Dominion Strategy Forum
Dominion => Dominion General Discussion => Topic started by: Chris is me on October 12, 2016, 10:46:43 am
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I want to get an idea what percentage of boards are engines, based on actual math and data. What are the different ways we could approximate this?
I thought of two, both of which have their flaws, and would need to be drilled out.
1. Analyze a bunch of game logs, flag those whose gameplay matches some criteria?
2. Calculate the odds that a board has draw, payload, gainer, village in some combination?
I'm far too tired / loopy to start thinking about this, but just thought i'd start the discussion.
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I think the first option would be the better one. Just look at logs of some of the best players and see how many engine games they played in their overall games. Of course just count full random games and games that were won by an engine player.
Both methods have flaws, the first one has the disadvantage that players might not see an available engine and play something else, which can be compensated by looking at the games of the very best as suggested. The second one seems nearly impossible to do correctly as all cards and their interactions cannot be taken into consideration just by categorizing the cards.
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86.4%
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90-93%
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A useful distinction is between boards where you could hypothetically build an engine and one where an engine is actually a good strategy. I think this adds to the appeal of Method 1, since it looks at when people actually consider an engine worth going for rather than including boards where you could make an engine but shouldn't.
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90-93%
I.e. far more than people think.
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92.27-94.48%
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100%
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100%
Unpossible, because then King's Court would not be more skippable than people think.
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Any approximations based on odds of components available is going to be imperfect, but probably in the right ballpark. Some engines don't need every component and some boards that have every component don't make great engines. I'm fine with a rough guesstimate that includes some false positives / negatives. I just want to get an idea.
My hunch is that the popular perception is 85+%, and the reality is more like 60%? I think it's confirmation bias / we enjoy engines more and remember them.
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Any approximations based on odds of components available is going to be imperfect, but probably in the right ballpark. Some engines don't need every component and some boards that have every component don't make great engines. I'm fine with a rough guesstimate that includes some false positives / negatives. I just want to get an idea.
My hunch is that the popular perception is 85+%, and the reality is more like 60%? I think it's confirmation bias / we enjoy engines more and remember them.
I'm not sure if 60% is high enough, but I think you're right in general (in addition to that people actually go for engines less often than they should). Even in the King's Court's skippability thread, the OP was saying that you have to go for King's Court 90-93% of the time, which he claimed to be far less often than people thought and people even didn't have that much of a problem with the notion that the general consensus would have been a higher percentage, and later on it turned out that high level players didn't even go for it that often (IIRC it was something like 85%).
And well, if King's Court is only worth going for in 85% of the games where it's on the kingdom, that pretty much rules out any estimates higher than 85% for this thread's question.
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I'd say 85% are engines. I wouldn't call throwing a jack of all trades together with a few festivals as an engine.
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I'd say 85% are engines. I wouldn't call throwing a jack of all trades together with a few festivals as an engine.
There's just no way you can get an estimate of percentage of engines to 85% without a liberal enough definition to include stuff like Festival Jack or COTR + terminals decks or whatever.
85% would imply more than 5 of 6 Dominion League matches are engine boards. If this were the case the league would be way more interesting. :)
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You're going to run into borderline cases either way, though. Is a 'good stuff' deck an engine or BM? How about a Hunting Party stack, is that an engine? Or a Hermit/MS combo deck?
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At first, one needs to consider how large the probability is that at least one of the cards give more than 1 extra action on a play (villages or some other means). Yeah, cantrip engines are a possiblility, but they are at least a lot more scarce. I guess that this probability is roundabout the amount of valid engine situations.
Another option is to randomize boards and optimize their strategies, but this is much harder to accomplish, I guess. Still, it can be tried, at least.
Another problem is: What do we consider engines? Minion stacks, HP stacks, etc, are they engines? Some combo's, are they engines?
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Seriously, with all cards except old base and intrigue it should be somewhere near 90%. Empires and replacements make the engine so much more likely.
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I think I'd go for something like this:
- take a bunch of games involving the top x players into account (where x is at least 100 to avoid gross biases, I'd say)
- look at the deck of the winner of those games, even when the winner is not the topX player (this also avoids biases. If the winner beat the topX player without an Engine themselves, we can safely call that board a nonEngine one)
- if the winner has drawn more than half of their deck on at least three turns, and has had at least three different nonruin Actions in their deck, it was an Engine board.
My guess would be around 2/3 of the boards are won by an engine.
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I think I'd go for something like this:
- take a bunch of games involving the top x players into account (where x is at least 100 to avoid gross biases, I'd say)
- look at the deck of the winner of those games, even when the winner is not the topX player (this also avoids biases. If the winner beat the topX player without an Engine themselves, we can safely call that board a nonEngine one)
- if the winner has drawn more than half of their deck on at least three turns, and has had at least three different nonruin Actions in their deck, it was an Engine board.
My guess would be around 2/3 of the boards are won by an engine.
I would at least give a constraint to the 'drawn more than half of their deck'-property here. I mean, playing a turn 3 Smithy means the player has drawn half of their deck, but this doesn't necessarily provide an engine deck. I would say that this only counts after turn 4, and if there are at least 10 cards in the deck.
But it is hard enough to give the idea of engines a concrete property.