Simulation Challenge: Dominant Strategy

Hiatus! I didn’t want to let folks down because theory thinks he needs to study, so here is some light content:

Theory and I played a series of epic games a few weeks back, some of which will probably get written up while he is “studying”.

The least interesting of these was http://councilroom.com/game?game_id=game-20110408-191900-6a229632.html.

<img class="size-full wp-image-1898" title="dominant-strategy" src="https://dominionstrategy.files.wordpress.com/2011/04/dominant-strategy.png" alt="cards in supply: Chancellor, Envoy, Lighthouse, Mining Village, Native Village, Secret Chamber, Treasure Map, Treasury, Upgrade, and Village” width=”640″ height=”404″ />

(Click for enlarged link at dominiondeck.com)

In this game, theory was upset that he drew a 5/2.  I sized up the board, and then executed one of the most boring strategies, coined as “Grand Envoy” (or Single Envoy Big Money if you prefer more specific names)

This strategy (with the goofiness of theories Penultimate Province Rule removed for readability) can be summarized as follows:

Do I have an Envoy?  Play it.  Opponent discards highest treasure.
Do I have 8 and at least 1 gold?  Buy Province
Do I have 5 AND the game is somewhere around half over (provinces <= 5ish) ? Buy Duchy
Do I have 2 AND the game is really over AND it might make a difference? Buy Estate
Do I have 6?  Buy Gold
Do I have 4 and No Envoy's? Buy an Envoy
Do I have 3? Buy Silver
Do Nothing

It was a predictably fast boring match… over in 14 turns, although theory didn’t even try to stretch the game out with duchy dancing. I had 5 golds by turn 8, and then it was province x2, gold, province x2, duchy, province. Theory tried treasure maps, hit them, but even by then I already had more gold.

I honestly don’t enjoy playing this way, but because because it was a ranked match with theory, I couldn’t really afford to experiment (see this match with yaron for an example where experimentation with bad cards failed in epic fashion)

Afterwards, in our typical debrief, we went though the logs to see what we could learn from this experience. Our gut feel was that there really weren’t alot of options here, especially for theory sitting on 5/2.

Possibilities:

  •  Treasury is usually a slow engine card… very useful if you want to repeatedly buy mid cost cards to build up your engine.  Not great if you need to be green card rushing because your opponent will buy 5 provinces by turn 14.
  •  Upgrade / Nothing looks like it might be slightly stronger than Native Village per the opening buy analysis, maybe move into Envoy with the upgrade after.
  •  Treasure Map / Native Village is interesting?
  • Envoy / Nothing is strictly worse than Envoy / Silver, but perhaps the p1 advantage might make up for it?

On the 4/3 side

  • Nothing involving village will work here, the only thing that needs extra actions is Envoy.
  • Treasure Map / Chancellor is a little crazy.  Crazy like a fox perhaps?

Without extra buys, we didn’t see anything that would realistically beat (as defined by win more often)  Grand Envoy.  Unfortunately, I don’t have any fully functional simulators, so I figured I could pose the challenge out to the simulator community…

On this board is Grand Envoy a “Dominant Strategy“?

I’m defining Grand Envoy is defined as any strategy (regardless of parameters) that only buys 1 Envoy, and the rest coins and victory, even if the parameters are slightly different than what I outlined above, as I make no claim to knowing for sure that the optimal parameters are.

It is going to be very difficult (if not impossible) to prove that this strategy is dominant, but it should be possible to demonstrate that it is not, if a strategy can be defined that beats it.

You’ll only get partial credit for winning if the answer is

Do you have 4/3? -> Play Grand Envoy
Otherwise buy Upgrade / Nothing -> Play Grand Envoy, with trashing states into Silvers.

Contact us if you think you have an answer and want to discuss further! Alternatively, discuss how you would play the set in the comments below.

Any ideas on what theory could have done differently besides treasure map desperation? I had luckier than average draws, IIRC Grand Envoy typically has 4 provinces by turn 14, not 5.

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24 Responses to Simulation Challenge: Dominant Strategy

  1. chesskidnate says:

    what about at least upgrade/lighthouse, it probably wont beat grand envoy but it seems like the upgrade deck could use more early cash. Also using upgrade to create a village- envoy deck looks plausible although probably a bit too slow.

    • Zaphod says:

      According to councilroom.com, upgrade/lighthouse is the best opening in this set. However, that’s probably skewed by the number of times it was bought with attack cards in play.

    • Kirian says:

      In a few solitaire games I’m finding 5/2 -> LH/Upgrade/MV trashing to be around as fast as Grand Envoy, i.e. 14-16 turns to get 4 Provinces.

      Since I’m not a simulator runner, I’ll post the base idea in pseudocode here and let someone else figure out if it gets 50%+ win vs Grand Envoy. It can probably also use tweaking, especially the case of having two MVs.


      If Lighthouse in hand, play it.
      If Upgrade in hand:
      If Copper, Estate, or second Upgrade in hand, play it, with priority:
      Estate-->Silver; Copper-->Nothing; Upgrade-->Gold
      If Mining Village in hand, play it:
      If deck contains any Gold:
      If trashing MV would get hand from below $8 to $8, trash it.
      Else
      If trashing MV would get hand from below $6 to $6, trash it.
      If $8:
      If deck contains any Gold, buy Province
      Else buy Gold
      If $5 or more:
      If Province stack <5, buy Duchy
      If $2 or more:
      If Province stack = 1:
      If my score = opponent's score + 6, buy Estate
      If $6 or more, buy Gold
      If $5:
      If deck contains <2 Upgrades, buy Upgrade
      If $4:
      If deck contains <2 Silvers, buy Silver
      Else, buy MV
      If $3, buy Silver
      If $2, buy Lighthouse

      I’ll try it a few more times solitaire; it should be noted that it has the disadvantage of needing an extra Duchy.

    • Kirian says:

      Quick tweak here: If Upgrade is in hand, and you have exactly $8, buy a Province even if other conditions are fulfilled.

      I have doubts that this strategy is dominant, but I think it’s very competitive as a 5/2 opening. I wonder how it does buying Upgrade on $5 with an Envoy/Silver opening…

      • tlloyd says:

        Couple other suggestions:

        – You may want to consider the possibility during the endgame of upgrading a MV to a Duchy. Probably won’t come up that often given your willingness to trash them for the +$2, but the ability to Upgrade into VP while also buying VP is one of the few advantages of your strategy over Envoy+Money with no extra buys.

        – Another unlikely scenario, but it seems from your “code” that you could end up trashing a MV to go from $6 t0 $8 before you had bought a Gold, and therefore would end up buying a Gold for $6 instead of a Province for $8, which makes your trashing the MV a waste.

        • Kirian says:

          Interesting idea with Upgrade/MV, it’d be uncommon but useful in the late game. As to the second, that’s the reason for the “If the deck contains at least a Gold”–don’t trash to go to $8 unless there’s a Gold in the deck.

          For an AI to follow this it’d need some tinkering, and that assumes that any of the simulator types want to take on the challenge.

  2. minced says:

    i can see upgrade/envoy/village coming close to envoy/money because upgrade can create duchies from envoys and villages from estates. The extra duchies might be enough to compensate for envoy/money’s speed.

  3. Momomoto says:

    Spamming Village/Envoy/Upgrade sounds like fun. Just *think* of all the Treasure Maps you could acquire!

  4. DG says:

    I’m not sure if setting insolvable puzzles is a great idea but here’s an obscure solution anyway. You *might* get some play from upgrade/native village, just using the village to shelve starting cards then upgrading the village to a silver with the junk still on the mat. Use a chancellor as the terminal action to cycle, trash as much copper as you can with upgrades, use mining villages for invisible value in the deck or treasure maps if you feel lucky, but get some gold and hope the deck is quick enough to beat the envoy.

  5. novalis says:

    Chancellor/TM does not, by my simulations, win — no matter how hard I jiggle the shuffling rules for chancellor.

  6. novalis says:

    I also can’t get native village/treasure map working better than envoy.

    • captainfrisk says:

      Yeah, Envoy is damn near a guaranteed gold every time you play it. As in my game with theory, I expect that just playing envoy will result in more gold, on average, by the time the treasure maps finally hit.

      • tlloyd says:

        That being said, if you get $5/$2 your best shot may still be to go for broke and get Treasure Maps. You’re still at a disadvantage, but the Treasure Maps give you a shot.

  7. ipofanes says:

    Why did theory pass on turn 9 with 2 Coppers, a Village, and a Native Village in hand? Was he that afraid of drawing only one Treasure Map? That doesn’t make much sense to me.

    • theory says:

      Yes. With that hand I cannot possibly activate Treasure Maps, and if I drew one I was definitely absolutely dead.

      As it turns out, it was the right call, since my next two cards were both Treasure Maps…

    • Matthew Ryan says:

      At turn 9, the sole intent of Theory’s 15-card deck is to get his Treasure Maps together. Village can only get him a single card, which is useful if fishing for a 2nd Treasure Map but harmful if fishing for a 1st. There is nothing he can buy for 3 that would be worth this risk. He might have even passed if he had 3 copper in hand — Silver would just dilute his upcoming Gold.

  8. WanderingWinder says:

    Only thing I can think of (that I think has a reasonable chance (this discludes lighthouse/Envoy) and hasn’t been mentioned yet) is Native Village/Envoy as an alternative, but this is going to be really hard to simulate perfectly, as the decision for Native Village is actually really complicated.

  9. dominionation says:

    i gave a quick shot to the draw heavy style of envoy/village and in my test i had a 4/3 opener and was able to “get there” in 15 turns. mainly i bought an upgrade, and more envoy/village; instead of coin i put in two secret chambers. i believe that starting with a 5/2 would allow you to start upgrade/chamber, which then pumps villages in for the estates and uses the chamber to hit 4 for envoy. all told pretty damn fast since u don’t need any coin, and of course upgrade’s copper destruction allows the user up to 7 “dead” cards without needing to increase the base amount of villages/envoy necessary to combo

  10. Epoch says:

    Is it really the case that Treasury isn’t good in this set with a 5/2 opening? I mean, yes, I understand that it’s better if you want to buy a lot of $5’s, but starting to hit a consistent bonus $1 every turn from turn 3/4 (or 5 if you’re unlucky) up until whenever you start buying greens seems like it’s at least reasonably strong. Not as good as Envoy when Envoy is played, but you get its benefit for probably five-ish straight turns when you’re ramping up your money.

  11. guided says:

    Why are we talking about “/nothing” openings when Lighthouse is on the board? A single Lighthouse is much, much better than nothing.

    I’d open Upgrade/Lighthouse here and feel like I was doing OK. Certainly I wouldn’t curse the fates for giving me 5/2.

    • captainfrisk says:

      Looks like you’re right:

      From The Openings Page:
      2.685 ± 1.492 Treasury / Lighthouse 5/2
      1.211 ± 0.951 Treasury 5/-

      4.702 ± 1.876 Upgrade / Lighthouse 5/2
      2.961 ± 1.027 Upgrade 5/-

      1.722 ± 0.889 4 Envoy / Silver 4/3
      1.427 ± 3.856 Envoy 4/-
      0.927 ± 2.828 Envoy / Lighthouse 4/2

  12. pendog says:

    How lucky was it to get golds on turn 3 and 4 (and 5, 6,7!)? I am running some solitaire games and have not been able to get that.

  13. Geronimoo says:

    According to my simulations you’re screwed if you have a 5/2 opening against a 4/3 on this board. Best result I got was opening Treasury/Lighthouse (34% wins). Upgrade/Lighthouse was 32% wins.

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