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1
Puzzles and Challenges / Re: Best polynomial asymptotic point scoring
« on: February 02, 2020, 12:43:55 pm »
Here's a more substantial kingdom that gives O(n^18) VP:

Artisan, Bank, Cellar, Cobbler, Counting House, Gardens, Ill-Gotten Gains, Masterpiece, Page, Vampire.

There are no +Buys, so we can only buy one card a turn. There's a chain of gainers, Artisan -> Vampire -> Cobbler. In n turns, we can have O(n) Artisans, O(n^2) Vampires, and O(n^3) Cobblers, and at least O(n^4) of any <=4 cost. None of these gainers can gain themselves or anything before them in the chain, so we won't have exponential growth.

With one Page, we can have Champion and so we don't need to worry about Actions. We can gain O(n^4) Pages, so we can also have O(n^4) Heros, letting us have at least O(n^5) of any treasures we desire. Also, using O(n^5) Ill-Gotten Gains, we can have O(n^6) Coppers. Our draw engine can use these Coppers with Counting House and Cellars. We can have O(n^4) Cellars and O(n^3) Counting Houses, so with O(n^3) Counting House/Copper pairs, we will be able to draw O(n^6)*O(n^3) cards in a turn (supposing we had that many cards). With O(n^5) Banks, we can get O(n^10) money, so we can overpay for Masterpiece to have O(n^9) silvers in our deck on our second to last turn. On our last turn, we can draw O(n^9) Silvers and O(n^5) Banks to hit O(n^14) money, overpaying for masterpiece.

Our final deck will have O(n^14) cards (mostly silvers) and O(n^4) Gardens, giving O(n^18) VP.
It took me some time to digest this.  I would not have expected the exponents to grow as they do by just buying one Artisan per turn.  Quite a stunning result.
One quibble.  Overpaying for Masterpiece with O(n^10) coins yields O(n^10) Silver, so you can bump your result up to O(n^19) VP.

2
Puzzles and Challenges / Re: Best buying strategy
« on: January 26, 2020, 06:39:06 pm »
So I've implemented the changes outlined in the last post, corrected the card gained count concerning Changeling exchanges, tracked all card trashing, and here's the new summary.

166,712 Tunnels, 2 Exorcists, 124,919 Catacombs, 125,043 Monasteries: 2,604,348,207,451,841 VP

With Sewers:

166,749 Tunnels, 2 Exorcists, 124,862 Catacombs, 125,070 Monasteries: 5,208,599,683,738,762 VP


3
Puzzles and Challenges / Re: Best buying strategy
« on: January 26, 2020, 05:03:24 pm »
Quote
On the other hand, we could consider keeping a Changeling sometimes, since they can be turned into Exorcists or Monasteries. On the margin, we save an Advance to gain the Exorcist/Monastery, and have to pay the cost of drawing the card again in the Night phase. Drawing the card again in Night phase costs 1/3 of an Exorcist-Catacombs in hand pair. That Exorcist-Catacombs in hand cost 2 + 2/3 Advances in the first place, so the total cost of that draw would be 8/9 Advances, so this should be a net savings.
Would it be?  I'm too tired to think about it now, but it's 1/3 of a Cultist draw to gain the Changeling in hand, then 1/3 of another Cultist draw to draw the gained card.  I'll think about it when I finally get another good night of sleep.  It's 3 AM locally as I write this.
You're right of course.  When buying Catacombs, we can keep every other Changeling.  Then buy the Monasteries and Exorcists as before, trashing their Border Villages.  Trash enough Cultists to draw the Exorcists and Monasteries, but then enter Night Phase with the rest still on the deck.

Night phase play then starts out with this loop:

Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and a Changeling.
Play Changeling on Exorcist.
Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and an Exorcist.

We save the cost of drawing all of the Catacombs into our hand.  Big win.

(This replaces an earlier post where I miscalculated the number of Exorcists required.  We still need one for every two Catacombs, plus 1.)
I've been pondering this a great deal.

The old method

  Play Exorcist, trash Catacombs, gain Ghost, Gain Exorcist
  Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw 2 Ghosts and an Exorcist.

The altered method

  Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and a Changeling.
  Play Changeling on Exorcist.
  Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and an Exorcist.

Both gain the same amount of Ghosts and consume the same amount of Exorcists and Catacombs. (1 to 2 ratio)
The 1st loop creates two Ghosts and an Exorcist and draws them. 3 cards drawn per iteration.
The 2nd loop creates two Ghosts and an Exorcist and draws them plus 2 Catacombs.  Effectively 5 cards drawn per iteration.
In both cases, we did not have to buy the Exorcist, we created it and drew it.
The win in the second case was that we got all of the Catacombs into our hand for free.
Though the 2nd loop actually drew 6 cards per loop, it only effectively drew 5 since we had to draw a Changeling to make the Exorcist.

We can do better if we draw the Changelings into our hand before the Night phase.  It is cheaper than drawing them in the Night phase. That way we get full efficiency from the Night phase draw.  We can no longer use the Changelings gained from buying the Catacombs because we can't get the right deck ordering.  But we will have more Monasteries than Catacombs.
If N is the number of Ghosts we want and M is the number of Monasteries, this is the order to buy.

Buy 2 Monasteries, no Changelings.  (Just wraps up the draw nicely)
Buy N-1 Catacombs, no Changelings.
Buy 1 Exorcist, no Changeling.
Buy 1 Catacombs, no Changelings.
Buy 1 Exorcist, no Changeling.
Buy M-N Monasteries, no Changelings.
Buy N-2 Monasteries, with Changelings.
Use Cultists to draw all the top Monasteries, Changelings, and 1 Exorcist, and 1 Catacombs.

Night phase starts with:

Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and an Exorcist.
-- repeat this loop N-2 times
   Play Changeling on Exorcist.
   Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and an Exorcist.
-- end loop
Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, and 2 Monasteries.

Instead of buying and drawing N/2 Exorcists into our hand before the Night phase, we are drawing N free Changelings into our hand before the Night phase.  Since a draw is cheaper than a buy, it's another win.  You were really onto something.


4
Puzzles and Challenges / Re: Best buying strategy
« on: January 26, 2020, 01:04:43 pm »
Quote
On the other hand, we could consider keeping a Changeling sometimes, since they can be turned into Exorcists or Monasteries. On the margin, we save an Advance to gain the Exorcist/Monastery, and have to pay the cost of drawing the card again in the Night phase. Drawing the card again in Night phase costs 1/3 of an Exorcist-Catacombs in hand pair. That Exorcist-Catacombs in hand cost 2 + 2/3 Advances in the first place, so the total cost of that draw would be 8/9 Advances, so this should be a net savings.
Would it be?  I'm too tired to think about it now, but it's 1/3 of a Cultist draw to gain the Changeling in hand, then 1/3 of another Cultist draw to draw the gained card.  I'll think about it when I finally get another good night of sleep.  It's 3 AM locally as I write this.
You're right of course.  When buying Catacombs, we can keep every other Changeling.  Then buy the Monasteries and Exorcists as before, trashing their Border Villages.  Trash enough Cultists to draw the Exorcists and Monasteries, but then enter Night Phase with the rest still on the deck.

Night phase play then starts out with this loop:

Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and a Changeling.
Play Changeling on Exorcist.
Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw Ghost, Catacombs, and an Exorcist.

We save the cost of drawing all of the Catacombs into our hand.  Big win.

(This replaces an earlier post where I miscalculated the number of Exorcists required.  We still need one for every two Catacombs, plus 1.)

5
Puzzles and Challenges / Re: Best buying strategy
« on: January 26, 2020, 02:59:08 am »
I believe that exchanging for Changeling doesn't count as an additional gain, meaning the Catacombs gain gets 2 cards total and the Tunnel or Exorcist or Monastery gain gets 3 cards, lowering the point totals.
So it's like Trader then, the on-gain effects happen for the card, but then you don't actually gain it.  That makes sense.  That would reduce the VP, but not significantly.
Quote
On the other hand, we could consider keeping a Changeling sometimes, since they can be turned into Exorcists or Monasteries. On the margin, we save an Advance to gain the Exorcist/Monastery, and have to pay the cost of drawing the card again in the Night phase. Drawing the card again in Night phase costs 1/3 of an Exorcist-Catacombs in hand pair. That Exorcist-Catacombs in hand cost 2 + 2/3 Advances in the first place, so the total cost of that draw would be 8/9 Advances, so this should be a net savings.
Would it be?  I'm too tired to think about it now, but it's 1/3 of a Cultist draw to gain the Changeling in hand, then 1/3 of another Cultist draw to draw the gained card.  I'll think about it when I finally get another good night of sleep.  It's 3 AM locally as I write this.

Some other mistakes I made.  My program was off by one on the Tunnel count, so I unexpectedly had 2 coins left.  After buying another Tunnel, I had a free buy but no coins.  Triumph was an insignificant purchase.  I could have bought another Tunnel.

I was so focused on card costs, the card gain count, and the sequence of things that I did not track card trashing (other than for the Monasteries).  That would add up considering we could trash all the gained Gold.

And of course those Tunnels are worth some VP just for being Tunnels.


6
Puzzles and Challenges / Re: Best buying strategy
« on: January 25, 2020, 10:38:01 pm »
Ignoring the infinite solutions, I think there's a solution that scales better than N^2.  You can buy a bunch of Tunnels, followed by a bunch of Cursed Villages.  Not sure how much you're allowed to stack hexes, but War should allow you to gain a bunch of gold (using Canal to skip past tunnels and Watchtower to trash Cursed Villages.)  Then buy a bunch of triumphs.  This doesn't sound very efficient, but it should scale as N^3, so with enough coffers it should eventually be better.

Here's how I think it looks so far.

Squire, Watchtower, Fortress, Tunnel, Catacombs, Cultist, Border Village, Changeling, Exorcist, Monastery.
Alms, Ball, Advance
Tomb

Each buy is proceeded with Travelling Fair, all buys (not trashed) will be topdecked, except Tunnels.

Buy Ball for Watchtower and Blessed Village, gain Sea's Gift, draw Watchtower
Buy Alms for Fortress, reveal Watchtower, trash it.
3 cards gained; 999,990 coins remaining.

We will now be purchasing Tunnels, Catacombs, Exorcists, and Monasteries.
Each with the same method for 2 coins each.

Play Advance on Fortress, gain Border Village and Catacombs.  After resolving on-gain for Border Village, exchange it for a Changeling and trash with Watchtower.
   Either keep Catacombs or reveal Watchtower, trash it, and gain one of {Tunnel, Exorcist, or Monastery}.

The process of gaining 1 Catacombs gains 3 cards total.
Gaining 1 Tunnel, Exorcist, or Monastery gains 4 cards each.

Now we have to draw all the Catacombs, Exorcists, and Monasteries into our hand.

Play Advance on Fortress, gain Border Village, Catacombs, and Changeling. Trash Catacombs, gain Squire. Trash Squire, gain Cultist.  Trash Cultist, draw 3 cards.  Trash Changeling.

This process for drawing 3 cards costs 2 coins and gains 5 cards.

Night Phase

Play Exorcist, trash Catacombs, gain Ghost, Gain Exorcist
Play Exorcist, trash Catacombs, gain Ghost, Gain Squire, trash it, gain Cultist, trash it, draw 2 Ghosts and an Exorcist.

1 Exorcist and 2 Catacombs are combined into 2 Ghosts, gaining a total of 5 cards in the process.

Play all Ghosts
Play all Monasteries, trashing Fortress       

---- breaking down the numbers ----

Buying 166,654 Tunnels costs 333,308 coins and gains 666,616 cards.
Buying 41,666 Exorcists costs 83,332 coins and gains 166,614 cards.
Buying 83,330 Catacombs costs 166,660 coins and gains 249,990 cards.
Buying 125,009 Monasteries costs 250,018 coins and gains 500,036 cards.
Drawing 41,666 Exorcists + 83,330 Catacombs + 125,009 Monasteries takes 83,335 Cultists.  Cost 166,670 coins gaining 416,675 cards.
We have exactly 2 coins left.  Buy Travelling Fair, gain a Tunnel (as above) and then buy Triumph.
The Estate gave us a total of 1,999,936 gained cards.  That's our score so far.
Night Phase
Combining our 41,666 Exorcists and 83,330 Catacombs into 83,330 Ghosts and drawing them gains another 208,325 cards.
Playing each Ghost gains another 166,655 Gold, which brings our total card gain to 13,889,361,086.
Playing each Monastery gains that many more VP, for a total score of 1.7362951e+15 VP.

We started with one million coins and effectively gained 1.7 billion VP per coin.

I want to thank everybody who helped get us this far.  IMHO, collaboration is highly underrated in the real world.

And now that I'm all done with this analysis and have written it up, I just realized that Sewers would practically double the total VP.

7
Puzzles and Challenges / Re: Best buying strategy
« on: January 25, 2020, 05:23:32 pm »
Great improvement again!

I'm not sure I understand what you're saying about Ghost going through a deck twice. From my understanding, a single Ghost can't reveal any card more than once, because when it reveals cards, it temporarily sets them aside so that they're not shuffled if the deck needs to be reshuffled.
You're quite right.  Once again, my error.  So Night Watchman is useless.

8
Puzzles and Challenges / Re: Best buying strategy
« on: January 25, 2020, 10:47:09 am »
Ignoring the infinite solutions, I think there's a solution that scales better than N^2.  You can buy a bunch of Tunnels, followed by a bunch of Cursed Villages.  Not sure how much you're allowed to stack hexes, but War should allow you to gain a bunch of gold (using Canal to skip past tunnels and Watchtower to trash Cursed Villages.)  Then buy a bunch of triumphs.  This doesn't sound very efficient, but it should scale as N^3, so with enough coffers it should eventually be better.
I like the idea.  The use of War seems problematic.
There are 12 Hexes.  The stack is not infinite.  You're allowed to choose the shuffle order, but you have to slog through all of them.  (Even if you interpreted it to be an infinite stack, it would be 12, followed by another 12, etc.).  That means only 1 in 12 Cursed Villages will trigger War.

Might I suggest trying it in the Night Phase?  Ghost will nicely discard the Tunnels and Monastery is a great replacement for Triumph.
With Vampire, this would be unbounded.  Even without Vampire, the night cards can give the strategy a boost.

I'd stock up on a lot of Catacombs, keep Changelings whenever possible, then buy a few Exorcists and Monasteries.
Before proceeding to the night phase, put Ferry on Border Village.
Then play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Border Village, and another Exorcist card costing less than 4 coins, maybe a Monastery.  Exchange the Border Village for a Changeling.
To draw them in, play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Border Village, and a Squire.
Trash the Squire with Watchtower, gain a Cultist, trash that with Watchtower, draw 3 cards.  Exchange the Border Village for another Changeling.
Play the Monasteries last to trash Fortress and gain Tomb points.
The Changelings can gain you more copies of Exorcist and Monastery.
I haven't worked out the ratios or best order, but I think this will do better.
Okay.  First, let it be known that I've been getting little sleep.  I was up again most of the night thinking about this.  Puzzles like this prevent me from turning off my brain.  Who the hell posted this infernal ... Oh, wait.

So I've been thinking that Monasteries are probably cheaper to gain and draw in the buy phase, so I'll skip discussing those.
Another tweak I've been thinking about is deck management.
Edit:  Complete nonsense follows; ignore it.
After playing a Ghost, your entire deck will be in the discard pile.  If you immediately play another Ghost, you have no draw pile, your discards will be shuffled and your entire deck will then be scanned and discarded.  So you only get to discard all the Tunnels once.  It doesn't help to topdeck some gained Gold, they'd just be discarded, then the deck shuffled and scanned once.  But if you force a draw, your deck will become your draw pile and a Ghost will scan it twice.  You could  achieve this by overdrawing with a Cultist, i.e. topdeck 2 cards, draw 3.  But this is the waste of a card draw and you might actually draw a Tunnel.  Still helpful, but better is Night Watchman.  It's also cheaper and gained to the hand.

So after some initial setup, the loop would be
Play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Border Village, and a Night Watchman (to hand).  Exchange the Border Village for a Changeling.
Play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Squire.  Trash the Squire with Watchtower, gain a Cultist, trash that, draw 2 Ghosts and a Changeling.
Play Changeling, gain a Night Watchman to hand.
Play Night Watchman to load the draw pile.
Play Ghost to scan your deck twice.
Play Night Watchman to load the draw pile.
Play Ghost to scan your deck twice.

So for 2 Exorcists and 2 Catacombs, we've done some extra gaining and scanned the deck four times.

9
Puzzles and Challenges / Re: Best buying strategy
« on: January 25, 2020, 02:55:13 am »
Ignoring the infinite solutions, I think there's a solution that scales better than N^2.  You can buy a bunch of Tunnels, followed by a bunch of Cursed Villages.  Not sure how much you're allowed to stack hexes, but War should allow you to gain a bunch of gold (using Canal to skip past tunnels and Watchtower to trash Cursed Villages.)  Then buy a bunch of triumphs.  This doesn't sound very efficient, but it should scale as N^3, so with enough coffers it should eventually be better.
I like the idea.  The use of War seems problematic.
There are 12 Hexes.  The stack is not infinite.  You're allowed to choose the shuffle order, but you have to slog through all of them.  (Even if you interpreted it to be an infinite stack, it would be 12, followed by another 12, etc.).  That means only 1 in 12 Cursed Villages will trigger War.

Might I suggest trying it in the Night Phase?  Ghost will nicely discard the Tunnels and Monastery is a great replacement for Triumph.
With Vampire, this would be unbounded.  Even without Vampire, the night cards can give the strategy a boost.

I'd stock up on a lot of Catacombs, keep Changelings whenever possible, then buy a few Exorcists and Monasteries.
Before proceeding to the night phase, put Ferry on Border Village.
Then play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Border Village, and another Exorcist card costing less than 4 coins, maybe a Monastery.  Exchange the Border Village for a Changeling.
To draw them in, play an Exorcist, trash a Catacombs gaining a Ghost, then gaining a Border Village, and a Squire.
Trash the Squire with Watchtower, gain a Cultist, trash that with Watchtower, draw 3 cards.  Exchange the Border Village for another Changeling.
Play the Monasteries last to trash Fortress and gain Tomb points.
The Changelings can gain you more copies of Exorcist and Monastery.
I haven't worked out the ratios or best order, but I think this will do better.

10
Puzzles and Challenges / Re: Best buying strategy
« on: January 24, 2020, 12:34:52 am »

A simplistic calculation goes like this. (no recent optimizations added; all cards except Vampire and Monastery get trashed).
Buy Canal, Ball for Watchtower and Blessed Village, Alms for Fortress.  Only 19 coins.
Advance Fortress, gain Border Village and Catacombs; trash Catacombs, gain Squire; trash Squire, gain Vampire or Cultist (3 Vampires to 1 Cultist).  2 coins.
In the buy phase, we can gain 374,991 Vampires having gained 1,999,960 cards and trash 1,999,960 cards.
The night phase is similar.
Play Vampire, gain Border Village, Bat, and Catacombs; trash Catacombs, gain Squire; trash Squire, gain Vampire or Cultist or Monastery.
For every four Vampires we play, we end up with three more in hand, having gained another 20 cards and trashed another 17.
So we can do 93,747 iterations, bringing the total gained to 3,874,900 and total trashed to 3,593,659 with 281,241 new Vampires in hand.
We do 70,310 more iterations, bringing the total gained to 5,281,100 and total trashed to 4,788,929 with 210,930 Monasteries in hand.
Playing all of these allows us to trash the Fortress 5,281,100 * 210,930 times to bring the total Tomb VP points to 1.114*10^12.  This is not the optimal switchover point.  I just guessed.
So overall, the scores are on par to the Triumph method.
Whoa!  My first engine used Stonemason/Squire to gain Vampires for 3 Vampires per 6 coins.
For this last calculation I switched over to Advance/Fortress because I thought it was simpler and the same cost (and trashed more cards).  But it gains 3 Vampires per 8 coins.  I should have 33% more Vampires at the end of the buy phase.  With quadratic increases, that should increase my score by about 1.333^2 = 1.7777.  So I think it may have been better overall.  (But still trumped by unbounded).

11
Puzzles and Challenges / Re: Best buying strategy
« on: January 23, 2020, 11:54:52 pm »
Oh, didn't realize that Monastery didn't make you trash all the cards at the same time, letting it trash the same Fortress over and over. It definitely takes less than 7 money to gain a Monastery and draw it into hand. At the very least, we can Advance -> BV -> Catacombs -> Monastery 3 times and Advance -> BV -> Catacombs -> Squire -> Cultist 1 time to get 3 Monasteries in hand for 8 money. This is going to get a lot more VP, but I'll put off a calculation for now.
Yes, I was surprised at your comment that it would perform worse.  Triumph is 1 VP per card gained.  Monastery/Tomb would also be 1 VP per card gained.  But there is the problem of getting the cards into the hand.  On the other hand, there is the usage of Vampires to gain more Vampires.

A simplistic calculation goes like this. (no recent optimizations added; all cards except Vampire and Monastery get trashed).
Buy Canal, Ball for Watchtower and Blessed Village, Alms for Fortress.  Only 19 coins.
Advance Fortress, gain Border Village and Catacombs; trash Catacombs, gain Squire; trash Squire, gain Vampire or Cultist (3 Vampires to 1 Cultist).  2 coins.
In the buy phase, we can gain 374,991 Vampires having gained 1,999,960 cards and trash 1,999,960 cards.
The night phase is similar.
Play Vampire, gain Border Village, Bat, and Catacombs; trash Catacombs, gain Squire; trash Squire, gain Vampire or Cultist or Monastery.
For every four Vampires we play, we end up with three more in hand, having gained another 20 cards and trashed another 17.
So we can do 93,747 iterations, bringing the total gained to 3,874,900 and total trashed to 3,593,659 with 281,241 new Vampires in hand.
We do 70,310 more iterations, bringing the total gained to 5,281,100 and total trashed to 4,788,929 with 210,930 Monasteries in hand.
Playing all of these allows us to trash the Fortress 5,281,100 * 210,930 times to bring the total Tomb VP points to 1.114*10^12.  This is not the optimal switchover point.  I just guessed.
So overall, the scores are on par to the Triumph method.

Quote from: bitwise
    Oh wait, there's an infinite combo with Vampire: play Vampire to gain Cultist, trashing it to draw 3 cards, and "gain" Bat (it goes to our discard but doesn't count as a gain for other effects) drawing 3 cards. Play Bat (trashing Fortress) to "gain" Vampire. This loop can repeat indefinitely, and nets a draw of 1 card every time. With Tomb, this is already infinite, but we can also use the extra card draw to sometimes not gain Cultist but gain other <= 5 costs instead and use those too. Heck, we can just gain Estates and draw them with the infinite extra draw + gains.
When I started this puzzle, I never imagined that a Night Phase engine could be created.  That you found an unbounded one is amazing.  It is sort of a spoiler for the puzzle now.  I don't think further work on it is worthwhile.


12
Puzzles and Challenges / Re: Best buying strategy
« on: January 23, 2020, 05:34:17 pm »
Oh, we can get way more efficient by making our buy Advance on a Fortress in our hand for Border Village, getting E = 6 / 2.

So C = 1000003 - 13 = 999990, and the approximate VP is 1/2 * (999990)^2 * 3^2/(14*3-1) = 109,753,902,450 VP.
Well it appears that Triumph is very well named.  Good job all!  I had considered Triumph, but the "efficiency" I achieved was not high enough to beat my Duke/Duchy strategy.  You've done far better.
I'm going to summarize my strategy here anyway since it uses a mechanism not yet considered and it may spark more ideas.
Purchase Canal, Ferry on Stonemason, Ball for Watchtower and Blessed Village.
Then buy Stonemason, overpay by 1 to gain 2 Squires, trash them with Watchtower to gain 2 attack cards, repeat 333,326 times.
Finally, Alms for a Duchy
The attack gards we gain follow this sequence:   Gain 3 Vampires and topdeck them.  Every 4th attack card is a Cultist which we trash and draw the Vampires into our hand.
NIGHT PHASE
We can play our 499,989 Vampires to gain Duchies and Dukes for about 62.5*10^9 VP.
A devious idea just popped into my head.
It's sort of a Night Phase north of the Artic Circle as it lasts nearly forever.

Previously we had ~500,000 Vampires to play in our Night Phase.
They can be exchanged for any card, up to 5 coins, except another Vampire.
Well, we can use one to gain a Squire, trash it with Watchtower, and gain a Vampire that way.
We can even stretch this out a bit more since we have Canal and Border Village.
Play Vampire, gain Border Village and Catacombs, trash Catacombs, gain Squire, trash Squire, gain Vampire and topdeck it.
Meanwhile, the original Vampire is exchanged for a Bat.
Every 4th iteration, substitute a Cultist, and draw the new Vampires into our hand.
Every iteration gains 5 cards.
If we continued doing this, our 500,000 Vampires could end up playing ~2,000,000 Vampires in total before being exhausted.
Here's the payoff.  Don't play Vampires all the way to extinction.  At some point, switch over and start gaining Monasteries.
We can play these to trash Fortress millions of times for big Tomb points.
I'd flesh it out more, but I'm off to work.


13
Puzzles and Challenges / Re: Best buying strategy
« on: January 23, 2020, 03:38:15 pm »
Oh, we can get way more efficient by making our buy Advance on a Fortress in our hand for Border Village, getting E = 6 / 2.

So C = 1000003 - 13 = 999990, and the approximate VP is 1/2 * (999990)^2 * 3^2/(14*3-1) = 109,753,902,450 VP.
Well it appears that Triumph is very well named.  Good job all!  I had considered Triumph, but the "efficiency" I achieved was not high enough to beat my Duke/Duchy strategy.  You've done far better.
I'm going to summarize my strategy here anyway since it uses a mechanism not yet considered and it may spark more ideas.
Purchase Canal, Ferry on Stonemason, Ball for Watchtower and Blessed Village.
Then buy Stonemason, overpay by 1 to gain 2 Squires, trash them with Watchtower to gain 2 attack cards, repeat 333,326 times.
Finally, Alms for a Duchy
The attack gards we gain follow this sequence:   Gain 3 Vampires and topdeck them.  Every 4th attack card is a Cultist which we trash and draw the Vampires into our hand.
NIGHT PHASE
We can play our 499,989 Vampires to gain Duchies and Dukes for about 62.5*10^9 VP.

14
Puzzles and Challenges / Best buying strategy
« on: January 23, 2020, 01:31:06 am »
Another pick-your-kingdom-and-maximize-your-VP problem.  But in this one, you only have one turn.  And you have just trashed the last card in your deck.  You have no cards in your hand, no cards set aside, no cards on a Tavern mat, no cards on a Native Village mat, no cards on any mat, no cards at all.  You have not purchased any projects or events.  But you do have one million coffers!  How will you spend them?

Pick any legal kingdom except it cannot contain Innovation, Villa, or Mission.  They would allow unbounded VP gains by allowing actions to be played.  All stacks in the kingdom are infinite and never run out of cards.  Split piles will have their normal contents repeated.  For example, the Catapult/Rocks pile would contain 5 Catapults, then 5 Rocks, then 5 Catapults, etc.  You can choose the makeup and order of the Ruins pile.  Assume solo play.

Clearly, Travelling Fair will help the task of buying many cards.  Canal is a good prospect as well.  Will you buy Colonies?  Dominate?

How about Obelisk on Forum?  No Travelling Fair needed since it comes with an extra buy.  You could buy 200,000 Forums for 400,000 VP.  Not so great.  Of course you are not limited to purchasing from a single pile and there are many non-victory cards you can add to your kingdom to help.

As an example, Iíll share the best strategy I came up with for purchasing Castles just to get you thinking and also so you donít have to analyze it yourself for comparison.

Action cards: Stonemason, Watchtower, Cultist, Castles, Forge
Landmarks: Tomb, Obelisk on Stonemason.
Events: Travelling Fair, Ferry, Alms, Ball, Salt the Earth, Triumph
Project: Canal

All purchases are proceeded with buying Travelling Fair.

Buy Canal.  (All cards are 1 coin cheaper.)
Buy Ferry for Stonemason.  (Ferries are free.)
(Ferry canít be applied to Castles since it is not an action supply pile.)
Buy Alms for a Watchtower.
Buy Salt the Earth, trash a Cultist, draw Watchtower into hand.
--- start of Castle buying loop ---
Buy Ball, gain Humble Castle and Crumbling Castle.  Topdeck both.
We will be topdecking all Castles, discarding all Stonemasons, and trashing everything else.
Next Castle in the rotation is Small Castle which is an action.
Buy Stonemason, overpay by 4, gain Small Castle and Cultist.
Reveal Watchtower, trash Small Castle, gain Haunted Castle which comes with a Gold.
(We trashed Small Castle, because itís on-gain effect is to gain the next Castle.  We effectively skip over it and rotate through the stacks faster, gaining more of the better Castles.)
Reveal Watchtower, trash Cultist, discard -1 card token from Ball, draw two Castles into hand.
Buy Stonemason, gain Opulent Castle and Forge.
Buy Sprawling Castle, gaining 3 Estates.
Buy Grand Castle.  This comes with a bonus of 1 VP per Castle in our hand.  We have two.  Next iteration, we will have four, etc.
Buy Kingís Castle.
--- repeat a total of 19,607 times ---
We have just enough money to do an additional partial iteration up to buying Opulent Castle, then use our last buy (without Travelling Fair) on Triumph which leaves us in debt.


We will have gained 137,253 Castles worth 294,105 basic VP.   Our 19,608 Humble Castles are worth 1 VP per Castle gained which is 2,691,256,824 VP.  19,607 Kingís Castles yield 2 VP per Castle for 5,382,239,142 VP.  Grand Castles yield bonus VP for Castles in hand which accumulated 384,454,056 VP.  The Stonemasons yielded 78,428 Obelisk VP.  Tomb also yielded 78,428 VP.  We gained 58,822 Estates.  And triumph gave us 313,724 VP for a grand total of 8,458,773,529 VP.

EDIT:  Oops.  Salt the Earth cannot trash a Cultist.  Instead, to get the Watchtower in hand, buy a Blessed Village and receive the Sea's Gift as a boon (+1 card).  This does not change the VP calculation.

EDIT 2:  Singletee has pointed out that I also made egregious errors with Ball and Small Castle.  I'm not going to recalculate the significant reduction of VP that this would cause.  Just ignore the example.  Thanks singletee.

This is not the best possible kingdom or strategy.  Letís see what you come up with.



15
Puzzles and Challenges / Re: Maximum points
« on: January 04, 2020, 05:07:43 pm »
Here's a spreadsheet with my calculations.
https://docs.google.com/spreadsheets/d/1DWxCZJj6KovasSzS8nmJj9L2Wv3ynD4kqQltLj087J8/edit?usp=sharing
I checked the spreadsheet and it only is counting two trashes per action card in the buy phase.  The majority of purchases are non-actions and that's correct, but for actions, it should be:
Buy Plan for <action>
Buy <action>, trash with Watchtower, trash Fortress (Sewers), trash Fortress (Plan), trash Fortress (Sewers).
You get nearly double for remaining actions.

16
Puzzles and Challenges / Re: Maximum points
« on: January 04, 2020, 04:49:34 pm »
I had a similar argument for not trashing the Mandarins that we gain from the kingdom.  But on further reflection, they should be trashed.  It's a shame, since they generate coin and are considered treasure so they can be gained back from play, but the necessity to topdeck is a big nuisance.
Quote
Ah, I have a method of keeping all of the Mandarins and Watchtowers until the end.  The key was getting rid of the 7 Copper.  On the last 4 plays of Priest (with Sewers), trash all the Copper.  We get near maximum benefit for trashing them and only lose the 7 coins they would have provided.
 
Then our final hand is 1 Fortress, 10 Watchtowers, 10 Mandarins.

Play Mandarin, topdeck Fortress
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Watchtower
Play Watchtower, draw 3 Watchtowers, 2 Mandarins
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Watchtower
Play Watchtower, draw 2 Mandarins, 1 Watchtowers, Fortress
Play Mandarin, topdeck Fortress
Play Mandarin, topdeck Watchtower
Play Watchtower, draw Watchtower, Fortress (the two cards we need to keep in hand)
I'm not sure I see the value in doing this, since we can keep the Mandarins in the supply. They are worth a lot more in the supply since Plan lets us get an additional trash from them.
Ooh.  Quite right.

17
Puzzles and Challenges / Re: Maximum points
« on: January 04, 2020, 02:51:30 pm »
I had a similar argument for not trashing the Mandarins that we gain from the kingdom.  But on further reflection, they should be trashed.  It's a shame, since they generate coin and are considered treasure so they can be gained back from play, but the necessity to topdeck is a big nuisance.
Quote
Ah, I have a method of keeping all of the Mandarins and Watchtowers until the end.  The key was getting rid of the 7 Copper.  On the last 4 plays of Priest (with Sewers), trash all the Copper.  We get near maximum benefit for trashing them and only lose the 7 coins they would have provided.
 
Then our final hand is 1 Fortress, 10 Watchtowers, 10 Mandarins.

Play Mandarin, topdeck Fortress
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Watchtower
Play Mandarin, topdeck Watchtower
Play Watchtower, draw 3 Watchtowers, 2 Mandarins
Play Mandarin, topdeck Mandarin
Play Mandarin, topdeck Watchtower
Play Watchtower, draw 2 Mandarins, 1 Watchtowers, Fortress
Play Mandarin, topdeck Fortress
Play Mandarin, topdeck Watchtower
Play Watchtower, draw Watchtower, Fortress (the two cards we need to keep in hand)

18
Puzzles and Challenges / Re: Maximum points
« on: January 04, 2020, 02:04:51 pm »
Quote
It's also possible to use Procession instead of Upgrade for a similar role. At the beginning of the turn we can Procession a Lurker (with Ferry on Crown) to trash/gain the Priest and gain the Crown. Subsequent Processions can be used on Fortress just like Upgrade, with a bonus of drawing an extra card. In subsequent Processions, we could also Procession a Lurker to gain a Lurker from the trash, and gain the Mandarin. This replaces the Lurker in the trash with a new one. It has the disadvantage of forcing us to gain a 3 cost action, which is currently bad (the Watchtowers), but has the positive effect of enabling Necromancer to be another source of playing Lurkers, if we had more piles. If we're allowing Black Market, this would be an improvement.
Not sure about Procession.  You'd have to give up a Lurker (one iteration) for more trashes.  Also, playing Procession on a Lurker to gain a Lurker and Mandarin is not a benefit unless you can use the 3 cost action.
Necromancer is a great idea and one I hadn't thought of.  But we're out of piles.
We can start the turn with Procession+Lurker to trash/gain the last Priest and gain a 3 cost (Crown with Ferry on it). This would do the same thing as starting the turn with two Upgrades to get the Priest and Crown, but is slightly better as we don't need to have the extra Watchtower in our deck to start. Subsequent Processions can just go on Fortress to do the same thing that Upgrade would (except draw an extra card).

Agreed on Procession on Lurkers not helping unless Necromancer is in the kingdom or we want to gain 3 costs.

The original plan called for the Overlord and Band of Misfits to be emptied before the megaturn.  Your plan to grab the last Crown and Priest right away is great, but we don't have to do it in that order.  It would be slightly better to have the extra Crown and Priest first, so we can use them right away.  Then with Ferry on Band of Misfits, we'd use your Procession on Lurker tick to get the last Overlord and Band of Misfits, which aren't needed until later.
That would mean that we could later do that Procession on Lurker trick to gain the Lurker, Mandarin, and Watchtower.  We're forced to gain the Watchtower but we can save them, play them at the end and trash them with Bonfire for maximum trash benefit.
I had a similar argument for not trashing the Mandarins that we gain from the kingdom.  But on further reflection, they should be trashed.  It's a shame, since they generate coin and are considered treasure so they can be gained back from play, but the necessity to topdeck is a big nuisance.
Quote

Here's an argument that we can use Expedition instead of Sinister Plot:

We would like to be able to build our deck without trashing any of the cards in it, and wind up being able to buy enough Expeditions before our mega-turn to draw our deck.
Near the start of the game, we can Expedition on some turn, then hit 6 or 7 on the following turn to buy Lost Arts on Priest.
After that, it is possible to get a hand with Fortress and 4 Priests, hitting 2+4+6+8=20, which lets us buy Pathfinding (and Training and Seaway) on Priest.
Then, it is possible to buy 9 Crowns, 9 Priests, 9 Band of Misfits, and 9 Overlords, and use them all as Priest on Fortress in the same turn. This will play 36 priests for 36 + 36*37=1368 money and 1+36=37 buys. It is possible to buy 288 Expeditions with that, which is more than enough. (Also, we could buy slightly fewer Expeditions, and buy some of the other cards we need to build up our deck.)

As pitythefool suggested, this allows us to include Sewers instead of Sinister Plot, which doubles all the trashing we can do. I'm fairly sure that over 99% of our generated money comes from trashing, so this approximately doubles our money and VP.
On using Expedition/Sewers instead of Sinister Plot.  Just some ideas.
Start with Ferry on Lurker.  We will later move it to Band of Misfits.  Priority should be Capitalism, not Lost Arts, as it is cheaper.  Capitalism allows all Priests to be played in the treasure phase. I'd next go for Seaway on Priest.  Buy Sewers early and put Plan on Lurker.  Then Fortress and just 3 Priests, or 1 Priest with some combination of 2 (Priest/Overlord/Crown), yields 2 + 6 + 10 = 18 and 4 buys.  Buying 3 Lurkers (zero cost) adds 18 coins (from additional trashing), leaving one buy.  More buys are available from Travelling Fair.  Just an example.  So I think it is very doable.

19
Puzzles and Challenges / Re: Maximum points
« on: January 03, 2020, 06:36:16 pm »

As an estimation, if P is the number of priests we play per loop, X is the number of extra trashes we get per loop (e.g. the Death Carts), and L is the number of loops, then the average trash is worth about P*L (at first worth around 0, then at the end worth around 2*P*L, growing linearly), and in each loop, we trash X+P cards. Putting that all together gives around P*L*(X+P) for the average loop, or P*L*(X+P)*L = P(X+P)L^2 for all loops.

Your solution has P=18, L=40, X=9 for 18 * 27 * 40^2 = 777,600 which looks consistent with your 758,000 figure.
Nice equation.  I should have done something similar to sanity check my spreadsheet.
Quote
We can replace City with Sacrifice since our kingdom doesn't have any Victory cards that can be recovered from the trash. Sacrifice gives us the card draw we need but also lets us trash. This should change X=9 to X=17, which will make the total around 18 * 35 * 40^2 = 1,008,000, which is around a 230,400 money improvement.
Yes.  A good improvement.
Quote
  • We should buy as many Treasures as possible beforehand and just play them in our Buy phase, since we can Bonfire them (and they give money!). Not the Silvers, of course.
Yes.
Quote
  • The same would apply to all the other actions that we could play at the very end of the turn, except...
  • If we include Plan, then buying actions gives double the value from before.
Yes.  Plan would be the way to go.
Quote
  • Delve
Yes.  I only took it out to simplify things.
Quote
  • Triumph on the last Estate
I actually did the math on this one to see if VP from Triumph beat VP from trashing the Estate and gaining more Conquests.  D'oh.  I forgot you could do both.
Quote
I believe that spending two Upgrades at the beginning to gain Crown/Priest (Upgrade a Fortress and an extra Watchtower) would be slightly better
I really like the idea of picking up the 10th Crown and Priest at the beginning.  Big win.
Quote
It's also possible to use Procession instead of Upgrade for a similar role. At the beginning of the turn we can Procession a Lurker (with Ferry on Crown) to trash/gain the Priest and gain the Crown. Subsequent Processions can be used on Fortress just like Upgrade, with a bonus of drawing an extra card. In subsequent Processions, we could also Procession a Lurker to gain a Lurker from the trash, and gain the Mandarin. This replaces the Lurker in the trash with a new one. It has the disadvantage of forcing us to gain a 3 cost action, which is currently bad (the Watchtowers), but has the positive effect of enabling Necromancer to be another source of playing Lurkers, if we had more piles. If we're allowing Black Market, this would be an improvement.
Not sure about Procession.  You'd have to give up a Lurker (one iteration) for more trashes.  Also, playing Procession on a Lurker to gain a Lurker and Mandarin is not a benefit unless you can use the 3 cost action.
Necromancer is a great idea and one I hadn't thought of.  But we're out of piles.

20
Puzzles and Challenges / Re: Maximum points
« on: January 03, 2020, 02:56:22 pm »
Use Travelling Fair to buy Conquest 141,623 times for 5,664,920 VP.
I have a minor tweak to the method in my last post.
Remove Death Cart from the kingdom and add Upgrade.
Setup is the same as before, except 9 Upgrades in hand instead of 8 Death Carts.
The City, Crown, Priest, Lurker loop sequence is the same (except no Death Carts).
We get fewer coins per iteration, but after all the Lurkers and Lurker variants have run out, we can play an Upgrade, trash Fortress, and gain a Mandarin from the kingdom, and trash it with Watchtower.
This lets us iterate the sequence 9 more times.
Total earnings is now 808,592 coins and trashing additional cards now gains 1,764 coins each.
Trash the remainder of the kingdom and Bonfire the cards in play, and we end up with 1,268,193 coins.
We can buy Conquest 158,524 times for 6,340,960 VP.

21
Puzzles and Challenges / Re: Maximum points
« on: January 02, 2020, 11:50:43 pm »

Some thoughts I had:
  • If we use Inheritance, then we have to set aside a Priest and can't use that 10th Priest in our looping. Given that, it might not be worth it to have it on Priest?
  • Bonfire lets us also trash all the cards we've played for money without enabling an infinite combo.
  • Does Forge really work out better than Watchtower? Getting to pay beforehand for things is definitely nice, but we don't get to trash all those silvers that we're buying.

Also, there is some non-infinite strategy with Lurker if you take out Scepter. You can buy Mandarin, returning Crowns/Priests to your deck, Bonfire everything else in play, buy Villa, then do some KC+Lurker-ing to recover your actions and play those again. This doesn't seem obviously better though.

Redo of my previous post. Improved strategy with suggestions from Bitwise.

The kingdom will have:

   Platinum/Colony

Action cards

   Priest
   Fortress
   Watchtower
   Mandarin
   Crown
   City
   Lurker
   Overlord
   Band Of Misfits
   Death Cart
   Young Witch

Events

   Inheritance
   Pathfinding
   Seaway
   Training
   Lost Arts
   Travelling Fair
   Bonfire

Projects

   Capitalism
   Sinister Plot

Setup to be done before the megaturn (in no particular order):

Inheritance on Lurker
Pathfinding, Seaway, Lost Arts, and Training on Priest
buy Capitalism
buy Sinister Plot
Acquire only these cards (should be easy using Lurker)
   10 Overlords
   10 Band of Misfits
   9 Lurkers
   9 Priests
   9 Crowns
   9 Cities
   8 Death Carts (comes with 10 Ruins)
   7 Estates (for a total of 10)
   1 Fortress
   1 Watchtower
   1 Mandarin
   Acquire sufficient tokens on Sinister Plot to draw your entire deck.

Megaturn:
Trigger Sinister Plot to draw our entire deck.

Play 8 Cities, leave 1 in hand
Play Crown on Priest, trash Mandarin, trash Fortress
Play 5 Crowns on 5 Priests, trash the 10 Ruins
Play all remaining Crowns on Priests, trashing Fortress
Play the 8 Death Carts, trashing Fortress
Play Lurker, gain Mandarin from trash, trash with Watchtower
   All Cities, Crowns, Priests, and Death Carts are returned to deck.
   Put Cities on top, followed by an alternating sequence of Crowns and Priests, and then the Death Carts.
------- 2nd iteration, same play sequence -------
Play 8 Cities, leave 1 in hand
Play 9 Crowns on 9 Priests, trashing Fortress
Play 8 Death Carts, trashing Fortress
Play Lurker, gain Mandarin, trash with Watchtower, stack deck as before
--------------------------------------------------
We continue to play this loop until we are out of Lurkers.
Then we continue with Estates, then Band of Misfits, then Overlords as Lurkers.
The sequence is thus repeated 39 times for a total of 40 executions.
We play Priest 18 times and we trash 27 cards per iteration. (Only 26 for the last iteration)
Death Carts and Cities add coins and buys.
Everytime we play Priest, the reward we get for trashing a card goes up, hence the earnings go up with every iteration of the loop.
[edit: Due to a late night spreadsheet error, my original earnings were way too big.  They have been corrected.]
The 1st iteration earns 698 coins.
The 2nd iteration earns 1,634 coins.
The 3rd iteration earns 2,570 coins.
...
The last iteration earns 37,202 coins for a grand total of 758,000 coins and also 1,040 buys.
Additional trashing earns 1,440 coins per card.
Finally, play the Fortress.
(treasure phase)
Play your 7 Copper
(buy phase)
There are 206 cards left in the kingdom.
   {1 Priest, 9 Fortress, 9 Watchtower, 9 Mandarin, 1 Crown, 1 City, 1 Lurker,
   2 Death Carts, 10 Young Witch, 10 Curses, 46 Copper, 40 Silver,
   30 Gold, 12 Platinum, 1 Estate, 8 Duchies, 8 Provinces, 8 Colonies}
Buy everything and use Watchtower to trash them.
There are 55 cards in play, buy Bonfire to trash them all.
   { 10 Overlords, 10 Band of Misfits, 10 Estates, 9 Lurkers, 8 Death Carts, 1 Fortress, 7 Copper }
Total money spent so far = 860 coins.
All the trashing earns another 261 x 1440 = 375,840 coins for a total of 1,132,987 coins remaining.

Use Travelling Fair to buy Conquest 141,623 times for 5,664,920 VP.

22
Puzzles and Challenges / Re: Maximum points
« on: January 01, 2020, 11:06:41 pm »
Nice work going through all that!

Some thoughts I had:
  • If we use Inheritance, then we have to set aside a Priest and can't use that 10th Priest in our looping. Given that, it might not be worth it to have it on Priest?
Darn.  You're right.  I originally had it that way for that very reason; choosing to empty the Estate pile rather than the Priest pile.  But then I forgot and changed it when I realized that Mandarin doesn't return Estates back to the deck.  It means that we'd play two less Priests every iteration.  I still think Inheritance is the way to go as it increases the number of Priests that we can play.
Quote
  • Bonfire lets us also trash all the cards we've played for money without enabling an infinite combo.
A good addition.  I missed it.
Quote
[/li][li]Does Forge really work out better than Watchtower? Getting to pay beforehand for things is definitely nice, but we don't get to trash all those silvers that we're buying.[/li][/list]
Watchtower is nice, but we'd be using coins and buys at the end.  I don't think you end up trashing any more cards, so the total VP would be less, unless I'm missing something.
Quote
[/list]

Also, there is some non-infinite strategy with Lurker if you take out Scepter. You can buy Mandarin, returning Crowns/Priests to your deck, Bonfire everything else in play, buy Villa, then do some KC+Lurker-ing to recover your actions and play those again. This doesn't seem obviously better though.
The big advantage to Lurker is not gaining Crowns/Priests, but regaining Mandarins.  Without gain-from-trash, you can only gain Mandarin 10 times.  Each time enables the entire loop.  But reclaiming trash gets really complicated.  There's probably something brilliant Lurking there though.  (see what I did there?)

I'm also wondering if there is some action I can drop to add Black Market.  We only need one Forge or Watchtower.  If we had an alternate drawing scheme, we'd only need one Fortress.
Also, if we drop one of the Projects, we could add Sewers and double the number of trashes.

23
Puzzles and Challenges / Re: Maximum points
« on: January 01, 2020, 03:51:01 pm »
... the real winner here is probably Conquest, as it is only limited by our money+buys.

The best way I can think of to get lots, but not infinite money, is with Priest/Fortress/Watchtower and Travelling Fair.
Kudos to Bitwise for suggesting Conquest.  It is an excellent way to acquire VP, granted that you can buy the event many, many times after acquiring all of the Silver in the same turn.  I worked on an alternative to using Priest and trashing to generate coin.  I decided to just use Copper!
In a nutshell, it went like this:
   King's Court a ton of Coppersmiths (with the help of Overlords, Band of Misfits, Inheritance, Crowns, and Scepters)
   Play 52 Copper for a ton of coin
   Buy a Mandarin; Coppers all return to deck.
   Buy a Villa
   Play a Messenger; Coppers go to the discard pile
   Play a Counting House; Coppers go back to my hand
   Repeat.

I managed to buy Conquest more than 10,500 times for ~420,000 VP.
How does this compare to Bitwise's strategy?  I decided to flesh it out more to find out.
TO BE CLEAR, this strategy has all been suggested by Bitwise.  Use of Priest, Forge, Mandarin, Villa, Crown were all spelled out by him.  I just put it all together in a (hopefully) optimal implementation.

The kingdom will have:

   Platinum/Colony

Action cards

   Priest
   Fortress
   Forge
   Mandarin
   Villa
   King's Court
   Overlord
   Band Of Misfits
   Scepter
   Crown
   Young Witch

Events

   Delve
   Inheritance
   Ferry
   Pathfinding
   Lost Arts
   Seaway
   Training
   Travelling Fair

Projects

   Capitalism
   Sinister Plot

Setup to be done before the megaturn (in no particular order):

Ferry on King's Court (allows play by Overlord)
Inheritance, Pathfinding, Lost Arts, Seaway, and Training on Priest (it ought to be Pope by now!)
buy Capitalism
buy Sinister Plot
Acquire
   All the Priests
   All the Overlords
   Other than leaving the Silver, Mandarin, and Villa piles alone, buy everthing else you can without emptying a third pile.
   Acquire sufficient tokens on Sinister Plot to draw your entire deck.

Megaturn:
Trigger Sinister Plot to draw our entire deck.
(Every time we play a Priest, we will trash a Fortress, so that will not be mentioned again.)

(action phase)
Play 9 King's Courts and 8 Overlords as King's Courts
Play 10 Priests, 2 Overlords, 10 Estates, and 9 Band of Misfits as Priests (3 times each).
   The 1st time we play a Priest, we get 3 coins
   The 2nd time we play a Priest, we get 3 coins + 2 coins for trashing
   The 3rd time we play a Priest, we get 3 coins + 4 coins for trashing
   The nth time we play a Priest, we get 3*n + 2*(n-1) coins
[Priest has been played 93 times]
(treasure phase)
Play 8 Crowns (saving one), each playing Scepters, replaying Priest each time.
Play the last Scepter, replaying Priest.
[Priest has been played 110 times]
(buy phase)
Buy Mandarin; all Priests, Crowns, Scepters, Villas that are in play are put on deck.
   Alternate Priests and Crowns on top, then remaining Priests, then Scepters.
Buy Villa
(action phase)
Play Crown on Fortress; draw a Crown and a Priest
Crown the Priest; draw another Crown and Priest
Repeat until you draw the last pair, then just play the Priest (saving the last Crown); draw another Priest.
Play that Priest to draw the last Priest.
Play the last Priest to draw a Scepter.
Play Scepter to replay Priest; draw another Scepter.
Repeat until you've played all Scepters.
[Priest has been played 137 times]
Buy Mandarin, Villa, do it all again.

On the 8th iteration and beyond, we do the same, except we save one Scepter along with the one Crown.
On the 9th and 10th iterations, we do not want to play our last Fortress, so we Crown the Scepter instead to replay a Fortress twice.
After we buy the last Mandarin and Villa, the loop stops.  We play all of our Crowns, Priests, but not Scepters for the last time.
Priest has been played ~350 times for about 1,750 coins and 350 buys.  Trashing a card gains ~700 coins.
Our hand now contains:
   {10 Mandarin, 10 Villa, 9 Forge, 1 Fortress, 1 Scepter (others are on deck), 9 Young Witch,
   52 Copper, 29 Gold, 11 Platinum, 7 Duchy, 7 Province, 7 Colony, 9 Curse}
Play one Forge and trash everything left in our hand for 161 x 700 = 112,700 coins, bringing our total to around 114,450.

Buy Delve 38 times
Use Travelling Fair to buy Conquest ~14,300 times for ~572,000 VP.

And thus my strategy has been beaten.  Curses Bitwise, I have been foiled again!  (good job)

You also mentioned Lurker, but it becomes possible to repeat the iteration an unbounded number of times.
Something like:  Crown Scepter, replay Priest twice, trash Mandarin, trash Villa.
   Crown Scepter, replay Lurker twice, gain Mandarin, gain Villa.
   I suppose this could be sufficiently crippled by limiting the draw into the hand, but I'm busy working on a different scheme.



24
Puzzles and Challenges / Re: Maximum points
« on: August 31, 2019, 06:42:05 pm »
Alright, easier definition (suggested by SirPeebles): Among kingdoms with an upper bound on available VP, what is the highest attainable score?

Old theme, but new cards!

Kingdom:
   Platinum/Colony, no Shelters

   Ferry
   Inheritance
   Travelling Fair
   Capitalism
   Lost Arts

   (The last three Events are not a necessity, but they speed things up considerably.)

   Young Witch
   Native Village (bane)
   Goons
   Band Of Misfits
   Overlord
   Page/Travellers
   Peasant/Travellers
   Scrying Pool
   Count
   Cultist/Ruins
   Rats


Steps:

Buy Ferry for Goons.  Goons now has a price of 4 and can be selected by Band Of Misfits, Overlord, and Inheritance.
Buy a Goons.
Buy a Native Village.
Use Native Village to transfer cards to the mat until they can be pulled in for a 7 coin buy.  Buy Inheritance for Goons.  Our 3 starting Estates are now Goons.
Buy Capitalism.  Goons and Estates can now be played without actions in the buy phase.
Buy a Page.

We will cycle the Page to a Champion.  Only play Treasure Hunter and exchange to Warrior after a turn which did not gain a card;  we don't want to gain any Silver.  When playing Hero, we are forced to gain a treasure; pick Potion.  We will only obtain 1 Champion.  That Potion, along with the Goons set aside for Inheritance will be the only two cards in the entire kingdom that we will not purchase.  When we get around to buying the other travellers, we will do the maximum exchanges on the other Pages, up to Hero.  Since Pages get returned to the supply, buying the last Page will be the 26th purchase.  We will also do the maximum number of exchanges on Peasants.  That pile therefore represents 30 purchases.  I will mention that it is possible to play an Overlord (or BoM or Inherited Estate) as a Page.  And when it is exchanged, the Overlord is returned to the Overlord supply pile, not the Page pile.  This does not allow any unbounded purchasing, as the number of possible exchanges is still bounded by a small fixed number.  It is disadvantageous to do this.

While cycling for our Champion, buy Estates (but don't empty the pile), buy a Count, buy Lost Arts for Count.
Start moving all Copper to the Native Village mat one at a time by using Count to topdeck, followed by Native Village.
After the Potion is gained, buy 2 Scrying Pools, then move the Potion to the Native Village mat.

After the Champion is in place, play proceeds as follows:
Play Scrying Pool, draw entire deck.
Play Count, topdeck a Scrying Pool (for next turn).
Play all Goons, Estates (Goons), Band of Misfits as Goons, Overlords as Goons.
Buy more actions.
Repeat.

After buying all but one Estate, buy all but one Goons. (One must remain for enabling BoM and Overlord).  Then you can empty the Band of Misfits and Overloard piles.  You should not empty any more piles until the last turn.
Next, buy 4 more Counts and 3 more Native Villages.
Now we continue to buy all the actions we can, but also start buying non-action cards.  We will be limited to buying four per turn.  First buy Travelling Fair, then we can topdeck the non-action cards, draw them into our hand for the next turn, use Counts and Native Villages to transfer them to the mat.
Priority on non-action cards should be 7 more Potions, then the Platinum, Gold, Silver.
Priority on action cards should be Page and Peasant to start the long exchange cycles.
When we gain Teachers, we might as well benefit:  +1 coin to Band of Misfits, +1 buy to Overlords.

There is no need to buy any Colonies, Provinces, Duchies, or Copper by using this relatively slow method.
After all but one Platinum, Gold, Silver remain, and only one card in each of the kingdom piles remain (excepting the 8 Scrying Pools), we can jump right to the last turn.

Play Scrying Pool, draw deck.
Play all 9 Counts, topdecking actions and gaining +3 coins each.
Play the second Scrying Pool to redraw the topdecked actions.
(We may not need those actions, but Scrying Pool is an attack card.)
Play all 38 Goons variants as usual.
Play all 9 Groundskeepers.
Play all 9 Peasants for +buys, +coins.
Play all 5 Warriors.  Does nothing, but they are attack cards.
Play Abandoned Mines.
Play all 5 Soldiers (this generates 245 coins!)
Play a Native Village, pull in all of the cards from the mat.
Play all of the Patinum, Gold, Silver, Copper, and Potions you have.
You have enough coin to buy all of the Duchies, Provinces, Colonies, Copper, and all other remaining cards.
You have only 57 buys and there are 92 cards left, but there is sufficent money to buy Travelling Fair as needed for the extra buys.

Scoring analysis:

   8 Colony - 80 VP
   8 Province - 48 VP
   8 Duchy - 24 VP
   11 Estates - 11 VP
   10 Curses - -10 VP

80 + 48 + 24 + 11 - 10 = 153 VP

9 Groundskeepers * 25 victory cards gained (only 1 Estate is counted) = 225 VP

Number of each card (out of total in kingdom) purchased with 38 effective Goons in play.
 
   Copper - 46 of 53
   Silver - 40
   Gold - 30
   Platinum - 12
   Potion - 15 of 16
   Colony - 8
   Province - 8
   Duchy - 8
   Estate - 1 of 11
   Curses - 10
   Peasant/Travellers - 30
   Page/Travellers - 25 of 26
   Cultist/Ruins - 20
   Rats - 20
   Young Witch - 10
   Goons - 1 of 10
   Band of Misfits - 0 of 10
   Overlord - 0 of 10
   Native Village - 9 of 10
   Scrying Pool - 8 of 10
   Count - 9 of 10

463 cards * 76 VP each = 35,188 VP

Ignoring the not insubstantial VP earned while buying the cards for the engine (over a thousand), we end up with a total of 35,188 + 225 + 153 = 35,566 VP

Any of the following Landmarks would add some VP, noted in parentheses:

   Tower (281)
   Palace (90)
   Museum (76)
   Orchard (76)
   Keep (75)
   Obelisk (40)
   Triumphal Arch (30)
   Defiled Shrine (22)
   Aqueduct (16)
   Fountain (15)
   Arena (12)
   Basilica (12)
   Baths (12)
   Battlefield (12)
   Colonnade (12)
   Labyrinth (12)
   Mountain Pass (eight)

Final note:  I expected Vineyards to be one of the final kingdom piles.  With Groundskeepers being played and all of the action cards gained, I expected 8 Vineyards to beat out a pile of 10 action cards.  And it does.  But it does not beat out a pile with 20 cards, hence Rats wins.

An obvious way to increase the score would be to add a Black Market deck, but I'll leave that to someone else.


25
Puzzles and Challenges / Re: The Ultimate Legal Fairground
« on: August 30, 2019, 07:17:56 pm »
In my next post to this thread, I will reconsider the title "The Ultimate Legal Faiground".

How much can a Fairgrounds be worth in a legal kingdom?
I will calculate an answer, both with and without Black Market.
Let's look at the contributions to unique card counts.

Basic Supply (with Platinum and Colony) - 9
Shelters - 3
Young Witch - 1  (it's a free 11th pile)

We have 10 kingdom cards to fill.  One must be Fairgrounds.  That leaves 9.

Fairgrounds - 1
Knights - 10
Castles - 8
Marauder/Ruins/Spoils - 7
Tournament/Prizes - 6
Page/Travelers - 5
Peasant/Travelers - 5
Exorcist/Spirits - 4
Secret Cave/Magic Lamp/Wish - 3
any Alchemy card/Potion - 2

Total: 64 unique cards.  Only two piles need to be emptied so there is no three-pile concerns.  All can be obtained, given time.  Fairgrounds is worth 24 VP.

I note that Necromancer comes with 3 unique Zombies, but we'd have to give up a kingdom pile for Lurker, Graverobber, or Rogue in order for the Zombies to be obtained, so no advantage here.
It's not a problem with a Black Market Deck though.  We will allow 60 cards, like ShuffleIT.

Basic Supply (with Platinum and Colony) - 9
Shelters - 3
Young Witch - 1

Fairgrounds - 1
Black Market - 1
Knights - 10
Castles - 8
Page/Travelers - 5
Peasant/Travelers - 5
Encampment/Plunder - 2
Patrician/Emporium - 2
Settlers/Bustling Village - 2
Catapult/Rocks - 2

Black Market Deck:

Marauder/Ruins/Spoils - 7
Tournament/Prizes - 6
Exorcist/Spirits - 4
Necromancer/Zombies - 4
Secret Cave/Magic Lamp/Wish - 3
any Alchemy card/Potion - 2
Vampire/Bat - 2
Hermit/Madman - 2
Urchin/Mercenary - 2
Other Heirlooms x6 - 2
Lurker - 1
other cards - 44

Total: 130 unique cards.  The Ultimate Fairgrounds is worth 52 VP.

I note that there wasn't enough room to fit two additional split piles into the kingdom;  Gladiator/Fortune and Sauna/Avanto.

If I missed something, please leave a comment in the thread.  I'm thinking that it may be fun calculating the values of the Ultimate Gardens, the Ultimate Silk Road, and the Ultimate Vineyards.  I did a search of the puzzle forum and I couldn't find these questions being asked before.
There was, however, this somewhat related question that was asked a few times:

Most points with no VP chips. http://forum.dominionstrategy.com/index.php?topic=1047
Theoretical Maximum Points in Deck  http://forum.dominionstrategy.com/index.php?topic=2586
Maximum Points http://forum.dominionstrategy.com/index.php?topic=9097

New cards make it possible to beat all of the posted solutions.

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