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26

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 29, 2012, 11:21:08 am »

To clarify "line" because it might be confusing in that usage: a Line is the path/build/game of a single player.

Polarized results really should make some sense by now given all the context and examples provided. 

Thanks for the explanation of line. That was not at ALL in my mind when I read your paragraph, any of the several times I read it. Now it makes much more sense.
On the polarized thing... well, maybe you think it should be clear by now, but it's obvious you thought that before (well, either that or you just wanted to say something cryptic and confusing, but I don't peg you for the kind of person to do that). I'm TELLING you it's not clear to me, so please, explain it.

Edited to fix a quote blocking issue.

I'm not a master of the English language but I think what he means with "polarized results" is results that lean themselves to the extreme ends of the spectrum (or poles). For example a card that will produce polarized results is Treasure Map because you'll either get crushed (negative extreme) because you don't manage to get your 2 Treasure Maps together. Or you'll get a comfortable lead if you manage to play both your maps on turn 5 (positive extreme).

On the other hand Silver would be an example of not producing polarized results. I mean with silver you get what you payed for after all.

Yes. You can also call it 'heavy tails' or 'non linear behavior'. BM is -by essence- as close to a linear strategy as you can get in dominion. Of course, the inherent structure of the green cards add some non-linearity even to BM (hitting 8 is twice as good as hitting 7), but overall, you just try to ramp up your average moneyness, knowing that the law of large numbers will reward you in the long term for it.

Maybe the best way to visualize it is the vp/turn graph. Do not forget this is a random graph (what you see in simulators is its 'average').

Engines (especially heavy trashing ones or golden decks) tend to have a very narrow number of possibilities for that graph: there is basically the average one, and a little bit of wiggle room (sometimes a lot more towards the end when you start playing risky again).

Big money has a broader range of possible 'greening' paths, but they are very well behaved around the mean indicated by the simulator. Basically, add the standard deviation around each point and you have a perfect picture of the thing.

Then there are one-turn explosions, TM, or other 'risky' or 'messy' strategies (these terms are not necessarily synonymous). Maybe the most counter-intuitive example is alchemist. It gives the false impression of an engine, when really, it often has a much higher chance than other engines of fizzling, leading to a much more 'polarized' greening curve: basically, there is usually around 80% of the weight at the 'typical' shape and 20% around the much lower 'fizzle' shape. It therefore has a lot of downside, while the upside is very limited (so you trade off your upside for a more stable outcome in most cases) Of course, you can try to ramp it up to 90, 99% or whatever, but that often costs time. Hence playing alchemist loops is often a risk (at least, when you are tight with turns). Treasure map is the opposite: it has a lot of upside, but ends up often in the 'down' scenario.

This makes me wonder if the simulator could draw all possible paths. Hopefully all the superposing ones would give a visualization of the probability mass of a possible outcome. Or maybe it'll just look like a mess xD.

PS: before someone tells me that engines fizzle too: yes but once an alchemist loop is broken, there is a lot of auto-correlation, and it fizzles for longer.

27

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 28, 2012, 09:04:50 pm »

I remembered that I had two mild examples in my article a few weeks ago. Tell me if these fit the bill!

First a game where my opponent opens pirate ship/Xroad, with only black market and tribute as virtual dollars. I counter by loading up on a lot of variance: BM/TM. My idea is that he will trash my coppers, and I'm going to grab a few Xroads and menageries, making a TM collision somewhat feasible (menagerie mitigates the pirate ship attack and the TM signleton, as well as combos with BM). In the mean time, I need enough money to buy the second TM, and there were a few interesting things in the BM pool. I get lucky with the BM, grabbing embargo (on pirate ship) and remake early on. My TM gamble was not successful at first, but it gives me a big money boost on T12 once I have more engine parts. Note that I always only have two TM! It could be argued that I was lucky, or that I just countered his opening, but I thought Xroad/pirate ship was pretty scary, and probably a good opening for p1.

The second game is one of my few wins against WW. It's one of those games I dread to play against him, because it contains all kinds of BMish cards I dislike and he knows how to play well. So I decide to spice up the opening by getting the NB, successfully stealing WW's first silver, with the afterthought that I can always upgrade NB later on, and that it's actually a decent terminal in the BMish start of the game. This initial gamble gives me enough time to build an engine, forcing WW to do the same. I definitely got lucky on this one. Tell me if I'm wrong WW, but if you had opened CY, I would have been toast playing BM!

PS: I also agree that my game is way oversimplified. But it does make the idea come across as to why variance can help p2 more than p1. The question is, as WW points out, whether this effect is important enough to be really taken into account. I have the impression the answer is yes, but that is my opinion. Truth be told, I just like thinking about these concepts during the veto to 'train' myself to think in terms of mean/variance tradeoff. I think most of us agree that it definitely is an important concept in the midgame when there is a clearer leader and lagger.

28

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 28, 2012, 02:14:23 pm »

But my larger point is... like, if it increases your win% as player two to play the 'riskier' strategy, then it probably also increases your chances as player 1 to play the 'riskier' strategy, at least just looking from the outset.

Well, the point is that this is a useless question.

Maybe, but a question was raised, so I try to answer.

I think way too much emphasis is being put here on the p1 vs p2 thing.

There's obviously some cards that benefit a little more than others from being p2 in pre-set simulated strategies. This fails to prove anything meaningful for the game.

So, would you open tournament or baron? It would be consistent if you were not allowed to make that depend on being p1/p2.

I should change my behaviour off of the 'optimized' bot (BTW, this tournament bot is NOT optimized) based on whether I'm p1 or p2, more importantly based on where the game stands, and also very importantly based on what you do.

Agreed, which is why I only reasoned in terms of openings. The simulation is just a crude measure of the quality of the two openings with respect to p1/p2 position. I am sure that methodology has been used in the past.

Sure, you can get some benefit if they put their heads down and only play some pre-written strategy like a simulator would. The whole point of this article is that you should NOT do that - you have to react to them, meaning that you should stray from your script.
The simulator does NOT answer this question. And while it can sort of be made to, it will take you way way way way too long to do that - you need to program decisions for at least tens of thousands of different circumstances, and probably meaningful differences on hundreds.

A sub-part of the article which you vehemently disagreed with was the impact of the p1/p2 bias on openings (regardless of reactions later in the game). Which is why my two examples are basically purely reactions on opening luck: how to react to a 5/2 vs 3/4 or a p1/p2 position. Reading anything beyond that is a waste of time.

Sorry if this sounds negative, I usually really like what you do WW: but it really feels like you are the one being somewhat vague in this topic. Sorry if we are slow and force you to double-post and expand on your posts a bit.

29

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 28, 2012, 12:01:33 pm »

Simulation is good at answering *very targeted* questions. Here the question was: give an example where there is a mean-variance trade-off happening from a baron opening where p2 and p1 have differing strategies.

Any other comment?

30

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 28, 2012, 11:04:05 am »

 
Stef used Baron as a passing example.  I don't think Stef should be required to teach everyone how to build with Baron in order to use the concept in high-level article about risk-taking. 

So first it's a concrete example, now it's a passing example? I agree, it's a passing example. I don't think he needs to explain every card in this article. But I would like some examples of 'I played this risky strategy here, here's why I did it.' If it had that, it could be one of the finest articles I've read (since it's already pretty good).

Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

You literally don't know what he is talking about.  Regardless of any specific example the whole point is precisely "how to think about when the right play is not always the right play and if the risks are worth it."

And my whole point is that he isn't explaining how to think quite right. Because you shouldn't be taking more risks as p2 than p1. Okay, you should, but it's a really really small difference. You'll notice the difference once every hundred games, at most. Probably once every few hundred games. Does this make it un-important? In the scheme of things, yeah. I'm fine talking about it, because it's not nothing. But I think way too much emphasis is being put here on the p1 vs p2 thing. I think prima facie that the difference in positions at the start of a game p1 to p2 is being blown out of proportion here. The larger points that he's trying to make about taking risks, particularly when behind (though I think here only later in the game, where you actually are significantly behind!) are absolutely important, and sort of getting lost with this p1 vs p2 thing.

Example:
Consider two strategies: Geronimoo's optimized tournie bot, and a tournie/baron bot I quickly scrambled together.

p1/p2 (both with 4/3)

tournie/tournie: 58/39
tournie/baron: 57/41
baron/tournie: 55/43

Code: [Select]

<player name="Baron/tournie"
 author="Empathy"
 description="Baron trying to race an early province to block the tournie p1.">
 <type name="Generated"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="TwoPlayer"/>
 <type name="UserCreated"/>
 <type name="SingleCard"/>
   <buy name="Followers"/>
   <buy name="Trusty_Steed"/>
   <buy name="Princess"/>
   <buy name="Bag_of_Gold"/>
   <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="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Baron">
      <condition>
         <left type="countCardsInDeck" attribute="Baron"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Tournament"/>
   <buy name="Silver"/>
</player>

Agreed, it's a small effect. But I think veto allows you to create (or remove) a lot of such scenarios: therefore, you should be thinking about it while vetoing (I think).

31

Dominion Articles / Re: Taking risks & driving the P2 seat

« on: May 27, 2012, 09:49:50 pm »

Liked the article.

My preferred example for the "p2 likes variance, p1 likes certainty" is the following game:

First to 43 points wins. Each player has two available strategies:

-Safe: 43 points in 20 turns, no matter what
-Risky: 10% chance of getting 43 points in 15 turns, 90% chance of self-destructing and never getting 43 points.

p1 will always play the safe strategy, and p2 the risky one.

As for the domi example:

Governor (5/2 as p1) vs Smuggler (3/4 as p2)?

I'm not sure to what extent this proves the point, or just my failure at using the simulator, but I hope it makes sense.

32

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

« on: May 23, 2012, 03:59:22 pm »

Dear Schtroumpf, I am sorry you thought I was a novice who only had a lucky draw. throneroom/feast is indeed a thing that can turn around a game. Though, so is opening throneroom/swindler and hitting my opening 5 card on T5.

That was a bit of a rollercoaster.

Opened Throne Room/Swindler...
They missed the reshuffle...
Together!
Hitting Copper/Cartographer!

Agreed, it was a randomfest. Which called for non-linear thinking. Throne room/Feast was the only way to get something vaguely resembling buying power.

If he had opened correctly and hit 6 early, the game would have been over.

33

Game Reports / Re: The WW Makes an Engine Collection

« on: May 20, 2012, 12:45:02 am »

http://councilroom.com/game?game_id=game-20120518-073338-9c446eaa.html

My opponent goes for a respectable Monument/money strategy, augmenting with a margrave and bank, and a couple walled villages (the second of these must be a mistake....?), with some islands. I use some upgrades for light trashing, margrave gives me cards, a few villages, LOTS of monuments, and ALL the throne rooms. Get a big 37 point hand to end it, but I could have gone on building, and, because of the monuments, scoring, while sticking my opponent to 3 card hands, for quite a while if necessary.
So a big thing here is that, well first of all, VP chips make the world go 'round, but secondly, throne room - you don't really need actions with it, if you can get big card draw and a big mass of throne rooms. A little bit of actions is going to help though, especially letting you get there.

Nice!

I tend to underestimate just how effective margrave-based engines are, so it's nice to see another good example.

34

Game Reports / Re: another round of province tennis

« on: May 18, 2012, 11:18:27 pm »

All my comments are in complete hindsight: in real life I would have done the opening and then just improvised.

But I think you want to open amb/quarry. if amb/silver/amb is competitive, then so should amb/quarry/amb. And the thing is, that early quarry should give you a big early economy boost. Hopefully that will allow you to grab a bazaar (or at least a spice merchant). In any event, it should really help you win the bazaar race, which sounds important (though not enough, as the log shows). But being able to grab stuff while ambing/bishopping via quarry even makes me wonder if you don't want two (they also help for getting possession)

Long term, go heavy on bishop, attempting a golden-deck with a potential possession splash, depending on how the trashing works. Go heavy on possession if the other player goes BM. Race for golden deck if he goes bishop.

35

Help! / Re: WW needs help - how does Marin do it?

« on: May 18, 2012, 06:09:26 pm »

Apparently Marin's voodoo powers extend outside of isotropic... Festival/Watchtower, now there's an engine, Festival/Moat is just ... spinning your wheels...

You have 6 alchemists. That means you start with a 12 card hand. You have 20$ total in your deck, spread over 30 cards (25 on T16). That means that, without other drawers, your average alchemist hand will be 10$ (12$ on T16) if you keep up the loop (which is not guaranteed with 12cards/24).

Marin has 48$ over 40 cards (30 on T16), of which 11 are 'cantrips' (assuming moat/festival pair as 2 markets) and 3 labs. That means just a 10$ hand on average (13$ on T16).

So as long as your loop does not break, you have an edge. The moment it breaks, he has an edge. Marin doesn't need a loop to function, though the alchemist bonus can sometimes provide a boost.

So he has limited downside, you have limited upside. Non-linear bets are hard to value, and going for the 'typical' scenario tricky. The simulator can probably tell you what the probability of your loop collapsing is.

My quick computation is 17/19 * 16/18 *... *6/8 = 0.123 for not drawing 2 potions amongst the 19 non-alchemist cards, assuming you play all 6 alchemists. The half-life of your loop is around 5 turns.

Your turn 16 had a probability of roughly 20% to happen at exactly that turn, given the initial hand.

I agree moat/festival is no engine. But then, neither are 6 alchemists with one plat in a 25 card deck. The way I visualize this, your probability distribution has some probability p of producing a steady flow of money, and q of fizzling (because of low moneyness). His just produces on average 10ish dollars a turn, with more 'gaussian' swings around this mean. His variance is high, but because of the number of buys he has he can make more out of the higher numbers (though not hitting 11/8 will hurt).

36

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

« on: May 18, 2012, 05:05:41 pm »

Feature request:

Change ending condition (and victory condition).

In particular, first deck to gain a specific card (plat, follower), who 'wins' the split of a certain card (fool's gold, peddler, curse), first to reach a certain hand (KC/Bridge, KC/KC/card drawer, KC/possession) or deck size (golden deck).

The point is to simplify simulations. Endgames are hard to code for some games, but often the first step to a complicated kingdom is to be the first to reach a certain important benchmark. It doesn't always guarantee victory, but the simulation would help find out 'which strategy gets there faster', or even just the expected number of turns versus a different strategy. After that you assume the human player knows how to take advantage of his edge.

37

Help! / Re: WW needs help - how does Marin do it?

« on: May 18, 2012, 11:25:27 am »

meh, maybe I'm just irked by the fact that a top player actually thinks a 1-card strategy is fundamentally better than a 3 card one. I can't say for sure what Marin's plays did to his winning probability (in both possible directions), but he definitely tried to adapt and squeeze out what he could.

I don't know why that irks you. It's very often true. BM Wharf is better than thief-transmute-counting house. Now, the three cards here actually have some synergy to work together. But it look at festival-moat. It gives you... 2 money, no net cards, no net actions, a buy. Alchemist gives you a card, no money, no buys. So the festival moat is a little better, except... it's a little harder to get? And more importantly, you need to draw them together. Not 100% sure which is 'right'.
By the way, it seems to me that one of Marin's best skills is coming up with exotic combinations that make you say "WHAT?" but which aren't actually bad at all. And always engines.

Oh, I agree, most kingdoms favor streamlined strategies. Quite often, the best strategy is a well-known 2-card strategy, though just as often, it's one of the best strategy, and just happens to be more often rehearsed. I am still unsure whether Veto helps or hinders the phenomenon.

I just think that, if the positions had been reversed and Geronimo had had Marin's initial draw and gone alchemist with a silver down, the game would not have been worth posting.

I completely agree with the festival/moat vs alchemist analysis. festival/moat is a bit better than alchemist (also cheaper and makes you use up every single drop of money), but alchemist has definitely the more stable average scenario. On the flip side, it has a lot more lower tail, as shown in the game. Difficult call, and interesting game.


edit: @Voltgoss: I still wouldn't play festival/moat without upgrade/alchemists to support it .

38

Help! / Re: WW needs help - how does Marin do it?

« on: May 18, 2012, 10:55:30 am »

Played a game yesterday against Marin. He went for a silly Festival/Moat engine while I went for a more standard Alchemist deck. All was going more or less according to plan and then my 2 Potions decide to hide on the bottom of my deck turn 16. I completely tilted and trashed them in the next turn which very likely cost me the (easy) game.

I guess he really has some kind of voodoo power

The way I read the start of the game, Marin adapted well to 'awkward' draws (T3 would you have bought potion with 5$?, T4 he does not trigger reschuffle to not skip his upgrade and moat). I agree that alchemist is the stronger engine, but how would you have reacted to Marin's hands? I think he just wanted to add festivals/moats to an alchemist deck that was trailing behind, because his initial draw did not favor him going head-first into alchemist arms-race. Also, alchemist does help moats connect with festivals, making it very likely that each festival/moat is basically a market. A plethora of festivals allows him to squeeze out every single dollar out of each hand (Your $/hand graphs are identical up to T16, and you don't use all of it). He ended up losing the alchemist race badly (T11 maybe trash silver=>potion instead of copper?) but his deck had a lot more money in total, with all those virtual markets and the the two plats. This gave him an edge in the greening phase. Now of course, the potion draws on your side did not help, and you probably had a higher chance of winning (imo, mostly caused by the first reschuffle) in the 'average' outcome.

meh, maybe I'm just irked by the fact that a top player actually thinks a 1-card strategy is fundamentally better than a 3 card one. I can't say for sure what Marin's plays did to his winning probability (in both possible directions), but he definitely tried to adapt and squeeze out what he could.

39

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

« on: May 14, 2012, 10:30:12 am »

Dear Schtroumpf, I am sorry you thought I was a novice who only had a lucky draw. throneroom/feast is indeed a thing that can turn around a game. Though, so is opening throneroom/swindler and hitting my opening 5 card on T5.

40

Game Reports / Two refreshing games

« on: May 14, 2012, 09:57:16 am »

One where I get trounced at the only BM strategy I enjoy: trader.  I thought it was the standard trader/gardens pool. Saw the scheme/peddler combo (had actually played it a couple of games before), but thought it would put you down too much in the trader/gardens race, failing to foresee Hampuse's brilliant trader on peddler play. I saw all the combo pieces separately, but Hampus saw the big picture.

Now the next game is less impressive, because my opponent just went for a boring alchemist loop, leaving me all the time in the world to do some non-sensical comboing via mint, HoP and KC. I do wonder, however, what the optimal tactics is if both players went for the 'complicated' strategy. Any thoughts?

41

Game Reports / Feast fun.

« on: May 12, 2012, 10:05:54 am »

Gaining feast on feast is fun.

I'm pretty sure I played very far from optimum in terms of tactics, but it was one of those unforgiving strategy games.

42

Simulation / Re: Ranking BM+X terminals

« on: May 11, 2012, 08:42:33 am »

Haggler?

Though the lack of 4 will hurt it a lot.

43

Game Reports / Re: Unusual HP vs Crossroad/Vault opening

« on: May 09, 2012, 09:57:06 am »

The simulation messes up the simulation by totally misplaying the HP against the vault. Having said that, Vault may well be the way to go here.

True!  Somehow, it seemed obvious to me that vault-reactions were misplayed against crossroad, but I oversaw HP (again xD).

44

Game Reports / Re: Unusual HP vs Crossroad/Vault opening

« on: May 09, 2012, 08:34:40 am »

I'm pretty sure quarry/horse trader does that pretty systematically.

The thing is, once you have 2-3 HPs, they will make it increasingly likely you get the quarry/HT combo, which makes for a double HP turn.

Of course, nothing prevents your opponent from trying the same. But the point is, if he has a structural advantage in not doing so (mostly opening/first shuffle outcome), then yes.

Unless you think he should have contested the HPs instead of buying province? Even then, you could imagine my combo triggering before T8 (it had a 50% chance of happening T6 onwards...). I could have had 9 HPs by T10 (but instead went for a fairground and 8 HP). I am pretty sure the average is T9 for 8 HPs. (edit: ok, maybe I was a bit optimistic. hitting 3$ is pretty bad: examples 8@T9, 8@T11, 8+province@T13, 9@T10, 9@T11. Mind you, in my game, the vault helped me on T5, which probably lowers the average turn to T10?).

edit: quick simulations using barely modified versions of the optimized vault and HP bots.

Vault-Xroad outperforms regular Vault against a non-vault player (80-16 instread of 76-19 against BMU). Unfortunately, the simulator makes the Vault-Xroad player discard greens on other player's vaults, even if an Xroad is in hand, making a direct comparison somewhat meaningless (the numbers are 46-49 in favor of regular vault).

Now Vault-Xroad outperforms HP-HT 51-44 assuming no p1/p2 bias (but 5/2 vs 4/3). It turns into 74-20 with the p1 bias (which is ridiculously fast). I obviously did not code my fairgrounds thing... but my point is that me playing regular HP/HT was not an option... unless p1 wasted his early 8$ hands contesting HPs, in which case I don't *need* 8 HPs, as I can now race provinces and be competitive.

And again in the second case, HP/HT is pretty well hurt by the anti-vault play rules - discards way too often.
I don't understand how opponent is getting a significant number of $8 hands before HPs are run out, if you're running them so fast. Indeed, in my experience, in these kinds of matchups, early in the game, $8 and 2 buys should be HP+silver. Now, I understand that Quarry/HT/HP is going to be pretty darn fast at picking HPs up. And sometimes, it will get you an 8/2 split, or better, I just don't see you doing that reliably against a HT/HP player, who after all is going for lots of HPs as well, with reasonably good chances of getting them. Heck, there's a pretty good chance he has 2 before the 2nd reshuffle...

Edit: That's a 27.2% chance: http://forum.dominionstrategy.com/index.php?topic=30.msg265#msg265

Absolutely correct! But again, in this particular case, my opponent opened 5/2 as p1, so he can't open HT/silver. Now he could open HP/Xroad, but I am pretty convinced vault/Xroad is the better option... at least against HP/HT, given that it gives him a 74-20 edge. Now, in a HP/HT mirror match, I would not go so aggressively for HPs, but rather buy gold+HP (something that's easy to do with quarry) the first time, then probably province+HP or maybe just stick to regular HP/HT according to first reschuffle luck.

The reason for the p1 advantage of vault/crossroad is pretty easy to see, both on the log and when you click a few sample games of the simulator. Vault/crossroads lacks +buy, and often overshoots the 5$ mark. Not only that, but it hits early 8s *extremely often* (Xroad+2estates draw into vault + silver), and greens much more aggressively than other strategies (both because of vault and Xroad). This forces an HP player to buy duchies, which in turn slows down his engine. In the game log I gave you, my opponent has Xroad,Vault,silver,gold,province,remake,province as his first buys).

Unless I've messed up my simulation, Vault/Xroad is the way to go for a p1 opening 5/2... and HP/HT just loses the province race very badly.

45

Game Reports / Re: Unusual HP vs Crossroad/Vault opening

« on: May 08, 2012, 09:47:35 pm »

I'm pretty sure quarry/horse trader does that pretty systematically.

The thing is, once you have 2-3 HPs, they will make it increasingly likely you get the quarry/HT combo, which makes for a double HP turn.

Of course, nothing prevents your opponent from trying the same. But the point is, if he has a structural advantage in not doing so (mostly opening/first shuffle outcome), then yes.

Unless you think he should have contested the HPs instead of buying province? Even then, you could imagine my combo triggering before T8 (it had a 50% chance of happening T6 onwards...). I could have had 9 HPs by T10 (but instead went for a fairground and 8 HP). I am pretty sure the average is T9 for 8 HPs. (edit: ok, maybe I was a bit optimistic. hitting 3$ is pretty bad: examples 8@T9, 8@T11, 8+province@T13, 9@T10, 9@T11. Mind you, in my game, the vault helped me on T5, which probably lowers the average turn to T10?).

edit: quick simulations using barely modified versions of the optimized vault and HP bots.

Vault-Xroad outperforms regular Vault against a non-vault player (80-16 instread of 76-19 against BMU). Unfortunately, the simulator makes the Vault-Xroad player discard greens on other player's vaults, even if an Xroad is in hand, making a direct comparison somewhat meaningless (the numbers are 46-49 in favor of regular vault).

Now Vault-Xroad outperforms HP-HT 51-44 assuming no p1/p2 bias (but 5/2 vs 4/3). It turns into 74-20 with the p1 bias (which is ridiculously fast). I obviously did not code my fairgrounds thing... but my point is that me playing regular HP/HT was not an option... unless p1 wasted his early 8$ hands contesting HPs, in which case I don't *need* 8 HPs, as I can now race provinces and be competitive.

46

Game Reports / Re: Unusual HP vs Crossroad/Vault opening

« on: May 08, 2012, 08:49:46 pm »

Interesting…I haven't seen Hunting Party used successfully in a deck with that kind of variety before. Very cool game!

If your deck has plenty of variety, than Hunting Party is merely as good as Laboratory.

Actually, most HP intuition is built on the usual 2-card archetype: HP-terminal-(gold-silver-copper). In that setup, you only need 4-5 HPs to nearly deterministically draw your whole deck. Buying any more usually means falling behind on the province race.

But in this case, Quarry/Horse trader *invites* you to go heavier on the HP, at the expense of losing the province race. Now, the first thing I noticed in playing an 8 HP deck (and which is a crucial point in favor of *some* diversity) is how much you waste HPs if you don't have enough deck diversity. Now, this runs very much against the classic intuition of the HP engine, but it truly means the following: the classic HP engine *only* makes a province a turn, and often ends up not playing all its HPs (or at least, they don't do much more than trigger a reschuffle) for lack of appropriate target. In this game, I was careful to balance enough diversity into the mix to *almost* draw my whole deck systematically (again, crossroad helped a lot), allowing me a few turns at more than just one green. Of course, the fact that the deck-diversity also boosted the fairgrounds at the end was what pushed the deck over the top. But I avoided reaching 15 differently named cards *too early*, and grabbed some extra crossroads before that.

Agreed, it's a lot messier than the elegant 2-card deterministic HP-terminal combo (or the super-fast crossroad/vault: by the second reschuffle, my opponent had grabbed a gold and a province!) but I think it's worth exploring those strategies.

47

Dominion Articles / Re: Request: Farmland

« on: May 08, 2012, 02:37:03 pm »

Let's not forget farmland+border village.

Just grab your favorite 5 with border village, then use the border village as fodder for farmland.

48

Game Reports / Unusual HP vs Crossroad/Vault opening

« on: May 07, 2012, 09:38:33 pm »

http://dominion.isotropic.org/gamelog/201205/07/game-20120507-081505-520e44c9.html

Crossroad/Vault as p1 was going to be hard to beat. Luckily, the board allowed for a nice quarry/horse trader interaction, although I pulled off the combo very late (T8), considering the presence of HP to accelerate the collision. Because of that, I was far too behind on the province race and had to look for alternative greening, leading to a weird HP deck that, despite 8 HPs, did not systematically draw itself every turn (but Crossroad helped). The transition from perfect (but vp-wise behind) HP engine to messy HP/XRoad/fairgrounds deck was fun to play, and I think, unexpected by my opponent.

49

Simulation / Challenge: asymmetric p1/p2 equilibrium

« on: May 05, 2012, 02:44:50 pm »

I want to ask you simulators out there if there are striking examples of simulation bots where the optimal strategy for p1 and p2 differ notably. My intuition tells me that p1 should opt for a low variance strategy, while p2 should aim for a high variance one, and that the game is probably very short.

So far, my first quick attempt is the following:

Set the first players to open with Governor/duchess and goes through the standard Governoring, finishing the game on average within 15 turns:

Code: [Select]

<player name="Governor 5/2"
 author="Empathy"
 description="A very strong p1 opening.">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
  <start_state>
    <hand contents="2 Copper, 3 Estate"/>
    <discard contents=""/>
    <drawdeck contents="5 Copper" shuffle="false"/>
  </start_state>
   <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="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Governor" strategy="GoldEarlyTrashMid"/>
   <buy name="Silver"/>
   <buy name="Duchess">
      <condition>
         <left type="countCardsInDeck" attribute="Duchess"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
</player>

Now if p2 tries to catch up using his own governor deck,

Code: [Select]



<player name="Governor"
 author="Empathy"
 description="A strategy traying to catch up to an early governor opening.">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="UserCreated"/>
 <type name="BigMoney"/>
 <type name="Generated"/>
   <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="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="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Governor" strategy="GoldEarlyTrashMid"/>
   <buy name="Silver"/>
</player>
He loses 58-37. Note that, in both cases, the optimal Governor policy is "GoldEarlyTrashMid". Also, buying governors over Gold is optimal for p1, but not p2 (which kinda makes sense). The average game takes 15 turns.

Now consider the following smuggler bot:

Code: [Select]

<player name="smugglers counter"
 author="Empathy"
 description="A smuggler-based counter to the strong p1 opening. Note that it plays the governors much more aggressively!">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
   <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="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Governor"/>
   <buy name="Smugglers">
      <condition>
         <left type="countCardsInDeck" attribute="Smugglers"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>
It actually nearly ties with the insanely fast governor 5/2 opening: 49-45! Note that the optimal governing policy for this bot is "Standard", but the optimal policy for the first player is still "GoldEarlyTrashMid" (it actually loses otherwise). The average game lasts 14.5 turns

Did I make a blatant mistake in the p1 bot (a "garbage in, garbage out" type thing)? Can other such situations be simulated?

50

Dominion Articles / Re: Thoughts on Strategy vs Skill

« on: May 05, 2012, 07:58:40 am »

I prefer the term tactics to skill like previous posters.

The problem with the messy strategies is that you probably came up with them when you started the game and your tactics implementing the strategy are going to be poor which will lower your win rate vs a proven strategy with easy tactics. Take the Talisman, Feast, City example. The strategy isn't bad because you will be able to empty 2 piles quickly thanks to Talisman/Feast, but buying Cities before the Feast pile was empty slowed the strategy down and figuring this out on the spot is going to be impossible unless you have a very deep understanding of the game already.

I'll edit Skill into tactics then. Thanks for the feedback.

I agree that messy strategies are harder from a tactical point of view: you often just have less experience playing them for the simple and easy reason that they don't repeat themselves that often! They are still worth exploring imo, though I'll be the first to admit that my tactics skills are severely lacking for my rank. For that specific game, I clearly did not do well in terms of buy decisions: there is definitely one crucial 3$+2talisman turn where buying feast over city would have been optimal (I think my fear was to have too many terminals, but buying village instead of silver would have fixed that).