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[Samuel]

Imagine, every stack contains infinite cards.

Is it then possible, within 20 moves to gain 10.000.000.000 Colonies?

(Annotation: "It is possible" means you can assume best case, e.g. start 2/5 etc.)

[Drab Emordnilap]

I assume, since you're presenting this as a puzzle, that you already have proven the solution one way or the other.

[Algebraist]

What is a "move"? Do you mean "within 20 increments of the turn-counter in solo play"? If so, then yes, this is easy.

[Robz888]

I have no idea, but if it is possible, I would assume Quarry, Bridge, King's Court, Wharf, and Worker's Village make it so.

[Grujah]

I think that with infinite stacks that CelestialChameleon combo can do anything on turn 4.

By that I mean this:
http://forum.dominionstrategy.com/index.php?topic=3225.msg92981#msg92981

With infinite Fortresses, Processions, Remakes, BoMs and Catacombs and whatelse not, you can probably do it by turn 4, most likely via some Bridges shenneigans with BoM and so.

[jonts26]

Exponential growth is really freaking fast. KC/Bridge loop would most likely be able to do it.

[Robz888]

I think that with infinite stacks that CelestialChameleon combo can do anything on turn 4.

I know. I'm just waiting for him to show up.

A wild Celestial Chameleon appeared! It used "Brilliant Logic." It was very effective!

[NoMoreFun]

If by 20 moves you mean 20 turns, well every turn from 4 onwards can be a Celestial Chameleon style megaturn, exponentially increasing in size. It is definitely possible.

[NoMoreFun]

A deck of a single scrying pool, a single council room  4 bridges and the rest King's Courts and Squires is all that's needed.

You'll be able to approximately increase your deck to 4.5 its old buying power every turn (each KC'd squire letting you buy 6 more cards, but you'll need to buy 1 KC for every 3 squires). Assuming this starts at turn 5, you'll have 37699792253 (6*4.5^15) buys by turn 20, which you can use on free colonies.

[Grujah]

Easiest way:

Proccesion1, Procession2, Procession3, Fortress1, Fortress2
Play Lab, draw

Play Procession1, Play Procession2 twice, Play Procession3 twice:

--With procession3 -
Play Fortress1 twice, get +2 actions, draw Watchtower and Diadem.
Trash Fortress1, gain BoM on top of your deck, fortress back into your hand.
Play Fortress1 twice , draw Bom + Whatever.
Trash Fortress, gain Bom on top of your deck.  fortress back into your hand.

With procession2
Play Fortress1 twice, get +2 actions, Bom + Whatever.
Trash Fortress1 gain Market on top of your deck, fortress back into your hand.
Play Fortress1 twice , draw Market + Whatever.
Trash Fortress, gain Market on top of your deck.  fortress back into your hand.

Now you have 1 processions in play, 2 BoMs and 2 markets and 2 Fortresses in hand.. Just repeat this indefinetely, with BoMs posing as Procession until you get 10.000.000.000 spare actions and same amount of spare Markets, than play Markets out.

Than play Diadem.

[jonts26]

The no buy method. We can create an exponentially increasing deck within one turn this way.

Assume we've already drawn our deck and have enough bridges in play to make everything free.

All we need is KC, Ironworks, and Nobles. Each nobles provides 10 cards of draw. 9 from the actual play and 1 from when the IW gains it. And each additional KC can triple 2 more actions. So if at some point we have a hand of n cards, we need n/10 nobles, n/3 KC's (the 2 it can double and itself), which leaves 17n/30 Ironworks. So we can triple 17/30 IWs each round, and get 51n/30 new cards which we can both draw and play in triplicate. Since we gain more cards than we use, and piles are infinite, we can do this until we have enough IW's to gain whatever number of colonies we are looking for.

Now to figure out how long that takes to set up.

EDIT: I think the second solution to puzzle #1 is sufficient to get this loop set up in 5 turns. Just don't dive into getting the last 2 bridges so soon and keep gaining KC, IW, and Nobles until you are ready to pop.

[Schneau]

I think that with infinite stacks that CelestialChameleon combo can do anything on turn 4.

By that I mean this:
http://forum.dominionstrategy.com/index.php?topic=3225.msg92981#msg92981

With infinite Fortresses, Processions, Remakes, BoMs and Catacombs and whatelse not, you can probably do it by turn 4, most likely via some Bridges shenneigans with BoM and so.

I want to upvote that CC post again, but I can't

[Samuel]

Hello,

of course I meant "within 20 increments of the turn-counter in solo play"
(sorry, english is not my native language).

Actually I did it within 12 increments.
(And I know nothing of Dark Age)

[TwiNight]

If this is solo, KC-KC-Possession-Possession-Possession

[DStu]

In 20 turns, you can certainly go  beyond exponential to infinite.  Don't want to mess with details, but get yourself in a situation where you have an empty draw/discard deck and played say 11 bridges/highways, and have a hand of (at least) KC/KC/IW/IW/Watchtower.

Now KC/KC/IW/IW gains you KC-KC-IW-IW-CR(put on deck with WT)-Colony(draw CR) and lets you play a KCd CR which gives you +3buys and draws the KC-KC-IW-IW-Colony. Now your hand is again (more than) KC/KC/IW/IW/Watchtower, you have more than enough actions from the IW to just restart the chain. But you won 3 buys and a Cololny by this chain, just repeat this chain as often as you like and buy 3times as many Colonies as you already have.