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26

Dominion General Discussion / Re: Semi-Interesting Dominion Moments Thread

« on: February 16, 2022, 10:15:28 am »

One of those extremely dumb games against Lord Rattington where I'm messing around trying to make something vaguely interesting happen and realize I'm actually losing badly to straight BM. But then manage to turn it around like a barge after 33 turns for the win.

Cuzz:
6 Golds, 5 Estates, 6 Duchies, 2 Provinces, a Steward, Dame Anna, Dame Josephine, Dame Natalie, Sir Bailey, Sir Destry, Sir Martin, Sir Michael, Sir Vander, 3 Soothsayers, 9 Hirelings, 6 Werewolves, 10 Border Guards, 10 Patrons and 8 Hunting Lodges

Lord Rattington:
5 Curses, 5 Coppers, 6 Estates and 6 Provinces

I'm counting 37 points for both of you. Did Lord Rattingdon end the game? Seems unlikely given the state of his deck and the Provice pile being empty. Were you just so happy with the tie that you mistook it for a win or am I missing something?

Miserable

27

Dominion General Discussion / Re: Semi-Interesting Dominion Moments Thread

« on: February 15, 2022, 10:33:17 pm »

One of those extremely dumb games against Lord Rattington where I'm messing around trying to make something vaguely interesting happen and realize I'm actually losing badly to straight BM. But then manage to turn it around like a barge after 33 turns for the win.

Cuzz:
6 Golds, 5 Estates, 6 Duchies, 2 Provinces, a Steward, Dame Anna, Dame Josephine, Dame Natalie, Sir Bailey, Sir Destry, Sir Martin, Sir Michael, Sir Vander, 3 Soothsayers, 9 Hirelings, 6 Werewolves, 10 Border Guards, 10 Patrons and 8 Hunting Lodges

Lord Rattington:
5 Curses, 5 Coppers, 6 Estates and 6 Provinces

28

Dominion General Discussion / Re: Seaside 2E Announced

« on: January 28, 2022, 04:33:53 pm »

Navigator is weak powerwise and sifting isn’t something that other cards don’t do.

Trash at the risk of blowing up good stuff isn’t something any other card does (well, Junk Dealer and Upgrade technically do but then you are actively gambling, having no junk in hand and only hoping to draw into junk) so Lookout is unique to some degree.

Coppersmith also did something no other card does 

29

Dominion General Discussion / Re: Interview with Donald X.

« on: January 27, 2022, 02:42:00 pm »

Is there a place where I can read your opinions on electoral reforms? I watched the youtube video and I'd love to hear/read more!

There is a place here where I crossposted a speech about my best voting reform. http://forum.dominionstrategy.com/index.php?topic=14544.msg655961#msg655961

This does seem really interesting. I think the one issue I notice is that in places without mandatory voting, you'll have very different election turnouts in different districts. A candidate who is a huge polling frontrunner in one district, for example, might suppress turnout for their whole election, and therefore have reduced power in the legislature. In another district, a close race between two candidates could inflate turnout and give both "winners" more voting power than the candidate in the first district, despite being less popular. The dynamics that result in total number of votes for a candidate are not necessarily comparable between representatives who didn't run directly against each other. It reminds me a little of why looking at total VP across multiple games is a bad tiebreaker in Dominion tournaments.

On the other hand, you might expect voter behavior to change based on a widespread understanding of how the new system works, and so maybe turnout would be pretty high overall.

30

Dominion General Discussion / Re: Best Uninteresting Moments in Dominion

« on: October 03, 2021, 03:24:15 pm »

C plays a Mastermind.
C draws 5 Coppers.

31

General Discussion / Re: Maths thread.

« on: September 01, 2021, 12:18:17 pm »

Some good math tweets:

https://twitter.com/ImogenBits/status/1428056037815431172?s=20

https://twitter.com/RadishHarmers/status/1427822902179770368?s=20

32

Dominion Articles / Re: Dominion is getting worse with each expansion

« on: August 18, 2021, 02:10:46 pm »

Speaking as an old person, Dominion is more fun now than it was a decade ago, although it's less addictive.

By remarkable coincidence, Dominion suddenly became less addictive exactly around the birth of my first child.

Mafia remained exactly the same amount of addictive which is why I can never play it again.

33

Dominion Articles / Re: Dominion is getting worse with each expansion

« on: August 18, 2021, 10:51:48 am »

Speaking as an old person, Dominion is more fun now than it was a decade ago, although it's less addictive.

By remarkable coincidence, Dominion suddenly became less addictive exactly around the birth of my first child.

34

Dominion Articles / Re: Dominion is getting worse with each expansion

« on: August 12, 2021, 04:22:05 pm »

There is no such thing as a "bad" kingdom, and in fact:

Theorem: All kingdoms are interesting.

Proof:

Suppose there exists an uninteresting kingdom.
Order the countably many kingdoms by the minimal number of decisions it takes to empty the supply in a two player game with perfect shuffle luck.
There then exists at least one minimal uninteresting kingdom with respect to this ordering.
But this property makes these kingdoms interesting.
This is a contradiction.

I see what you did there https://en.wikipedia.org/wiki/Interesting_number_paradox

But the reasoning doesn't quite work in this case, as there are plenty of kingdoms in which it is impossible to ever empty the supply - specifically, in any kingdom without +buy and without gainers, the 3-pile rule ends the game long before you could empty the supply. Your argument only proves that any kingdom in which you can empty the supply is interesting - but if the uninteresting kingdoms are a subset of the kingdoms in which you cannot empty the supply, there is no ordering and no "minimal number" exists ...

Just ignore the 3 pile rule to make it well-defined.

There is no such thing as a "bad" kingdom, and in fact:

Theorem: All kingdoms are interesting.

Proof:

Suppose there exists an uninteresting kingdom.
Order the countably many kingdoms by the minimal number of decisions it takes to empty the supply in a two player game with perfect shuffle luck.
There then exists at least one minimal uninteresting kingdom with respect to this ordering.
But this property makes these kingdoms interesting.
This is a contradiction.

I see what you did there https://en.wikipedia.org/wiki/Interesting_number_paradox

But the reasoning doesn't quite work in this case, as there are plenty of kingdoms in which it is impossible to ever empty the supply - specifically, in any kingdom without +buy and without gainers, the 3-pile rule ends the game long before you could empty the supply. Your argument only proves that any kingdom in which you can empty the supply is interesting - but if the uninteresting kingdoms are a subset of the kingdoms in which you cannot empty the supply, there is no ordering and no "minimal number" exists ...

It also fails on another level. The set of "minimal uninteresting kingdoms" could be very large; indeed, it is possible that the number of decisions is exactly the same for each uninteresting kingdom. Then being minimal with respect to the ordering gives no additional information, and hence no justification for making the kingdoms interesting.

The interesting number paradox sort of requires a unique minimal element, and that is not given here.

I don't think it's required. I'm claiming that the minimality property makes all such kingdoms interesting. Generically there will be some moderate number of minimal kingdoms and it will be fair to call these interesting, and on the other hand special cases like you mention where e.g. the number of decisions is exactly the same for each uninteresting kingdom are even more interesting.

35

Rules Questions / Re: Am I playing Skulk incorrectly?

« on: August 05, 2021, 09:39:05 am »

I think a major problem is that the two things you get are a bit at odds. Decks that want Skulk are usually engines that need some extra +Buy or have some free terminal space that can be used for attacking, decks that want Gold are usually more money-ish.

I feel like there are certainly engine games I've played where Gold was still my primary payload. Sometimes the engine payload isn't good enough, or it's terminal without villages on the board.

Sometimes it’s also just nice to get a gold in your deck before the first shuffle, even if you have little interest in treasure payload in the long run. It can be the best way to hit $5 ASAP on some boards.

36

Rules Questions / Re: Am I playing Skulk incorrectly?

« on: August 05, 2021, 09:36:57 am »

The same questions can be asked about Border Village. You get worth of value for only ! Well no, you actually get += worth of value for , which is still nice. But Border Village isn't close to strong enough to be a card in terms of what it does when you play it. It only costs because of the free card you get when you buy it. And with Border Village, it would be weaker if it cost less, because paying for a + a Village is better than paying for a + a Village.

This also works for cache in reverse. You get $6+$0+$0=$6 worth of value for only $5!

37

Dominion Articles / Re: Dominion is getting worse with each expansion

« on: August 03, 2021, 03:59:58 pm »

There is no such thing as a "bad" kingdom, and in fact:

Theorem: All kingdoms are interesting.

Proof:

Suppose there exists an uninteresting kingdom.
Order the countably many kingdoms by the minimal number of decisions it takes to empty the supply in a two player game with perfect shuffle luck.
There then exists at least one minimal uninteresting kingdom with respect to this ordering.
But this property makes these kingdoms interesting.
This is a contradiction.

38

Dominion General Discussion / Re: New online version of Dominion (with neural-network based AI) from Temple Gates

« on: July 07, 2021, 10:39:21 am »

It would be nice to have a single, official implementation.

The healthiest state of computer Dominion so far was in the pre-Goko era, when there were a variety of unofficial implementations that had different advantages for different types of players.

What was there other than isotropic that was actually being used by a substantial population?

39

Dominion Online at Shuffle iT / Re: A decline of rematching on Shuffle iT

« on: May 01, 2021, 11:54:31 am »

Sometimes if I am getting beaten badly I decide I’m just not in the mood and would rather roll the dice on getting matched with someone I have a better chance against.

40

Dominion General Discussion / Re: Anything coming in 2021?

« on: April 26, 2021, 09:06:15 am »

Last year, however, was a banner year (2nd best in fact) with 70 new things for Dominion (30 Kingdoms, 20 Events, and 20 Ways).

Yeah, then what happened?

41

Feedback / Re: The main site has gone down

« on: March 16, 2021, 11:25:05 am »

I totally forgot that dominionstrategy.com even was a website.

It's mainly about investigating voting machine fraud now.

42

General Discussion / Re: Maths thread.

« on: February 23, 2021, 08:39:49 pm »

Yeah I mean if it wasn’t technically “wrong” and “illogical” we’d just call it a “use of notation.”

43

General Discussion / Re: Maths thread.

« on: February 23, 2021, 12:56:22 pm »

So the exact same thing as f?

No, because "f(y)" would be a macro for "y^2-25," and those are two different strings, so they can't both be the exact same thing as f.

44

General Discussion / Re: Maths thread.

« on: February 23, 2021, 12:24:34 pm »

Since you think it's defensible, can you tell me what f(x) means here? Just, literally, what is it?

A macro for "x^2-25"

45

General Discussion / Re: Maths thread.

« on: February 23, 2021, 12:00:30 pm »

There are plenty of contexts where x^2 and y^2 are definitely not the same thing, like say in a polynomial ring R[x,y].


Eventually you want to actually do some math and communicate what you’re trying to do to an audience who you reasonably expect to understand what you mean when you write things without getting bogged down in formalism at every turn.

Like xt^2 is O(x) but not O(t). The label on the variable matters here. I could spend a lot of energy writing down the formalism that makes this make sense but everyone knows what I mean.

I think you think that I'm against various elegant ways of writing things down, but I'm not familiar with any example where what I'm saying forces you to be less elegant. f \in O(g) is shorter than f(x) \in O(g(x)) and doesn't convey any less information. And I have no issue with f \in O(n) or even xt^2 \in O(x).

Is there like a quote from a book or a paper or something that actually demonstrates what you dislike and how you would rewrite it? I admit I'm still confused about whether you're taking issues with the appearance of the actual character "x" or the entire concept of representing a function by a symbolic formula.

46

General Discussion / Re: Maths thread.

« on: February 23, 2021, 11:57:26 am »

I don't think anyone is claiming there is a full rigorous logic behind this. It's about whether you abuse terminology and notation in ways that aid the communication of whatever it is you're trying to communicate or obfuscate it.

I agree that "the graph of f(x)" is awkward.

"f(x) has a root..." might be defensible sometimes. For example, if it seems perfectly fine to say "f(x) = x^2-25" and "x^2-25 has a root at x=5," then I don't see why "f(x) has a root at x=5" should be automatically rejected.

Similarly, if you can say  "f(x) = x^2-25" and "x^2 - 25 \in O(x^2)" then why not "f(x) \in O(x^2)?" "f(x)" becomes a symbolic replacement for the expression "x^2-25" and it seems awkward to make that replacement illegal in some specific context.

I don't really think I'm gonna satisfy you, because I can tell that you just have a different attitude about math. But at the end of the day you're not really doing math if you can't clearly communicate your ideas, and that clarity of communication depends on the culture of how modern math is written, not all of which perfectly aligns with formalism or everything would be written in ZFC machine code and be completely worthless to any real audience. This blog post informs how I think about a lot of this https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

47

General Discussion / Re: Maths thread.

« on: February 23, 2021, 11:31:40 am »

what the independent variable is

This is not a thing! You've just written down the formalism for a function in the previous post. There is no independent variable that is part of what a function is. There is no difference between f(x) = x^2 and f(y) = y^2. Both are short hands for the same object.

There are plenty of contexts where x^2 and y^2 are definitely not the same thing, like say in a polynomial ring R[x,y].


Eventually you want to actually do some math and communicate what you’re trying to do to an audience who you reasonably expect to understand what you mean when you write things without getting bogged down in formalism at every turn.

Like xt^2 is O(x) but not O(t). The label on the variable matters here. I could spend a lot of energy writing down the formalism that makes this make sense but everyone knows what I mean.

48

General Discussion / Re: Maths thread.

« on: February 23, 2021, 11:20:59 am »

Are you objecting to the literal symbol “f(x)” or an actual spelled out expression like (3x^3-1)/x? Can you quote an instance of what you find so objectionable?

49

General Discussion / Re: Maths thread.

« on: February 23, 2021, 11:02:10 am »

And it's useful because while the definition of a function doesn't require any particular formula or pattern for specifying what the elements of S are, often in practice functions do arise from formulas and writing something like "the function f(x)" is less clunky than "the function f defined by f(x) = ..." or "the function f: x -> f(x)" or whatever. 

How does this apply to f(x) \in O(g(x))? I *don't* object to f(x) = x^2 to define a function, but that's not what's happening here.

Well for one it keeps track of what the independent variable is in cases where it might be ambiguous.

50

General Discussion / Re: Maths thread.

« on: February 23, 2021, 10:57:36 am »

Pedantically f is a function (an ordered triple (X,Y,S) where S is a subset of XxY satisfying the function axioms, or really better an equivalence class of such ordered triples where (X,Y,S) ~ (X',Y', S') iff S = S') and f(x) is an element of the codomain Y.

But using f(x) in place of f is one of the more ubiquitous and mild abuses of notation in mathematics. And it's useful because while the definition of a function doesn't require any particular formula or pattern for specifying what the elements of S are, often in practice functions do arise from formulas and writing something like "the function f(x)" is less clunky than "the function f defined by f(x) = ..." or "the function f: x -> f(x)" or whatever.