Dominion Strategy Forum

Dominion => Dominion FAQ => Topic started by: 420_No_Scope_Nixon_XxX__! on October 08, 2017, 08:12:44 pm

Title: Maximum Possible VP?
Post by: 420_No_Scope_Nixon_XxX__! on October 08, 2017, 08:12:44 pm
What is the maximum possible VP in a standard dominion game?

Using Peasant, Page, Gardens, Kings Court, Donate, Goons, Gardens, Tower, Bridge, Vineyards, I managed to rack up about ~1200 against Lord Rattington. This could be higher including Groundskeeper.

I'll advocate for an arbitrary limit of 20 turns so as to disqualify KC-KC-Monument-Monument-Monument - buy nothing until the end of time, along with max two events.
Title: Re: Maximum Possible VP?
Post by: Awaclus on October 08, 2017, 08:15:47 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on October 08, 2017, 08:27:27 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

Or with 5 Highways, a Goons and a Trader with Forum in the supply.
Title: Re: Maximum Possible VP?
Post by: 420_No_Scope_Nixon_XxX__! on October 09, 2017, 12:30:55 am
Awalclus, can you explain? I'm not seeing it

Highways/Goons/Trader/Forum seems quite ridiculous, it should be stopped when the supply is out of silvers. I suppose it's an extreme case.
Title: Re: Maximum Possible VP?
Post by: Awaclus on October 09, 2017, 05:37:50 am
Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
Title: Re: Maximum Possible VP?
Post by: Chris is me on October 09, 2017, 10:46:02 am
Awalclus, can you explain? I'm not seeing it

Highways/Goons/Trader/Forum seems quite ridiculous, it should be stopped when the supply is out of silvers. I suppose it's an extreme case.

You can still prevent the gain of Forum with Trader even without Silvers to gain instead. So you can do this indefinitely.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on October 09, 2017, 06:43:49 pm

If you replace Monument with Tomb, you can do it with one fewer Overlord (also you get 2 VP per iteration).
Title: Re: Maximum Possible VP?
Post by: Kirian on October 10, 2017, 02:58:07 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

Or with 5 Highways, a Goons and a Trader with Forum in the supply.

It'd be fun to troll people with this kingdom.  I mean, more fun than other trolling at least.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on October 10, 2017, 06:26:40 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

Or with 5 Highways, a Goons and a Trader with Forum in the supply.

It'd be fun to troll people with this kingdom.  I mean, more fun than other trolling at least.

It could make for interesting games I think. Surely (in 2p) if you win the Highway split you win the game. You'd probably benefit from some more trashing than Trader, but even without you have Forum for sifting, and once you get the combo you almost certainly have an easy 3-pile with Highway, Forum and Silver.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on October 10, 2017, 07:34:42 pm
I have another solution.

TL;DR: Use KC/Lurker/Bonfire to Trash and retrieve your cards, getting points from Tomb, while using Villa/Amb to repeatedly return to your Action phase.

Solitaire game, or all opponents have a Lighthouse in play.
Requires King's Court, Lurker, Ambassador, Villa, Bonfire, Tomb.
I also use Grand Market, Highway and +$1 / +1 Card tokens. This was the best way I came up with to get the draw, coins and buys necessary. There are countless variations, but most would require more KCs and Lurkers.

{6 cards} means King's Court*2, Lurker*2, Grand Market, Ambassador.

Your +$1 token is on the Lurker pile; your +1 Card token is on the Grand Market pile.
Your hand and the trash both contain {6 cards}; your hand also contains a Villa.
Your draw and discard piles are empty.
You have a Highway in play.


Play KC > KC > Lurker/Lurker/Grand Market, gaining {6 cards} from the trash and drawing them.
Play Ambassador, returning a Villa to the supply.

Buy Bonfire*3, trashing {6 cards} from play.
Buy Villa.
Title: Re: Maximum Possible VP?
Post by: Chris is me on October 11, 2017, 07:04:30 am
The main problem with Ambassador loops is they require all opponents to either have Champion or Lighthouse out so they don't receive the card you're returning instead.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on October 11, 2017, 10:04:07 pm
The main problem with Ambassador loops is they require all opponents to either have Champion or Lighthouse out so they don't receive the card you're returning instead.

I know; it's covered in the post.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 20, 2017, 12:48:36 pm
The main problem with Ambassador loops is they require all opponents to either have Champion or Lighthouse out so they don't receive the card you're returning instead.
In a 2-player game, if your opponent's deck is a single Copper, you can Ambassador them a Villa and steal it back with Cutpurse/Thief/Masquerade.
Title: Re: Maximum Possible VP?
Post by: faust on November 20, 2017, 01:28:50 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.
Title: Re: Maximum Possible VP?
Post by: Awaclus on November 20, 2017, 02:08:27 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Title: Re: Maximum Possible VP?
Post by: faust on November 21, 2017, 05:17:01 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?
Title: Re: Maximum Possible VP?
Post by: Awaclus on November 21, 2017, 05:36:42 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?

I demonstrated the infinite loop here:

Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
Title: Re: Maximum Possible VP?
Post by: faust on November 21, 2017, 06:11:14 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?

I demonstrated the infinite loop here:

Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
And at which time in this loop does your number of VP change from some finite number to infinite, in your opinion?
Title: Re: Maximum Possible VP?
Post by: Awaclus on November 21, 2017, 06:41:10 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?

I demonstrated the infinite loop here:

Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
And at which time in this loop does your number of VP change from some finite number to infinite, in your opinion?

Which finite number is the largest possible number of VP this loop can produce, in your opinion?
Title: Re: Maximum Possible VP?
Post by: Chris is me on November 21, 2017, 07:07:57 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?

I demonstrated the infinite loop here:

Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
And at which time in this loop does your number of VP change from some finite number to infinite, in your opinion?

Can you just say whatever you’re trying to get at instead of making everybody jump through hoops to guess what you mean? Awaclus’s log demonstrates a way to play Mounment an arbitrarily large number of times, which means your VP can be whatever arbitrarily large number you want.

I swear if this is an 8 post long argument that just leads to “haha well TECHNICALLY you meant UNBOUNDED instead of INFINITE” I’m gonna scream.
Title: Re: Maximum Possible VP?
Post by: faust on November 21, 2017, 07:32:53 am
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

Why?
Can you produce a game log that shows you having an infinite amount of VP?

I demonstrated the infinite loop here:

Awalclus, can you explain? I'm not seeing it

You have a Mandarin in the trash, your hand is 5x Overlord and 1x Watchtower. Then you can do this:

Play Overlord as Crown
-> Play Overlord as Crown
--> Play Overlord as Crown
---> Play Overlord as Crown
----> Play Overlord as Raze and trash itself
----> Play Overlord as Lurker (you can do this because it was trashed so you get to choose a different card), gain Mandarin from the trash (this topdecks all of the other Overlords because they are Treasures while they are Crowns) and reveal Watchtower to trash the Mandarin again
---> Play Overlord as Lurker (you can do this because it was topdecked), gain Overlord from the trash and reveal Watchtower to topdeck it
--> Play Overlord as Monument
-> Play Overlord as Watchtower

And then you have a Mandarin in the trash and your hand is 5x Overlord and 1x Watchtower, so you can do that again as many times as you want.
And at which time in this loop does your number of VP change from some finite number to infinite, in your opinion?

Which finite number is the largest possible number of VP this loop can produce, in your opinion?
There is none. What does that have to do with anything?

@Chris is me: Sorry  ;) I cannot resist feeding Awaclus some of his own medicine.
Title: Re: Maximum Possible VP?
Post by: Awaclus on November 21, 2017, 08:06:32 am
I cannot resist feeding Awaclus some of his own medicine.

Would be funnier if I ever actually complained about people using established terms whose meanings are completely clear to everyone.
Title: Re: Maximum Possible VP?
Post by: faust on November 21, 2017, 09:24:40 am
I cannot resist feeding Awaclus some of his own medicine.

Would be funnier if I ever actually complained about people using established terms whose meanings are completely clear to everyone.
The meaning of the word "infinite" seems unclear at least to you.
Title: Re: Maximum Possible VP?
Post by: ThetaSigma12 on November 21, 2017, 10:04:28 am
I cannot resist feeding Awaclus some of his own medicine.

Would be funnier if I ever actually complained about people using established terms whose meanings are completely clear to everyone.

Eeh, I think even then it would still be really unfunny and annoying.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 21, 2017, 10:47:53 am
The meaning of the word "infinite" seems unclear at least to [Awaclus].
I won't speak on behalf of Awaclus, but the set { n | n is an amount of VP you can have by repeating the loop in question some finite number of times } is infinite. I assume this is what Awaclus means by "going infinite". If I'm right, I see no evidence that his understanding of "infinite" is inaccurate.

The worst that can be said is that the phrase "going infinite" is vague or ambiguous.
Title: Re: Maximum Possible VP?
Post by: werothegreat on November 21, 2017, 11:01:12 am
Play 5 Highways then Goons. Have Trader in hand. Buy Forum forever, gain an arbitrary amount of VP.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 21, 2017, 11:19:26 am
[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant :P
Title: Re: Maximum Possible VP?
Post by: Cave-o-sapien on November 21, 2017, 11:43:24 am
The worst that can be said is that the phrase "going infinite" is vague or ambiguous.

I would agree that is one of the worst things one could say around here.
Title: Re: Maximum Possible VP?
Post by: werothegreat on November 21, 2017, 01:42:23 pm
[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant :P

An arbitrary positive real integer, happy?  Also, π as a number is not at all arbitrary.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 21, 2017, 04:55:25 pm
An arbitrary positive real integer, happy?
Oh, I was happy all along, I was just f.ds'ing :P

You can use the combo to gain 0 VP, which only makes sense if you're making the pedantic point that 0 is non-positive. I think "real" is superfluous, though if people around you think "integers" sometimes refers to the Gaussian ones (ℤ[ i ]), then cool—I want to hang around in your social circle ;)

Also, "positive" implies an ordering; I don't know that there's a default ordering on complex integers (or on the complex numbers), which would push the interpretation of "An arbitrary positive integer, happy?" towards ℤ over ℤ[ i ].

Also, π as a number is not at all arbitrary.
I'll restate the definitions of "arbitrary" I just looked up as "unconstrained", "without system" and "whimsical". Certainly π is not without system; IINM there's a formula mapping n to the nth digit of π. Is this what you mean? If not, what then? My choice of π is somewhat whimsical, though.
Title: Re: Maximum Possible VP?
Post by: ConMan on November 21, 2017, 05:01:42 pm
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Title: Re: Maximum Possible VP?
Post by: navical on November 21, 2017, 05:43:40 pm
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.
Title: Re: Maximum Possible VP?
Post by: Donald X. on November 21, 2017, 05:45:20 pm
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.
I used to think it was dangerous too, but over the course of my life I haven't so much as stubbed my toe over it. I'm beginning to think we can let it back on airplanes.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 21, 2017, 06:03:20 pm
Dominion is a cool guy. Eh uses 'infinite' and 'unbounded' interchangeably and doesn't afraid of stubbing toe or anything.
Title: Re: Maximum Possible VP?
Post by: fisherman on November 22, 2017, 07:10:35 am
[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are -1, i, φ, e, sqrt(2) and Chaitin's constant :P

An arbitrary positive real integer, happy?  Also, π as a number is not at all arbitrary.

Better to say "rational" rather than "real" to make clear you aren't in a number field: https://en.wikipedia.org/wiki/Ring_of_integers (https://en.wikipedia.org/wiki/Ring_of_integers).
Title: Re: Maximum Possible VP?
Post by: mith on November 28, 2017, 04:54:16 pm
$0* Event
Go Infinite

+ (https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb3462a86543187911778e6ff64ed1dc27b19f5) (http://wiki.dominionstrategy.com/images/thumb/9/92/VP.png/16px-VP.png)

*You may only buy this if you are trapped in an infinite unbounded loop of semantics.
Title: Re: Maximum Possible VP?
Post by: pacovf on November 28, 2017, 05:05:22 pm
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 28, 2017, 06:13:41 pm
... +aleph1 VP
Are (infinite) ordinal or cardinal numbers most appropriate here?
Title: Re: Maximum Possible VP?
Post by: crj on November 28, 2017, 07:38:17 pm
... +aleph1 VP
Uh... that wasnt aleph-one (https://en.wikipedia.org/wiki/Beth_number#Beth_one)...
Title: Re: Maximum Possible VP?
Post by: Cave-o-sapien on November 28, 2017, 08:11:35 pm
I'm no mathematician, but shouldn't it be aleph-null?
Title: Re: Maximum Possible VP?
Post by: navical on November 29, 2017, 04:50:33 am
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action $notenough
+1 VP
You may play this again.

Infinite VP Action $notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.
Title: Re: Maximum Possible VP?
Post by: LaLight on November 29, 2017, 05:01:25 am
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action $notenough
+1 VP
You may play this again.

Infinite VP Action $notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.

What about

Unbounded VP Action $notenough
+1 VP
Play this again.
Title: Re: Maximum Possible VP?
Post by: faust on November 29, 2017, 06:08:37 am
In the sense that infinity is shorthand for an unbounded limit, I am completely fine with Awaclus' loop producing "infinite VPs" in the sense that for any real number, the loop can always produce more points than that.
Not distinguishing between infinity and an unbounded limit is a very dangerous thing to do if you wish to make true statements.

What's the difference?

Unbounded VP Action $notenough
+1 VP
You may play this again.

Infinite VP Action $notenough
+1VP per whole number greater than 0.

The first one can get you any number of VP, but at some point you have to stop, at which point you only have some finite number of VP.
The second one actually gets you infinite VP, because you get them all at once.

What about

Unbounded VP Action $notenough
+1 VP
Play this again.
It gives you some finite number of VP, until some time in the future when you stop playing the card because you have starved to death.
Title: Re: Maximum Possible VP?
Post by: Chris is me on November 29, 2017, 07:09:24 am
And all of our lives were enriched from this discussion, on a thing that totally matters in this context at all, whether or not the colloquial use of the word “infinite” in a context that literally everyone understands is technically correct or not. F.DS at its absolute finest.
Title: Re: Maximum Possible VP?
Post by: mith on November 29, 2017, 09:12:31 am
I'm no mathematician, but shouldn't it be aleph-null?

Are we now going to quibble over what the transfinite point value of a made-up card should be? Aleph-null is a boring and inadequate number of points to gain given the extreme unlikelihood of ever being able to trigger the buy condit... oh, right.

(With such a transcendental and complex discussion taking place, I'm just trying to keep it real.)
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 29, 2017, 12:00:06 pm
Uh... that wasnt aleph-one (https://en.wikipedia.org/wiki/Beth_number#Beth_one)...
My post assumed the continuum hypothesis :P
Title: Re: Maximum Possible VP?
Post by: Haddock on November 29, 2017, 12:06:03 pm
I don't know that there's a default ordering on complex integers (or on the complex numbers), which would push the interpretation of "An arbitrary positive integer, happy?" towards ℤ over ℤ[ i ].
There is no ordering on the complex numbers.
By ordering I here mean "ring ordering", ie one which respects both addition and multiplication.
(ie. x+a<y+a whenever x<y  and 0<a.b  whenever a,b>0.)

I believe the same is true of Z[ i ].
Title: Re: Maths Thread
Post by: ThetaSigma12 on November 29, 2017, 12:15:29 pm
Hey I can do math too: 1 + 1 = 2.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 29, 2017, 12:15:59 pm
There is no [ring] ordering on the complex numbers [nor complex integers].
Absolutely agree. You could do the lexicographic ordering, but no one does that on complex numbers. Failure to respect multiplication is probably the reason why :)
Title: Re: Maximum Possible VP?
Post by: faust on November 29, 2017, 02:19:00 pm
And all of our lives were enriched from this discussion, on a thing that totally matters in this context at all, whether or not the colloquial use of the word “infinite” in a context that literally everyone understands is technically correct or not. F.DS at its absolute finest.
Well the thread title asks for the maximum possible VP, so it seems directly relevant whether the answer is ∞ or "there is no maximum possible number of VP".
Title: Re: Maximum Possible VP?
Post by: sudgy on November 29, 2017, 03:26:50 pm
Also, "positive" implies an ordering; I don't know that there's a default ordering on complex integers (or on the complex numbers), which would push the interpretation of "An arbitrary positive integer, happy?" towards ℤ over ℤ[ i ].

https://proofwiki.org/wiki/Complex_Numbers_cannot_be_Totally_Ordered
Title: Re: Maximum Possible VP?
Post by: crj on November 29, 2017, 03:35:13 pm
There is no [ring] ordering on the complex numbers [nor complex integers].
Absolutely agree. You could do the lexicographic ordering, but no one does that on complex numbers. Failure to respect multiplication is probably the reason why :)
Digression on a digression on a digression, but...

I love the fact you can express the Gaussian integers using the digits 0 and 1 in base i-1. And the resulting ordering is a dragon curve!
Title: Re: Maximum Possible VP?
Post by: mith on November 29, 2017, 04:24:32 pm
And all of our lives were enriched from this discussion, on a thing that totally matters in this context at all, whether or not the colloquial use of the word “infinite” in a context that literally everyone understands is technically correct or not. F.DS at its absolute finest.
Well the thread title asks for the maximum possible VP, so it seems directly relevant whether the answer is ∞ or "there is no maximum possible number of VP".

Except the post that you were disputing did not claim it was possible to gain an infinite number of VP. Only that it was possible to “go infinite”, which most(?) seem to have no problem understanding as “it’s unbounded by the rules of Dominion, and only bounded by the time it would take to physically play out and the heat death of the universe”.

I highly doubt the OP cares about whether we are using “infinite” in a strict mathematical sense or a colloquial one, nor does it matter in the slightest whether the answer is no maximum or infinite VP. At least not to this mathematician.
Title: Re: Maximum Possible VP?
Post by: Witherweaver on November 29, 2017, 05:11:19 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

Or with 5 Highways, a Goons and a Trader with Forum in the supply.

It'd be fun to troll people with this kingdom.  I mean, more fun than other trolling at least.

I came here to gain Silvers and troll kingdoms. And I'm all out of Silvers.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on November 29, 2017, 05:38:34 pm
And I'm all out of Silvers.

You better gain some then.
Title: Re: Maximum Possible VP?
Post by: Witherweaver on November 29, 2017, 05:50:45 pm
... the kingdom is, I mean.
Title: Re: Maximum Possible VP?
Post by: Jimmmmm on November 29, 2017, 06:07:21 pm
... the kingdom is, I mean.

Silver is not a kingdom card. Do you mean the supply? Do you have any Ambassadors? Are there Silvers in the trash - what about Graverobber or Rogue?
Title: Re: Maximum Possible VP?
Post by: mith on November 29, 2017, 06:14:15 pm
You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

Or with 5 Highways, a Goons and a Trader with Forum in the supply.

It'd be fun to troll people with this kingdom.  I mean, more fun than other trolling at least.

I came here to gain Silvers and troll kingdoms. And I'm all out of Silvers.

I mean, technically there is no rule limiting the number of Silvers in the supply, right? Play with aleph-null Silvers, go cwazy.
Title: Re: Maximum Possible VP?
Post by: jonaskoelker on November 30, 2017, 12:56:47 pm
I mean, technically there is no rule limiting the number of Silvers in the supply, right? Play with aleph-null Silvers, go cwazy.
Man, I had just found the perfect compact and extensible storage solution, but it only works for a finite number of cards :(
Title: Re: Maximum Possible VP?
Post by: crj on November 30, 2017, 08:11:27 pm
Seems like you need a bit of help from Banach and Tarski (https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox).