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##### Swingy, adj.: sometimes changes your win chance a lot when played
« on: January 02, 2018, 04:28:13 pm »
+3

Some cards are described as swingy.

User rrenaud once compiled a sorted list, based on how much entropy was left in the win-when-in-kingdom rates once rating was factored out, and concluded that Goons, Ambassador and Tournament are high-skill cards, whereas Embassy is a high-randomness card.

What makes Embassy high-randomness is the fact that there is an Embassy-centered strategy (Embassy BM) which is fairly strong and easy to play correctly.

What makes Tournament high-skill, I think, is that it requires good judgment and game sense to know when to go for it, how best to go for it, and which prizes to pick when you connect it with a Province. Somehow, [joke]rrenaud's ironclad mathematical proof—proof, I tell you![/joke]—that Tournament is high-skill seems not to have changed the common perception of Tournament as swingy.

I think I have a different definition of swingy which classifies Tournament as swingy. It allows for a 2x2 matrix of swingy yes/no and high-skill yes/no; we could for example use rrenaud's measure to indicate whether a card is high-skill.

Whenever you make a play, you can compare you chances of winning (assuming optimal play) in the game state before and after making that play.

Weak cards are cards that reliably only improve your win chances by a small amount (or not at all, or even harm you). Strong cards are cards that usually do something better than weak cards for your win chances.

Swingy cards are cards that are usually ok-ish but sometimes have an unusually large impact on your win chance when played. That is, your win chance after is significantly better than your win chance before. Playing it causes a big swing.

I equivocated between "making a play" and "playing a card". I only used the latter phrase for convenience—Cultist can be highly swingy, in particular if exactly one player opens 5/2 (but also if it misses shuffles, or the first ruins hit vs. miss shuffles). In the case of opening 5/2, it's the dealing of the opening hands that's the swingy play. That play is made by RNGsus, so really the definition should read "the move greatly changes the win percentages of the players", without using 'you[r]'.

And considering this further, having Province in hand when you play Tournament (and being first to do so) is often largely attributable to shuffle luck. When the shuffle has been made in a way that favors you, actually making the swingy play is just playing optimally—so really, I think swingy is something like "some of the moves made by RNGsus have the capacity to greatly alter the win probabilities of the players".

The degree to which a card is swingy is then the capacity of RNGsus to impact win chances, averaged across all the kingdoms in which the cards occur. The inherent swinginess of Tournament is attributed a little bit to e.g. Smithy, because they can occur on the same kingdom, but Embassy's randomness is also attributed a little bit to Smithy by the same logic. I claim without evidence that each card's inherent swinginess will be attributed overwhelmingly to itself, and each card's measured swinginess will be its inherent swinginess, adjusted a little bit in the direction of the average inherent swinginess across all cards, but the ranking by measured swinginess and the ranking by inherent swinginess will be the same.

A small pedantic footnote: instead of win probabilities I should probably use "expected number of match points" (loss=0 and win,draw=1/#winners), such that the players' win probabilities expected number of match points sum to 1.

I skipped over some rigor in a few places, but I think my definition roughly approximates what people mean by swingy. I would love to hear whether people agree or disagree, and especially if you think you can improve this definition. I think of it as a 'first draft'

Edit: today I relearned that the internet is a poor medium for carrying tone of voice, which is often crucial to indicate when you're joking. To address this, I have inserted [joke] tags in the appropriate places.
« Last Edit: January 02, 2018, 07:20:59 pm by jonaskoelker »
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#### Awaclus

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #1 on: January 02, 2018, 05:05:36 pm »
+3

Well, rrenaud's list isn't very nuanced. If I play against a level 40 player, Tournament is definitely going to help me win, but if I play against a level 55 player, it might help the level 55 player win. The list doesn't show whether or not that's true.
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#### Donald X.

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #2 on: January 02, 2018, 06:29:47 pm »
+3

What makes Embassy high-randomness is the fact that there is an Embassy-centered strategy (Embassy BM) which is fairly strong and easy to play correctly.
I think that's part of it, but also that terminal draw overall is more random than other things.

Somehow, rrenaud's ironclad mathematical proof—proof, I tell you!
Mocking rrenaud's actual data doesn't make your own hand-waving look any better next to it. If you want to compete with actual data, have actual data! When you say false things like calling actual data a mathematical proof, well it just makes it look like everything else you have to say will probably have false things in it too.

—that Tournament is high-skill seems not to have changed the common perception of Tournament as swingy.
There is no contradiction here. Skill and luck are not opposite ends of a spectrum. Dominion itself is overall a high-skill high-luck game, like Poker.
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#### Cave-o-sapien

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #3 on: January 02, 2018, 06:34:45 pm »
+2

Speaking of data, it would be great if it was available from the current system.
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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #4 on: January 02, 2018, 07:19:06 pm »
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Somehow, rrenaud's ironclad mathematical proof—proof, I tell you!
Mocking rrenaud's actual data
The internet is a poor medium for carrying tone of voice. It was exaggeration for the purpose of levity and merriment, but in no way did I intend to mock it. On the contrary, I greatly appreciate rrenaud's work and think it's a very clever way of trying to answer a tricky question. I also think it's very interesting, and I have learned something from reading it.

I think it captures some interesting aspect of the cards. I also think that what I think most people use "swinginess" to mean is not one of them. (If you read the OP, you already knew this one I guess.)

When you say false things like calling actual data a mathematical proof [I think some other things you say are probably false too]
I assume it matters whether I'm being sincere or not. Like, if say "A man walks into a bar; [...]" but you know that [...] never actually happened, I guess you're not going to subtract from my credibility... ?

—that Tournament is high-skill seems not to have changed the common perception of Tournament as swingy.
There is no contradiction here. Skill and luck are not opposite ends of a spectrum.

I agree:

[according to rrenaud's measure] Tournament [is a] high-skill card [...]. I think I have a different definition of swingy which classifies Tournament as swingy. It allows for a 2x2 matrix of swingy yes/no and high-skill yes/no; we could for example use rrenaud's measure to indicate whether a card is high-skill.
The implication of these two things together is that Tournament would be classified as (swingy, high-skill).

Dominion itself is overall a high-skill high-luck game, like Poker.
I agree. Maybe it's high-skill, moderate-to-high-luck, but that's haggling over pennies.

[I agree that part of what makes Embassy high-randomness is Embassy/BM being easy and good] [...] terminal draw overall is more random than other things.
Interesting. Do you mean terminal draw BM mirror games tend to be coinflips, or something more or less specific? Do you have an insight into why (as in 'by what mechanism')?
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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #5 on: January 02, 2018, 07:42:41 pm »
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Well, rrenaud's list isn't very nuanced. If I play against a level 40 player, Tournament is definitely going to help me win, but if I play against a level 55 player, it might help the level 55 player win. The list doesn't show whether or not that's true.
What was your level when you wrote this? From the non-numerical contents I assume >40, but I can't tell whether it's >55 or <55. Also, I'm not sure what to read into your use of "definitely" vs. "might".

Here are my interpretations:

1. Your level is ~54, and Tournament plays in all good strategies; due to skill you will approximate the optimal strategy significantly better than Mr(s). 40 and surely win. Versus Mr(s). 55 the difference in approximation quality is much smaller, and though both of you will play Tournament, playing Tournament is much less guaranteed to give Mr(s). 55 the win (due to the similarity in skill).

2. Your level is >55, maybe even >>55; due to great differences in skill, you'll definitely crush Mr(s). 40, but Mr(s). 55 still has a shot if they have good Tournament luck.

3. The low-or-high-luck-ness of a card is not constant wrt. the skill levels of the players. For example, if you understand some subtlety about shuffle control you might use that to tilt the mean of some high-variance distribution in your favor, but if your opponent also understands it they can compensate perfectly, and if both players do this it either increases or decreases the variance. Or, you know, something in this direction.

Which one, if any, is close to what you had in mind?
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#### Donald X.

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #6 on: January 02, 2018, 08:57:47 pm »
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The internet is a poor medium for carrying tone of voice. It was exaggeration for the purpose of levity and merriment, but in no way did I intend to mock it. On the contrary, I greatly appreciate rrenaud's work and think it's a very clever way of trying to answer a tricky question. I also think it's very interesting, and I have learned something from reading it.

When you say false things like calling actual data a mathematical proof [I think some other things you say are probably false too]
I assume it matters whether I'm being sincere or not. Like, if say "A man walks into a bar; [...]" but you know that [...] never actually happened, I guess you're not going to subtract from my credibility... ?
There's the message sent, and the message received. I only get to see the message I receive. I imagined you were smiling, but still, you put down rrenaud's stuff by lauding it unrealistically. I don't know if you actually then went on to say false things; the point was how you modified my expectations by doing this.

[I agree that part of what makes Embassy high-randomness is Embassy/BM being easy and good] [...] terminal draw overall is more random than other things.
Interesting. Do you mean terminal draw BM mirror games tend to be coinflips, or something more or less specific? Do you have an insight into why (as in 'by what mechanism')?
I wasn't saying anything about games being coinflips; obv. there's the usual, if we subtract out all skill, what's left is luck, and that's not so interesting generally, but still sometimes people will point to an instance of it. If we subtract out all skill by pursuing a formula-based strategy with Smithies and money, what's left is luck; no surprise there.

The mechanism that makes terminal draw more random is, you draw random cards. Sometimes you get to good numbers and sometimes not; sometimes you draw your other Smithy dead and sometimes not; sometimes you draw it with Village and sometimes not; sometimes it will trigger a shuffle at a poor time but your alternative is not great. It's lots of things.
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#### Awaclus

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #7 on: January 02, 2018, 09:19:21 pm »
+1

3. The low-or-high-luck-ness of a card is not constant wrt. the skill levels of the players. For example, if you understand some subtlety about shuffle control you might use that to tilt the mean of some high-variance distribution in your favor, but if your opponent also understands it they can compensate perfectly, and if both players do this it either increases or decreases the variance. Or, you know, something in this direction.

Which one, if any, is close to what you had in mind?

This one. To clarify, my level usually fluctuates between 59-62, so there's generally a minor skill difference in my favor when I play against a level 55 player. To use Tournament and Embassy as concrete examples, Tournament is a difficult card to play right and it fits into strategies that are difficult to play right and and playing it right makes a bigger difference than getting lucky draws, so it increases my win rate against someone who's significantly worse than me at playing Tournament right or just building engines in general, but it decreases my win rate against someone who's only a little bit worse because the luck factor that it introduces then becomes more important than that small difference in skill. Embassy, on the other hand, can allow a level 20 player to beat a level 40 player more often (at this point I'm just pulling these levels out of thin air) because of the games where it's just a mirror match of Embassy/BM, but it doesn't allow the level 55 player to beat me more often because both of us are probably doing something better and more skill-intensive than Embassy/BM, and if we're doing BM, it's not because Embassy is there, it's because the rest of the board is lacking.
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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #8 on: January 02, 2018, 09:38:04 pm »
0

[I agree that part of what makes Embassy high-randomness is Embassy/BM being easy and good] [...] terminal draw overall is more random than other things.
Interesting. Do you mean terminal draw BM mirror games tend to be coinflips, or something more or less specific? Do you have an insight into why (as in 'by what mechanism')?
I wasn't saying anything about games being coinflips; obv. there's the usual, if we subtract out all skill [e.g. by formulaic play of Smithy/BM], what's left is luck, and that's not so interesting generally [...].

The mechanism that makes terminal draw more random is, you draw random cards. Sometimes you get to good numbers and sometimes not; sometimes you draw your other Smithy dead and sometimes not; sometimes you draw it with Village and sometimes not; sometimes it will trigger a shuffle at a poor time but your alternative is not great. It's lots of things.
Cool, thanks for your answer. One thing in your answer that distinguishes terminal from non-terminal draw is drawing actions dead; it would be interesting to do the math (later, 'cause I'm tired-ish now) and see if that makes non-terminal draw have lower variance than terminal draw.

The internet is a poor medium for carrying tone of voice. It was exaggeration for the purpose of levity and merriment, but in no way did I intend to mock it. On the contrary, I greatly appreciate rrenaud's work and think it's a very clever way of trying to answer a tricky question. I also think it's very interesting, and I have learned something from reading it.

When you say false things like calling actual data a mathematical proof [I think some other things you say are probably false too]
I assume it matters whether I'm being sincere or not. Like, if say "A man walks into a bar; [...]" but you know that [...] never actually happened, I guess you're not going to subtract from my credibility... ?
There's the message sent, and the message received. I only get to see the message I receive.
I'm with you so far: you don't get to read the things I don't write, such as e.g. the [joke] tags I added in later.

I imagined you were smiling, but still, you put down rrenaud's stuff by lauding it unrealistically. I don't know if you actually then went on to say false things; the point was how you modified my expectations by doing this.
I was indeed smiling; the flavor of smile to be exact.

I think this is me being a total nitpick, but here goes:

If I had lauded rrenaud's stuff unrealistically by calling it something like "extremely convincing" but without implying the false claim that empirical data and mathematical proofs are the same thing, would you still adjust your expectations about the truth of what I would be about to say? I can see how it makes sense for you to think I'm a jerk, but not that I'm stupid—or ill-informed, muddle-headed, or whatever flavor of "has incorrect conceptions" you prefer.

... It sounds like maybe you're claiming something that would surprise me—but you've already half-surprised me once (but not in the way I conditionally expected), so maybe you'll do it again. And then I might learn something, again
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#### Donald X.

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #9 on: January 02, 2018, 11:42:14 pm »
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There's the message sent, and the message received. I only get to see the message I receive.
I'm with you so far: you don't get to read the things I don't write, such as e.g. the [joke] tags I added in later.
That's not what I meant at all.

All I ever experience is my experiences. Pragmatically that's a poor way to look at things; in some contexts it's helpful though, because it accurately points out the extra step in-between the thing and me. Synesthesia highlights this.

I never get the message you sent. I only ever get the message I receive. There is always whatever distortion in-between. You can however try to affect that. For example I used to like to say "meaning depends on context," where what I meant was, that meaning as in "is my life meaningless" depended on context. Then I realized everyone was receiving "the meaning of words depends on context," which wasn't what I meant at all. These days I don't say the short pretty "meaning depends on context" because I know the other person won't receive what I'm sending.

I told you about the message I received. When you said "ironclad mathematical proof" at the top of a post where it also sounded like you were going to argue against that description, it sure sounded to me, a name I call myself, like you were putting it down, like in fact you were saying "it is in fact not an ironclad mathematical proof, as I will soon demonstrate." It doesn't claim to be an ironclad mathematical proof though, those were your words. So, what is this nonsense? Blah blah blah you did not communicate clearly to me, hth.
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#### popsofctown

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #10 on: January 03, 2018, 10:45:02 pm »
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Tournament appears stable because people play against others of similar skill.  After many games of mirroring well understood engines against eachother and eking out percentage points knowing when Oasis is slightly better than Silver, you play with a card that permits a profound mistake (one with a high level of plausibility, every board let's us open curse).  Choosing to be the only guy with cost reduction/ buy, Village, or Followers, has a lot of impact.

The effect is kind of sort of doubled because your opponent may get the Prize you were supposed to take, so now you both don't have it, and they have it.

I bet for games with large skill differentials it doesn't hold up.
« Last Edit: January 05, 2018, 02:48:33 am by popsofctown »
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#### Awaclus

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #11 on: January 03, 2018, 11:10:44 pm »
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Tournament appears stable because people play against others of similar skill.  After many games of mirroring well understood engines against eachother and eking out percentage points knowing when Oasis is slightly better than Silver, you play against someone who might make a profound mistake.

Are you saying that you're more likely to play against someone who might make a profound mistake when playing others of similar skill than when there's a large skill difference? That doesn't make a lot of sense.
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#### popsofctown

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #12 on: January 05, 2018, 02:46:48 am »
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There's a swapping of nouns in my post that is incorrect.  I've editted it.
« Last Edit: January 05, 2018, 02:48:53 am by popsofctown »
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#### popsofctown

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##### Re: Swingy, adj.: sometimes changes your win chance a lot when played
« Reply #13 on: January 05, 2018, 03:25:52 am »
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Suppose players have spent an equal amount of playing Splendor and go.

Stables : Play a game of Splendor against your opponent.

Tournament : You and your opponent each roll six sided die named Provincy.  Highest number wins.  If you tie, play a game of go to break the tie.

Against a slightly weaker player, if we are both very practiced in both Splendor and go, I want tournament.  It's pretty plausible that I have a 60 - 40 margin on this guy in go, and 51-49 in winrate in splendor.  We've got Splendor halfway solved at this point.  Even a 1/6th chance of playing the less solved (for humans) game is worth it.

Against a much weaker player, I want Stables.  I want to guarantee I test my skills against his.  If he's bad, I can easily beat him nine out of ten games at Splendor.  I'll beat him ninety nine out of a hundred games at go, but the 9% additionally won games is not worth 38ish percent chance I lose on the spot.

« Last Edit: January 05, 2018, 03:35:50 am by popsofctown »
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