Dominion Strategy Forum
Dominion => Dominion FAQ => Topic started 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 KCKCMonumentMonumentMonument  buy nothing until the end of time, along with max two events.

You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.

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.

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.

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.

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.

If you replace Monument with Tomb, you can do it with one fewer Overlord (also you get 2 VP per iteration).

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.

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 3pile with Highway, Forum and Silver.

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.

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.

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.

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 2player game, if your opponent's deck is a single Copper, you can Ambassador them a Villa and steal it back with Cutpurse/Thief/Masquerade.

You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.

You can go infinite with Overlord, Crown, Mandarin, Watchtower, Lurker, Raze and Monument.
No you cannot.
Why?

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?

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.

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?

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?

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.

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.

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.

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.

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.

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.

Play 5 Highways then Goons. Have Trader in hand. Buy Forum forever, gain an arbitrary amount of VP.

[...] gain an arbitrary amount of VP.
π is pretty arbitrary, as are 1, i, φ, e, sqrt(2) and Chaitin's constant :P

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.

[...] 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.

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 nonpositive. 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.

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.

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.

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.

Dominion is a cool guy. Eh uses 'infinite' and 'unbounded' interchangeably and doesn't afraid of stubbing toe or anything.

[...] 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).

$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/16pxVP.png)
*You may only buy this if you are trapped in an infinite unbounded loop of semantics.

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?

... +aleph1 VP
Are (infinite) ordinal or cardinal numbers most appropriate here?

... +aleph1 VP
Uh... that wasnt alephone (https://en.wikipedia.org/wiki/Beth_number#Beth_one)...

I'm no mathematician, but shouldn't it be alephnull?

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.

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.

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.

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.

I'm no mathematician, but shouldn't it be alephnull?
Are we now going to quibble over what the transfinite point value of a madeup card should be? Alephnull 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.)

Uh... that wasnt alephone (https://en.wikipedia.org/wiki/Beth_number#Beth_one)...
My post assumed the continuum hypothesis :P

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 ].

Hey I can do math too: 1 + 1 = 2.

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 :)

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".

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

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 i1. And the resulting ordering is a dragon curve!

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.

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.

And I'm all out of Silvers.
You better gain some then.

... the kingdom is, I mean.

... 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?

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 alephnull Silvers, go cwazy.

I mean, technically there is no rule limiting the number of Silvers in the supply, right? Play with alephnull 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 :(

Seems like you need a bit of help from Banach and Tarski (https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox).