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[luser]

Assume that we would play dominion with say 10^100 card supply piles. What strategy would accumulate points at fastest rate?

[florrat]

Well, assuming perfect shuffle luck I'm quite sure that it is possible to empty the supply in turn 4 in such a way that you have 10^100 Goons in play for most of the game. So that would give you ~10^201 points in turn 4.

Without perfect shuffle luck, you can still empty the supply once you hit a hand of
Procession-Procession-Fortress-Watchtower-X
because once you get going, you topdeck almost everything you need in the correct order anyway. It will take more than 4 turns to set it up, but it will still give you ~10^201 points within 10 or so turns.

Is that fast enough?

[SirPeebles]

What does fastest rate mean in this discrete, finite context?

[Witherweaver]

There was a post before that linked to a site where someone did some asymptotics on VP gaining.  I think it was in the thread about determining Engine vs. Non-Engine.  I think the jist of it was that Big Money accumulated VP at a linear rate, while Engines can accumulate at a superlinear rate.  I think good strategies could get to quadratic.

[Witherweaver]

What does fastest rate mean in this discrete, finite context?

VP gained per turn.

[SirPeebles]

What does fastest rate mean in this discrete, finite context?

VP gained per turn.

Which turn?

[Witherweaver]

What does fastest rate mean in this discrete, finite context?

VP gained per turn.

Which turn?

Well I guess I can't speak to what the original poster meant, but I'm thinking of average VP per turn. 

[dondon151]

I think a better metric would be the average value of cards gained per turn.

[Witherweaver]

I think a better metric would be the average value of cards gained per turn.

Hm?  Like value in coin?

[silverspawn]

well it doesn't matter y'know? florrat is right

[navical]

There was a post before that linked to a site where someone did some asymptotics on VP gaining.  I think it was in the thread about determining Engine vs. Non-Engine.  I think the jist of it was that Big Money accumulated VP at a linear rate, while Engines can accumulate at a superlinear rate.  I think good strategies could get to quadratic.

Big Money is linear, though it isn't the best linear strategy. (4 Princes of Monuments is 10VP/turn to BM's 3VP/turn, for instance, while a 95% reliable engine with 10 Monuments as payload and not greening is 9.5VP/turn).

Alt-VP is generally quadratic - e.g. a Prince of Ironworks gaining a Gardens and buying a Copper gains 1 Gardens/turn and increases the value of each Gardens by 0.2 VP/turn, for 0.2n^2 + smaller terms VP, where n is the current turn. (But even the Money/Gardens strategy of buying Copper on 0-2, Silver on 3, Gardens on 4+ is quadratic, just a lot slower).

Engines are generally exponential, at least in terms of greening power: to take the extreme example, once you've trashed your starting cards and gained 8 Highways, a Highway-Market Square deck doubles the number of Market Squares in it, so having megaturn potential that grows like 2^n. But after the megaturn it'll stall horribly and be overtaken by the Big Money tortoise. If, as stated in the OP, the piles are very large but finite, then this is probably the best. If the piles are infinite, then it gets crushed.

A more traditional engine (with some +Buy) will also grow exponentially, but again if you start greening in the normal manner then you'll splutter a bit before choking entirely. However, it should be possible to build an engine that can increase in size exponentially and also gain green exponentially (with a smaller exponent) whilst still being able to reliably draw itself.

Better than that, though, would be the engine with Goons as payload, which also grows exponentially and gains VP exponentially, but has much less to choke on.

Now I've written this, I realise it's essentially what that article said, I think, though I can't find it either.

[lastly: no, florrat isn't right, because Dominion involves shuffling].

[liopoil]

florrat is right in that even with imperfect shuffle luck you will still be able to empty any finite supply in something like 15 turns at most, given that you can choose the kingdom.

[navical]

florrat is right in that even with imperfect shuffle luck you will still be able to empty any finite supply in something like 15 turns at most, given that you can choose the kingdom.

* navical fails at reading past the first few lines (just saw "with perfect shuffle luck" and ignored the rest). 

[luser]

florrat is right in that even with imperfect shuffle luck you will still be able to empty any finite supply in something like 15 turns at most, given that you can choose the kingdom.

That is still slow, my answer was around turn 7 empty upgrade/rats with fortress and get points from single gardens.

[liopoil]

florrat is right in that even with imperfect shuffle luck you will still be able to empty any finite supply in something like 15 turns at most, given that you can choose the kingdom.

That is still slow, my answer was around turn 7 empty upgrade/rats with fortress and get points from single gardens.

That's going to be far fewer points/turn, however. It mostly likely will be much faster than 15 turns, too.

[Witherweaver]

There was a post before that linked to a site where someone did some asymptotics on VP gaining.  I think it was in the thread about determining Engine vs. Non-Engine.  I think the jist of it was that Big Money accumulated VP at a linear rate, while Engines can accumulate at a superlinear rate.  I think good strategies could get to quadratic.

Big Money is linear, though it isn't the best linear strategy. (4 Princes of Monuments is 10VP/turn to BM's 3VP/turn, for instance, while a 95% reliable engine with 10 Monuments as payload and not greening is 9.5VP/turn).

Alt-VP is generally quadratic - e.g. a Prince of Ironworks gaining a Gardens and buying a Copper gains 1 Gardens/turn and increases the value of each Gardens by 0.2 VP/turn, for 0.2n^2 + smaller terms VP, where n is the current turn. (But even the Money/Gardens strategy of buying Copper on 0-2, Silver on 3, Gardens on 4+ is quadratic, just a lot slower).

Engines are generally exponential, at least in terms of greening power: to take the extreme example, once you've trashed your starting cards and gained 8 Highways, a Highway-Market Square deck doubles the number of Market Squares in it, so having megaturn potential that grows like 2^n. But after the megaturn it'll stall horribly and be overtaken by the Big Money tortoise. If, as stated in the OP, the piles are very large but finite, then this is probably the best. If the piles are infinite, then it gets crushed.

A more traditional engine (with some +Buy) will also grow exponentially, but again if you start greening in the normal manner then you'll splutter a bit before choking entirely. However, it should be possible to build an engine that can increase in size exponentially and also gain green exponentially (with a smaller exponent) whilst still being able to reliably draw itself.

Better than that, though, would be the engine with Goons as payload, which also grows exponentially and gains VP exponentially, but has much less to choke on.

Now I've written this, I realise it's essentially what that article said, I think, though I can't find it either.

[lastly: no, florrat isn't right, because Dominion involves shuffling].

Yeah that sounds familiar.  Anyone remember where that article was brought up?

[qmech]

Yeah that sounds familiar.  Anyone remember where that article was brought up?

This is is linked from the card list on the main blog in the pingback section.