Follow-up to Sample Game Planning

How about I kick off your working/studying/playing-dominion week with a few cool graphs and clever observations? I kind of had to after reading timchen’s request to simulate DG’s and Yaron’s game in the comments (you see, we at dominionstrategy really care for our readers…).  Let’s recap the game in question:

Yaron chose a pretty straightforward strategy of Masquerade into bigger and bigger money into Provinces, sprinkled lightly with a few Caravans. His opponent DG had a slightly different approach by going for the Remodel into Coppersmith/Caravans into big money and finally Provinces.

Simulating Yaron’s playing style was easy, because non of his cards involve difficult decisions. DG’s Remodel and Haven on the other hand gave my poor simulator fits. It kept making silly mistakes like Remodeling the wrong card at the right time and Havening away the right card at the wrong time. I’m not making much sense here, but hold on, the serious strategy is coming. Haven is an innocuous little card, but explaining to a computer how to set up future turns is a really hard thing to accomplish. As most of you will know even the crunchiest of number crunchers is dumber than the dumbest animal on this planet (google told me it’s a turkey):So unfortunately I wasn’t able to fully simulate DG and Yaron’s game. But seeing how a Coppersmith/Caravan and Masquerade/Caravan strategy match up should still prove interesting so here goes:

On with the games… a few thousand

Here are Yaron’s buy rules: Open with Masquerade/Caravan, buy Province if you have Gold, buy Duchy when there are 4 or less Provinces left in the supply, buy Estate when there is 1 Provinces left in the supply, buy Gold, Caravan and Silvers when you can.

DG’s buy rules are quite similar except for the opening (Coppersmith/Silver) and buying Duchies a little earlier (when there are 5 Provinces left in the supply). (These are the buy rules after optimising)

Here’s the delta-VP graph (which shows the average amount of Victory points gained each turn):

And here are the winning percentages (the ties bar shows how many games where tied):

So Yaron’s Masquerade strategy beats the basic Coppersmith/Caravan which shouldn’t be too surprising (just check out councilroom). This still doesn’t tell us if DG’s Remodel will tip the game in his favor, but I have a feeling it might not. DG is playing a “big money”-strategy and doesn’t really use his Remodel to build an engine, but rather cycle his deck a little faster (buy turning Estates into Caravans) and as an aid to win the late game race for Victory Points. As I’ve noticed from my simulations, trashing will only help “big money” strategies out a little or not at all:

Loan and Lookout are really terrible and will actually hurt you when you’re a Gold digger. Chapel will give a slight edge against an opponent who only buys treasures. Masquerade is a whole different story, but that’s because its draw-2 effect is very significant:

Remodel is a not a fast trasher like Chapel and doesn’t have any other direct benefits like Masquerade, so I’m guessing it will not have a big influence on your big money deck’s win rate. If you’re trying to build a real engine, it’s a completely different story! Take this solitaire game I played as an example: I built an engine to get to that one big turn where I played multiple Coppersmiths and bought 6 Provinces on turn 13. This would be impossible to achieve without the Remodels!

Skipping the Caravans

Although we’re just guessing at how good DG’s strategy was, we can try to improve Yaron’s. Here’s what happens when we don’t let him buy Caravans (just the one Masquerade and money):

Not jumping onto the Caravan results in a +15% win rate. This shows Masquerade’s similarity to Envoy which also hates to see other Action Cards in the same deck.

So why is it that one of the best players in this game (hello Yaron!) makes such an obvious mistake of buying extra action cards with his Masquerade? Is it because Caravan is such a sexy card: it’s got a different color than most cards, it gives you that adrenaline rush of drawing a card, not once but twice. And maybe most importantly it makes your starting hands bigger.  This might be a male thing: look, mine’s bigger than yours. Which brings me to something I’ve been wondering about. Is Dominion a game played mainly by guys? Please enlighten us and yourselves in this poll:

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38 Responses to Follow-up to Sample Game Planning

  1. Personman says:

    The whole premise about Remodel here seems totally wrong. Remodel doesn’t help you win by trashing cards, it helps you win by turning your Golds and Provinces into Provinces! I do think Masquerade is a fabulous card, and some brief, anecdotal testing shows that it might end up being a little faster than Remodel in a vacuum, but not by much, and the ability of Remodel to control the tempo of the endgame by turning Provinces into Provinces is something that can’t really show through in solitaire testing.

  2. Praion says:

    I’m male but i play mostly with my girlfriend and other female friends of ours.

  3. Stephen says:

    Remodeling a Estate into a Caravan is probably much better than using Lookout or Loan to trash: not only are you getting rid of a bad card but you get a good card in return, as Caravan is one of those things that you generally never mind having more of. It also has endgame tricks (whereas lookout is kind of dead in the endgame), as Personman said above, but I can see how it’d be hard to program those into the simulator.

  4. DG says:

    Perhaps you could explain a little more how these numbers are arrived at. Your graphs show 17 turns as an average game length but the remodel/caravan/coppersmith strategy will bring in 4 provinces in 13 turns fairly reliably (with a range of 11-14 turns). It’s a flimsy deck so perhaps you are taking games into a duchy race where it chokes horribly and that’s not how the deck should be played. Perhaps you are buying too much silver and gold, not making good decisions for remodels, or more likely using the havens on the wrong cards. The decisions provided by the havens are important in setting up a coppersmith turn followed by a remodel turn and I have some sympathy for anyone trying to set up decision rules in advance of seeing an exact hand.

    • Geronimoo says:

      Perhaps I didn’t state it clearly enough, but I wasn’t able to simulate your entire strategy because Remodel and Haven proved too difficult to implement properly. So I simulated a light version of your strategy which just buys Coppersmiths and Caravans as action cards and no Remodels or Havens. I realize this is far from how you played in the actual game, but I also think you’re overrating the average winning turn of your strategy. Playing solitaire games and seeing how fast you get to 4 Provinces doesn’t always correspond to how an actual game will play out.
      The simulations do end up in Duchie-dancing quite often which lets the average game length go up a lot, but when you don’t allow that behaviour, the win rate drops!

    • DG says:

      Apologies, having read the piece again I’ll accept that the remodel and haven choices gave the simulator a bad day at the office. I wouldn’t want to be writing a script for these choices.

      • Mean Mr Mustard says:

        Personally I don’t pay too much heed to simulators; there are circumstances where a single action deck may be best but simulators cannot replicate the play-by-play choices a competent player has to make. Are caravans poisonous to an envoy or masq strategy? Sometimes, sure. Or rather some turns, sure. A simulator would have to be well programmed indeed to understand the distinction of whether it is a good idea to draw dead cards blindly or not. I have never toyed with one mainly because the read-ups I have seen have failed to impress me. They usually devolve into big money strategies which are really no longer viable accept against very poor players. I fail to see why it is useful to know that the simulated results of one card and big money vs a different single card and big money means much at all.

        CR.com’s tools are way more useful to me in understanding the relative power of cards. Comparing my results against the whole community or single good players is a hell of a lot more useful.

        IMO.

        • Death to Sea Hags says:

          I agree in part, but I’m becoming more aware of the deficiencies in drawing conclusions from CR’s data.

          Most obviously, I think they *overstate* the importance of a few cards that are consistently underrated by newbies. Ambassador is great – but so is Caravan. But every new player can see the obvious benefits of Caravan, and therefore buys it – so winners and losers both always buy it, driving its win rate to 50%. Ambassador is skipped by a lot of new players, who then lose to it – pushing the win rate up, above where we should expect it to be for skilled players. The corollary is that whatever cards these new players ARE opening with are having their win rates depressed, at least relative to an expected win rate in the hands of a skilled player.

          But once you learn not to overlook those cards (which doesn’t take long), then what? I think we’re just not to the point yet where the data can offer any further help to good players in terms of evaluating cards or strategies.

          • Kazz says:

            I’d love to see CR options that only look at games between players with a few dozen games under their belts.

          • Mean Mr Mustard says:

            Yes, I totally agree. We may all sift the data differently or perhaps not. There are obviously excellent cards that fall in the middle range. We mostly recognize them. My point is that knowing that I win way more often when I avoid a sexy-looking card like Venture is more valuable to me than anything I have learned from simulation posts.

            • rrenaud says:

              Code contributions welcome😉.

              I generally dislike trying to slice data by a zillion different factors because it leads to a combinatoral explosion in the amount of time/space needed to track it all. But I guess player skill levels and #players per game are both worth trying.

  5. timchen says:

    I have to say thanks for the simulation.

    Nevertheless, a large part of what I wanted to see is still absent.😛 I have no choice but to play a little bit solitaire myself.

    Maybe I can propose the following buy rule:

    open Remodel+Silver (or haven).

    Buy Haven when you have $3.
    Buy Caravan when you have $4,
    Coppersmith when you have exactly 2 caravan and 0 coppersmith
    Buy Gold when you have $6.

    In the action phase, play caravans first. Then play Haven.
    Haven away:
    coppersmith (if you have $8) or (if you have both remodel and estate in hand) or (after playing coppersmith you still don’t have $8 and you have less than 3 coppers in hand);
    estate (if you have no remodel in hand);
    remodel (if you have coppersmith in hand and no estate);(if neither estate nor gold is in hand);
    Gold/Silver (if you have $8 without this card; if you have $8 after coppersmith without this card)
    Copper (if you have no coppersmith in hand)

    Play rule: Remodel>Coppersmith
    (i) estate-> caravan/coppersmith according to the rule above.
    (ii) gold->province.

    %note this is probably far from optimal, but seems closely enough to how I play.

    First is the question of how fast can this get to 4 provinces. Then we can see how it fares against various strategies.

    • timchen says:

      I cannot say I followed the rule 100% but I tried…
      in 10 games I always have 4 provinces in 14 turns. maybe half are 14 turns, and others are distributed rather evenly between 13, 12, 11.

    • timchen says:

      It seems however, that skip the coppersmith entirely in this strategy actually performs similarly (if not better.) Open Silver+Remodel, getting havens at $2 or $3, caravan at $4, gold at $6 seems to reach 4 provinces at turn 12 or 13.

  6. John_O says:

    My girlfriend played about 750 games on isotropic and a ton of games with the real cards, compared to the 150 games i played on iso. But she doesn’t read this blog – i guess i’m the more analytically minded of the two of us.

  7. Kirkq says:

    I’m a bit curious how opening 3/4 double masquerade weighs in against opening masquerade silver. (When only buying money afterward.)

    • Geronimoo says:

      Double Masquerade 38% Single Masquerade 54%

    • Last Footnote says:

      I often open with Masquerade/Silver, but then buy another Masquerade on my second shuffle. I wonder how that stacks up.

      • Geronimoo says:

        If you have 6 Golds simulations point out it’s better to buy the second Masquerade rather than Silver…. Not sooner!

        • Last Footnote says:

          Uh, at that point you’re better off buying some other +Cards card if it exists. Chances are you’ve done all the trashing you need to by then.

      • Arya Stark says:

        I open up with 2 masqs sometimes, it works out good as long as you dont get both in hand on the 3 turn

  8. caesuric says:

    I’m sure you’ve thought of this, but it’s worth noting that a sample of those who read this blog is not necessarily similar to a sample of who plays Dominion. Around half of the people I play Dominion with IRL are female, but I can almost guarantee you that none of the people I play physical Dominion with would go within a mile of this blog, or any theory blog for a card/board game.

    • theory says:

      Well, if it’s something we’re doing wrong, do let us know🙂

      • caesuric says:

        Oh no, obviously not. Polls can only get a sample of whoever’s present at your site. I was just pointing out the the literally parsed question ” Is Dominion a game played mainly by guys?” can’t necessarily be answered correctly here.

    • Arya Stark says:

      i just like to read the comments, graphs and the popular buys on councilroom is boring to me

  9. WanderingWinder says:

    One thing about these simulations that I think could improve the win percentage on every one, something that really good human players do which I’m fairly sure you don’t, is to pay attention to where your reshuffle is. I will buy different things based on the reshuffle. This comes up most in the endgame – do I want another gold, or a duchy? I ask myself a few questions – how much money do I have in my deck, how many VPs do I have in comparison to to my opponent, how many provinces (colonies) are left, and how close am I to a reshuffle? If I’m about to reshuffle, I’m more likely to buy the money. If I’ve just reshuffled, I am more likely to buy the VP; sometimes I’ll even grab an estate on 4 with like 3 prov left just because I’m pretty sure it isn’t going to come back to my next reshuffle.

    • cpflames says:

      I might not ask myself all of those questions, but I at least ask “will the game end before my next reshuffle”. That might be something that could be programmed into a simulator, but it would require the simulator having a sense of how the game will end (on colonies? on provinces? on piles? which piles?) and how many turns will happen before reshuffle (which will vary wildly based on whether players are using card-drawing engines or not) and how much money the players will pull on those turns, and whether they will employ the PPR or not…

      On second thought, this probably goes on the long list of incredibly daunting tasks that make a true Dominion AI highly unlikely to happen.

    • WanderingWinder says:

      One other thing about reshuffle is whether or not to play a card-drawer. If I have 8, I’m probably just going to not play that smithy I have in my hand if I’m close to reshuffling, but I’m much more likely if I’ve just reshuffled (I want to get back around to reshuffling those golds into my deck). The reshuffle also may dictate whether I play a drawer or a different action, say smithy against militia (though I can’t think I’d have both of those in my deck at the same time).

  10. Anonymous says:

    I also play with a lot of girls… the poll isn’t so much about do guys or girls play Dominion, as it is about who’s lame enough to read a blog dedicated to statistical analysis of a card game…. guys.

  11. vidicate says:

    Ha ha ha! It took me a whole week of this being the top article on the blog to see the pun in that cartoon. I almost laughed out loud in school. <— (this is sad)
    I wonder if others missed it as well.

  12. Anonymous says:

    When does theory get back?

  13. mwfeldman says:

    didn’t want that to be anonymous. so… congrats and hurry please🙂

  14. SleeplessDemelza says:

    Hmmm, aside from the two intentionally ridiculous answers to your poll about gender and Dominion-playing, your poll is skewed due to one very crucial reason: while there are plenty of female Dominion players on Isotropic’s fine site, I believe more males than females read gaming strategy websites. So naturally more men than women will show up on your poll. (Maybe I’m wrong…after all, I’m a lady, and I’m reading the strategy website…but i admit that my eyes glaze over and I skip all the statistics and graphs.)

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