 07, 2012, 11:57:55 am »

There was some discussion some time ago about the viability of a Cache/Chapel opening. This is rated lower than Silver/Chapel on the best/worst openings list, but it's hard to tell whether that's because it's actually worse or because kingdoms with Cache tend to be weaker for Chapel.

Another example is Young Witch/Lighthouse. Surely that's got to be better than Young Witch/Silver when both are possible (unless the concern is drawing the Lighthouse dead?), but it's rated lower, probably because YW is weaker with Lighthouse present.

Maybe it'd be interesting to have conditioned best/worst lists, similar to supply_win.

Edit: I forgot a classic example: Mint/FG is rated higher than Wharf/FG, but Wharf/FG dominates Mint/FG.

34

Dominion General Discussion / What can be tracked for advantage?

« on: July 04, 2012, 09:47:29 pm »

Recent discussion brought to mind the question: what can be tracked for advantage (in Dominion, particularly Isotropic)? The point counter extension tracks points and deck contents, but there's lots of other stuff that a player could also track to gain an edge.

Here, I'm thinking of information that otherwise you'd only know from memory.

Everything I can think of:

• Current points of every player (except for non-2-player Masquerade games).
• Deck size of every player (even with Masquerade present).
• Deck contents of every player (again excepting non-2-player Masquerade).
• Order of known cards in the Black Market deck. This would help a lot when a player misses a good card and it gets sent to the bottom. In fact, you could see strange situations where neither player wants to play Black Market on their turn, because there are 3 crap cards on top and 3 good cards after.
• Exact contents of your draw deck and discard pile.
• When possible, which cards are on the top of your deck and in what order. Maybe most useful when your opponent has been playing Spy-type cards.

Things that are impossible to track:

• Exact contents of your opponent's draw deck and discard pile, mainly because they don't need to show you everything they discard.

Things you don't need to track, because the rules allow you to check at any time (and isotropic tells you all of these):

• Number of cards in your draw deck (but not your discard!).
• Number of cards remaining in each supply pile.
• What's in the trash.

35

Puzzles and Challenges / By the rules: speaking

« on: July 04, 2012, 08:10:30 pm »

In what situations do the rules explicitly allow you to speak out loud? There are multiple right answers.

36

Dominion Isotropic / Watchtower/Embargo bug?

« on: June 29, 2012, 08:30:53 pm »

When you buy something Embargo'd with a Watchtower in hand, this happens:

You buy a Watchtower.
... ... You reveal a Watchtower.
... ... You trash the Curse.
... You gain a Curse.

Notice how the Curse is reportedly gained after being trashed, which seems to be just the logging messing up and not a gameplay bug. The point counter extension gets confused too.

For comparison, buying a Curse with a Watchtower in hand, then revealing the Watchtower to trash it, gives this:

You buy a Curse.
... You reveal a Watchtower.
... You trash the Curse.

37

Dominion Isotropic / So, ARTjoMS and ddubois changed their usernames...

« on: June 20, 2012, 07:38:19 pm »

What do they play under now? I have no interest in playing either of these two. "inverseParanoid" is ranked similarly to ARTjoMS and seems comparably obnoxious.

38

Puzzles and Challenges / Playing A is similar to playing B then C

« on: June 19, 2012, 02:09:42 am »

Inspired by the discussion of Margrave in some other threads, try to find examples of single card effects that combine the effects of two other cards. This can be pretty loose.

The Margrave example: Playing Margrave is like playing a Council Room followed by a Militia, except without the +$2.

A couple other examples:

Playing 2 Labs is the same as playing a Village then a Smithy. In both cases, you net +0 actions and +2 cards.

Playing a Festival is similar to playing a Village then a Woodcutter, except with an additional +1 action.

39

Dominion General Discussion / The term "multiplayer"

« on: June 09, 2012, 02:20:25 pm »

Does this bug anyone else? 2-player is already multiplayer, since there are 2 players and not just 1. If we're talking about having more than 2 players, wouldn't a term like "many-player" be more appropriate?

Also, arguably it's not useful to lump together 3- and 4-player (not to mention 5- and 6-player), since they are nearly as strategically different from each other as they are from 2-player.

40

Puzzles and Challenges / "Name a card, and do X"

« on: April 18, 2012, 02:54:29 pm »

From dougz's AMA on reddit:

Once there was a card that said in part, "name a card, and do X" (sort of like Wishing Well). But what X was meant it was always effectively deterministic which card you would name; assuming you were trying to win the server could have 'named' the card for you, saving you a click. Donald wanted it to do that, but I was like, "no, it says to name a card, so you have to name a card". Later that card got dropped so it's not an issue any more, but I'm still a stickler for things like that.

The puzzle: figure out what this card might have been!

41

Puzzles and Challenges / Not a misclick

« on: April 13, 2012, 06:28:50 pm »

You play an Ambassador, revealing a Colony and returning one copy to the supply. Why?

Rules:
- It is not a Possession turn. (That would be too easy.)
- Returning a Colony to the supply is the best move to make in the situation.

42

GokoDom / Tournament predictions by simulation (UPDATED: 2012-04-07)

« on: March 22, 2012, 04:41:05 am »

Update 2012-04-07.

(Edit: Given the revised tournament format, this post is now using the correct tournament structure to predict the chance of advancing to the bracket championship.)

Introduction

Using the same TrueSkill algorithm and parameters that are used to create the leaderboard, I've run some simulations to see who's likely to win their groups. There's no particular reason that this would be accurate (even assuming I didn't make an error), so don't take it too seriously.

Notes

• Ignorentmen, rspeer, and Tonks77 are missing from the current leaderboard, so they get the default 25 +/- 25 rating--meaning their results are not very predictive at all. If any of you have a name with a reasonable rating on it, I can add that to the simulation to get more interesting results.
• More than 1% of the time, there is more than a 2-way tie for the winner of some group. Since there isn't a rule for this case, I don't handle it correctly.
• I randomly sample player skills once before each simulation and hold them fixed throughout the simulation. Hopefully this is a reasonable way to interpret the TrueSkill ratings.

Results

Below are the results from 10,000 simulations. Here's how to read the results. The percentage shows the number of times that player wins their group. "mu" is the mean skill of that player (which is shown on the leaderboard), and "sigma" is the standard deviation of that player's skill (which is one third of the +/- shown on the leaderboard).

Brackets:
  Groups:
    Ranking:
      48%: shark_bait (mu = 50.2, sigma = 3.5)
      17%: dghunter79 (mu = 45.6, sigma = 2.4)
      16%: Titandrake (mu = 45.0, sigma = 3.4)
      14%: O (mu = 44.9, sigma = 2.4)
       2%: antony (mu = 37.8, sigma = 2.8)
       2%: gorgonstar (mu = 38.0, sigma = 2.5)
       1%: ednever (mu = 36.0, sigma = 2.9)
       0%: Insomniac-X (mu = 27.1, sigma = 4.0)

    Ranking:
      35%: tlloyd (mu = 48.3, sigma = 2.8)
      20%: perdhapley (mu = 45.9, sigma = 2.1)
      17%: Axxle (mu = 44.7, sigma = 3.7)
      13%: Jorbles (mu = 43.6, sigma = 3.7)
       9%: [MAD] Mergus (mu = 42.1, sigma = 2.8)
       3%: yuma (mu = 37.9, sigma = 3.0)
       2%: Coheed (mu = 38.0, sigma = 2.6)
       1%: Ignorentmen (mu = 25.0, sigma = 8.3)

    Ranking:
      42%: NinjaBus (mu = 50.5, sigma = 2.6)
      21%: michaeljb (mu = 46.9, sigma = 3.6)
      12%: mikemike (mu = 44.7, sigma = 3.0)
      11%: A_S00 (mu = 44.5, sigma = 2.8)
       8%: BJ Penn (mu = 43.7, sigma = 2.0)
       6%: mnavratil (mu = 42.5, sigma = 2.9)
       1%: CarpeDeezNuts (mu = 35.5, sigma = 2.5)
       0%: ebEliminator (mu = 27.6, sigma = 3.2)

    Ranking:
      76%: RisingJaguar (mu = 55.9, sigma = 3.6)
      13%: greatexpectations (mu = 46.1, sigma = 3.1)
      10%: Mean Mr Mustard (mu = 45.4, sigma = 2.5)
       1%: Brando Commando (mu = 38.1, sigma = 2.9)
       0%: ^_^_^_^ (mu = 33.9, sigma = 3.0)
       0%: rspeer (mu = 25.0, sigma = 8.3)
       0%: Nicki Menagerie (mu = 30.1, sigma = 2.6)
       0%: AHoppy (mu = 14.5, sigma = 3.8)

  Groups:
    Ranking:
      40%: Geronimoo (mu = 51.5, sigma = 3.0)
      36%: Rabid (mu = 50.9, sigma = 2.6)
      11%: lespeutere (mu = 45.6, sigma = 2.4)
       9%: MrEevee (mu = 44.9, sigma = 2.6)
       2%: Dubdubdubdub (mu = 39.1, sigma = 3.9)
       1%: luliin (mu = 37.0, sigma = 3.7)
       0%: Mangsky (mu = 27.0, sigma = 3.0)
       0%: Nucleus (mu = 26.4, sigma = 3.0)

    Ranking:
      61%: Fabian (mu = 55.9, sigma = 2.7)
      27%: Brathannes (mu = 51.2, sigma = 2.5)
       5%: StickaRicka (mu = 44.3, sigma = 3.3)
       3%: Lekkit (mu = 42.6, sigma = 2.7)
       3%: JanErik (mu = 41.9, sigma = 3.8)
       1%: ugasoft (mu = 37.1, sigma = 3.7)
       0%: Tonks77 (mu = 25.0, sigma = 8.3)
       0%: ArjanB (mu = 29.4, sigma = 3.5)

    Ranking:
      59%: WanderingWinder (mu = 51.3, sigma = 2.8)
      15%: Robz888 (mu = 44.8, sigma = 2.3)
       9%: Mic Qsenoch (mu = 42.6, sigma = 2.6)
       9%: blueblimp (mu = 42.4, sigma = 2.9)
       5%: Masticore (mu = 39.7, sigma = 3.5)
       2%: pops (mu = 37.7, sigma = 3.2)
       1%: zxcvbn2 (mu = 33.5, sigma = 3.5)
       0%: angrybirds (mu = 17.4, sigma = 6.8)

    Ranking:
      66%: jonts26 (mu = 54.3, sigma = 3.1)
      14%: DG (mu = 45.2, sigma = 5.2)
       6%: Kirian (mu = 42.7, sigma = 3.6)
       6%: Graystripe77 (mu = 42.5, sigma = 3.6)
       5%: The Real ~~**Young Nick**~~ (mu = 41.6, sigma = 3.7)
       3%: andwilk (mu = 40.6, sigma = 3.6)
       0%: elahrairah13 (mu = 33.4, sigma = 2.7)
       0%: fit1one (mu = 22.5, sigma = 2.9)

43

Dominion Articles / A theorem about drawing and density

« on: March 05, 2012, 05:02:16 am »

(Inspired by the discussion in the Venture thread.)

Summary: Certain cards (such as Venture) perform a complex drawing procedure but do not return cards to your draw deck. This post shows that these cards do not change the expected density of any card (or type of card) in your draw deck unless you knew something about your deck order to begin with or you trigger a reshuffle.

Disclaimer: This is going to involve some math. This might be overkill. If you think so, I can only apologize for not being sufficiently convinced by intuition. If you're overly skeptical like me, read on!

Assumptions:

• Everything within applies only when you do not trigger a reshuffle. Reshuffles make things more complicated. For technical reasons, I'll actually require that the drawing leaves at least 1 card remaining in your draw deck, but that's just because it doesn't make sense to talk about the density of an empty draw deck.
• I assume that the drawing samples uniformly randomly from your draw deck. This is often equivalent to the shuffling that occurs in a real game, but it doesn't apply if you know what the top cards of your deck are, either because you sifted them or your opponent put something there. So if cards like Cartographer, Rabble, etc. are in play, then nothing in this post applies directly. If the drawing procedure reaches beyond the cards you know about (e.g. you're playing Farming Village after your opponent played Rabble, in which case you are guaranteed to discard all the cards Rabble put there and then you're in unknown territory), then the results may still be relevant.
• I assume the card decides whether to continue drawing based only on the cards it has already drawn and does not put cards back on the deck. This is true for many cards, such as: Venture, Scrying Pool, Farming Village, Smithy, Swindler, etc. It is not true for a card like Courtyard.

Caveat: Density is a pretty crude measure of deck quality, and expected density even cruder. A more important number is the probability of getting $8 in hand, for instance. This is also much more difficult to get a handle on mathematically.

Math

Let D be the set of all cards in the draw deck. We require D to be non-empty.

A draw state (A,B) consists of a set A and a non-empty set B that partition D. Let S be the set of all draw states. i.e. S = {(A,B) : A U B = D, A /\ B = empty, B =/= empty}. (Note: I'll use /\ for set intersection.) We'll interpret A to mean the set of already-drawn cards and B to mean the set of remaining cards.

A draw policy is a function f : S -> {0,1}. The output 1 indicates to draw another card and 0 indicates to stop drawing. For example, for Venture,
  f(A,B) = 1 if A contains no treasure, 0 if A contains a treasure.

For a subset T of D, the remaining density function of T is
  d_T : S -> [0,1]
defined by
  d_T(A,B) = |B /\ T| / |B|.
For example, for Venture, you might be interested in letting T be the set of all treasure cards in your draw deck, and then d_T would indicate the proportion of cards in your draw deck that are treasures.

Theorem. Let f be a draw policy and let T be a subset of D. Suppose there is an integer N >= 1 such that
  f(A,B) = 0 whenever |B| <= N.
(In other words, we always stop drawing before emptying the draw deck.) Let (A_end, B_end) be the final draw state after drawing uniformly from D according to policy f. Then
  E[d_T(A_end, B_end)] = d_T(empty, D).
(In other words, the expected density isn't changed by drawing.)

Proof.

For all draw states (A,B), we prove
  E[d_T(A_end, B_end) | current state is (A,B)] = d_T(A,B)
by induction on b = |B|.

If r <= N, then f(A,B) = 0, so A_end = A and B_end = B, and the claim is trivial.
For r > N, if f(A,B) = 0, the claim is again trivial, so assume f(A,B) = 1.

Let c in B denote the drawn card. Then, using induction,

Code: [Select]

  E[d_T(A_end, B_end) | (A,B)]
    = sum_{c in B} E[d_T(A_end, B_end) | (A U {c}, B \ {c})] P[drawing c]
    = sum_{c in B} d_T(A U {c}, B \ {c}) / |B|
    = sum_{c in (B /\ T)} d_T(A U {c}, B \ {c}) / |B| + sum_{c in (B \ T)} d_T(A U {c}, B \ {c}) / |B|
    = [(|B /\ T| - 1) / (|B| - 1)] * [|B /\ T| / |B|]   +   [|B /\ T| / (|B| - 1)] * [(|B| - |B /\ T|) / |B|]
    = [|B /\ T| / (|B| - 1)] * [(|B /\ T| - 1) / |B|]   +   [|B /\ T| / (|B| - 1)] * [(|B| - |B /\ T|) / |B|]
    = [|B /\ T| / (|B| - 1)] * [(|B| - 1) / |B|]
    = |B /\ T| / |B|
    = d_T(A,B),
as we wanted. []

44

Dominion Isotropic / How do you set your auto-match bias?

« on: February 29, 2012, 06:33:09 pm »

I'm curious how people use the auto-match bias option (if they do at all).

A couple combinations I've found interesting:
Alchemy + Prosperity: This creates for really crazy, big games.
Intrigue + Hinterlands: This is a really good setting for hybrid VP cards. Crossroads becomes very nice and Scout is less terrible than usual.

45

Dominion General Discussion / Isotropic bot proof of concept

« on: February 26, 2012, 11:16:27 pm »

I've made a simple bot that plays on isotropic according to WanderingWinder's BigMoneyUltimate buy rules.

Demo video: http://www.youtube.com/watch?v=Iw4LZG7e9d0

I'm curious whether there is interest in being able to play against bots. The implementation is via a Chrome extension, which I haven't made public yet because it's not very polished.

This is only a proof of concept, so it has some major limitations:

• Currently it doesn't know how to make any choices, such as when playing against discard attacks. This would require play rules like the simulators have.
• It can't start games itself. I do that manually.

46

Game Reports / A rock-paper-scissors board?

« on: February 24, 2012, 09:10:04 pm »

Here is an interesting board:

http://dominion.isotropic.org/gamelog/201202/24/game-20120224-175545-c4faa9c1.html

Cards: Chancellor, Courtyard, Crossroads, Ill-Gotten Gains, Jack of All Trades, Masquerade, Quarry, Secret Chamber, Trade Route, and Trading Post

Is this maybe a rock-paper-scissors board? The three strategies which stand out to me are BM+Courtyard, BM+Masquerade, and Jack+IGG (which is usually better than doublejack). I believe that BM+Courtyard should beat BM+Masquerade, which should beat both IGG and Jack+IGG, and any sort of IGG approach should beat BM+Courtyard.

I did some rough sims with 4/3 starts. For Masquerade and Courtyard, I used the included bots, and for Jack/IGG, I took WW's bot and modified it to buy two jacks.

The results were that Masquerade beats Jack/IGG about 56/41, Jack/IGG beats Courtyard about 88/10, and Courtyard beats Masquerade about 55/40.

What do you think, and how would you play this board? My opponent and I were both a little lost. He went for Jack -> Courtyard -> IGG -> Masquerade, while I went DoubleJack -> IGG -> Masquerade, not bothering picking up the Courtyard. It ended up close but I doubt either of us were playing anywhere near optimally.

47

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>


48

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.

49

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>


50

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.