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Dominion General Discussion / Re: Strictly Better
« on: June 17, 2019, 06:53:00 pm »
Another thought: is being forced to choose Stash's position in the shuffle strictly better than not having any choice?
Nope, tried that too.Then it seems like an obvious improvement of the strategy to add a rule to buy the LAST flag bearer even if you already have the flag (and maybe even add a penultimate Flag bearer rule?).That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.More specifically, if there are 10 flag bearers, then the player who gets first flag loses 7%/90%. If there are 9 flag bearers, then the player who gets first flag wins 81%/14%.
So yes, the majority of the effect in this case, is who ends up with the flag in the long run.
The last Flag Bearer is much more important than the first when contested, unless the pile isn't emptied before the very end.
I also tried a strategy that opens Flag Bearer, and tries to snag an extra one so that it keeps the flag when the pile is out. This helps, but still worse than not opening Flag Bearer.The best I can do with this strategy is a 15% win rate.
That raises the question: How would the results differ with 9 or 11 Flag Bearers in the kingdom?
It also seems that if either player stops buying Flag Bearers before the pile is out, then that player loses.More specifically, if there are 10 flag bearers, then the player who gets first flag loses 7%/90%. If there are 9 flag bearers, then the player who gets first flag wins 81%/14%.
Why does buying the first Flag Bearer put you at a disadvantage?Once a bots gets the first Flag Bearer, both bots will keep on getting Flag Bearers until they pile. So the bot that got flag first does not actually have the flag more often. And on average, that bot will have more Flag Bearers in their deck (which is bad because of terminal collision). And finally, once the Flag Bearer pile empties, the bot who got the flag first loses it forever.
How strong is adding +Action to Cobbler? Gaining a $4 to the top of your deck is the effect of Armory, a $4 cost action. Drawing a card is the effect of playing a Laboratory from your hand, a $5 cost action. So Cobbler's effect can be thought of as non-terminal Armory + Laboratory. In contrast, getting an extra action is the effect of a Village. So the revision improves Cobbler's effect to that of non-terminal Armory + Laboratory + Village. I also doubt this take on Cobbler would lead to particularly fast 3-piles, because you need two Cobblers to gain one card per turn.The situation I was imagining is, what if Cobbler is the only village, and you really need that village? So you get more Cobblers than you really want, and there go the piles. I mean, it might be interesting, and perhaps not any worse than University. If you test it I'd love to hear about it.
The point of removing Hexes is to reduce the complexity of the cards. With that in mind, Envy and Misery are out. Cursed Village could be worth -1 VP, if that doesn't cause rules confusion. That may be too large a penalty. Leprechaun giving Poverty would make its drawback more severe in decks that draw and want to play it for the Wish than in money-heavy decks that never intend to play it for the Wish. That seems backwards.Misery and Envy are complex? I never would have thought so, not on their own. Anyway, it doesn't seem like you should constrain yourself to copying the hexes exactly. For Leprechaun, you could ignore the "envious" state, and just say "for the rest of this turn, golds give only $1". -1 VP is probably a close-enough approximation of Misery. I doubt that it's too large, given my experience with landmarks like Obelisk.
I have updated the OP considering your comments and labeled it Version 2. Hopefully I have fixed the typos, as well, but please double-check!The updates look excellent.
Still considering adding: Draw Card, Terminal Space, Build, Gainer. (If you would like these added, any suggestions for a good definition?)
Still considering removing: Village Idiot.
I was wondering about that too! I have two hypotheses. First, maybe Wolf Den is just totally overrated. It doesn't affect how you build in any significant way, and mainly you just buy second copies of each card as a substitute for duchies. Second, maybe Wolf Den just as often makes games shorter as it makes them longer. For instance, if you get a second Gold instead of a Duchy, maybe you can use that gold to end the game sooner.I agree with the intro that there are a lot of different metrics you can use to rank most cards, but landmarks have basically just one metric. On that note, let's take a look at Markus' statistics for landmarks!This is interesting, but clearly insufficient: According to those stats, Wolf Den has basically no impact. It does not impact game length or 3-piles, but it clearly forces you to build differently.
I like the idea of looking at change in gain rates, if only because it resembles the "impact factor" analysis I did last year, but I'm not sure how well it would work for landmarks. e.g. how much does Obelisk change gain rates on average? Depending on what Obelisk pile you choose, it might affect the gain rate of that particular pile, but this effect could be washed out when you average over all games.So what do you think? Seems like there's a pretty good case that Keep > Wall, although Wall leads to more games ending on provinces. I also think Tower should be higher, since it apparently causes a 3-pile in about 15% of games.
I like the idea of looking at the stats to determine landmark impact, and I agree with the intuition about game length. For the reasons you mention, though, I think neither length of game nor chance of 3-pile alone summarizes impact well. Combining the two works better, but are there other variables we could measure? Maybe average length of game given a province ending, or given a 3-pile ending. Maybe the chance of first player winning would also be interesting. Skill multiplier might also say something about impact, if we believe that better players are more likely to alter their strategy with the landmark, whereas worse players aren't.
More generally it would be cool to have some kind of aggregate of how much the gain distribution changes in the presence of landmark X. So, total over all cards of the difference between the gain rate of that card with landmark X and the average gain rate for that card.
[Flag Bearer] is the third most gained $4 card overall!From what I can see, it's in 4th, after Tournament, Magpie, and Silk Merchant.
Star Chart is overrated. It should be with Scheme, the two cards do mostly the same thing.I just tried a sim that opens Scheme + Conspirator, and then only buys estates whenever Conspirator is in play. Then I tried the same sim with Star Chart. The Star Chart strategy initially plays Conspirator every 2 turns, and drains estates by turn 20. The Scheme strategy initially plays Conspirator on about 50-60% of turns, and drains estates around turn 18. Oh and if you get neither, then it takes about 24 turns.
If by some fluke of the shuffle, Market Square always appeared immediately before one of the coppers in your deck, would that make a huge difference in its power level?Instead of comparing Ducat to Candlestick Maker, we should really be comparing it to Market Square.
Isn't that like comparing Gold to Smithy? How does that work?
Well, if you buy it and trash a copper, ducat is like a nonterminal +buy that doesn't take up space in your deck for $3.
Market square is also like that.
I feel like this only works if the card you draw when you play Market Square is a Copper.
16: Travelling Fair (10) - You all know this event is good. I think it's better. The stats for this one are actually shocking. It's bought by the winner in 81% of games, and in games where only one player buys it, they win a whopping 70% of the time! I have some doubt about the causation direction on that stat, because Travelling Fair might occasionally be something you only buy on the turn you win, but I don't think that can explain the full effect. Stats aside, +buy on demand is great, and topdecking is great. Buy this often.I am even more doubtful about the causation direction of Travelling Fair statistics than you. Often you want to buy TFair when you hit $7 or higher (either to get two useful cards out of it, or to topdeck a $5-cost). So we should be thinking of it like one of those really expensive cards like King's Court, where buying it isn't just a winning move, it's an indication that you were in a winning position to begin with. That said, I put TFair at #12, so I'm not in much disagreement.