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Messages - pitythefool

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1
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: January 27, 2021, 08:21:22 pm »
play Hero to gain Philosopher's Stone (topdeck)

There have been a lot of Scrying Pool/Stonemason engines posted here.  I really like the usage of Hero, though.  That's novel.  It takes 3 turns for gained Pages to be used as Heroes though.  That really dampens the growth.  Imagine that you could buy Heroes directly and use them the very next turn.  And also, imagine that they generate 3.5 Scrying Pools instead of just two.  Then the growth would be on par with an engine I posted in this thread earlier [Reply #24 on: November 10, 2018, 11:12:10 pm].

But having said that, I like when people post new ideas and yours has potential.  It has two things going for it that I see.
One:  Warriors produce a lot of coin.  Try calculating how much (and remember that Scrying Pools are also attack cards).  Once again, though, you would be looking at a two turn delay in Warrior growth;  training on Stonemason may generate more.
Two:  With Capitalism purchased, Hero is considered a treasure and may be returned to your deck by gaining a Mandarin.  Unfortumately, I can not come up with any way to limit Mandarin gains, in this kingdom, off the top of my head.

2
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: January 15, 2021, 06:43:41 pm »
This is all insignificant but fun to think about.
Another thing my model has let me discover is the optimum ratio of Falconers-to-Squires to gain.  Earlier analysis had pegged it at 0.5 (equal amounts of each).  This seemed reasonable since they contributed to the increase of Liveries nearly equally and neither Falconers nor Scrying Pools could be returned from play.  It turns out that the algorithm is not sensitive to this value at all.  If you place the ratio at the extremes (close to 0.0 or 1.0), the exponential growth drops off  to about 2.0, but anywhere in between and the growth tends towards 2.414.  But a ratio of 0.689655 gets there just a bit quicker.  It's because Falconers also produce Patrons and Patrons do get returned from play by gaining a Mandarin, hence they repeatedly contribute to gaining more Liveries.

If you start with just 5 Liveries, 5 Falconers, 5 Scrying Pools, and 7 Golems, along with the minimum number of other components, and acquire Falconers/Squires at the 0.5 ratio, you will end up with 3.967*10^310 Liveries.  At a ratio of 0.689655, you end up with 5.742*10^317 Liveries; more than 10 million times as many.  The fact that this isn't really significant is a testimony to how large these numbers are.

If you continue both for a total of 23 Golems the difference in Liveries is 10^(4.132*10^8) versus 10^(4.229*10^8).

3
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: January 11, 2021, 07:06:38 pm »
... seems a little bit sketchy to me.

I've had a chance to reexamine the analysis.  It was indeed a bit sketchy.
I was maximizing the right expression to find the best ratio of Falconers to Squires, but it was looking an iteration further ahead.  For growth, we should simply look at L' relative to L.  L' was correctly stated as O(L*F*S).
Regardless of the starting values, a couple of Golem iterations leaves the cards in very specific ratios;  F = S = H;  L = F^(sqrt(2))
I wrote a program that reimplemented and verified my spreadsheet.  I took it to 23 Golems.  It verified the exponential growth of Liveries to be 1+sqrt(2), which can be calculated from the relationships above, to eight decimal places: 2.41421356.

Liveries after G Golem iterations is L^(2.414*G).  In the final iteration we do not produce more Liveries but convert half the Horses to Golems for the next turn, so we end a turn with G = L^1.707, so growth can be expressed as L^(2.414*L^1.707)) per turn.

Also, a couple tweaks to the procedure.  For the main Hermit loop, I stated "Exit loop when only 4 Scrying Pools remain, or 5 Scrying Pools if there is only 1 Golem".  However, you can stay in this loop until you are down to 2 Scrying Pools.  The 2nd Scrying Pool will draw the entire deck which includes more Scrying Pools created by the Count when it trashed Squires.
Also, it left a very large number of Horses in our hand at the beginning of the buy phase.  I did not want to play the Quarry since I wanted to gain Horses in the buy phase.  But I could have played the Quarry, played the Horses as Hermits and gained Liveries.  We would not gain Horses for our purchases, but I think having more Liveries for the first iteration is a win.
But I thought of an even better strategy.  Do not play Quarry, but still play the Horses as Hermits and gain Squires.  Then in the buy phase, Donate and trash the Squires to gain Scrying Pools.  While at it, pre-trash the Mandarin as well.  Just a slight catch:  the Quarry which we topdecked gets shuffled again.  We can work around that by setting two Scrying Pools aside with Way of the Turtle and simply take Herbalist out of the kingdom.
This is all insignificant but fun to think about.

EDIT:  Corrected the number of Horses and Golems again.

4
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: December 22, 2020, 07:10:49 pm »
I believe that the latest Trader change kills the triple up arrow solution. It had a good run.  :'(
I tried to make a replacement for bitwise & paulfc's brilliant 3 up-arrow solution, which now seems invalid due to recent rule changes.  I am using Livery & Falconer in place of Black Market & Haggler.  But even with Mandarin thrown in, it does not achieve 3 up-arrow growth.  It is superior to the other 2 up-arrow solutions in this thread, but it does not lend itself to easy analysis.  I am hoping that working together, we may improve upon it.

Kingdom:  Squire, Changeling, Black Market, Scavenger, Patron, Falconer, Livery, Scrying Pool, Golem
Black Market:  Mandarin, Rogue, Vault, Count, City Quarter, Herbalist
Events:  Travelling Fair, Donate
Landmark:  Obelisk on Livery
Projects:  Capitalism, Academy
Ways:  Way of the Seal, Way of the Turtle, Way of the Mouse -> Hermit

Victory points are generated by Obelisk.

Getting started: (in no particular order):
    buy 2 Black Markets and then buy all the cards from the Black Market
    buy the projects Capitalism and Academy
    buy Seaway (using Quarry) and Training for Livery
    buy 2 Scavengers
    buy lots of Scrying Pools (or alternately Squires and trash them with Donate, gain Scrying Pools)
    buy lots of Liveries, Falconers, and Golems
    buy Donate to trash unwanted cards

Starting deck

     1 Mandarin
     1 Herbalist
     1 Vault
     1 Count
     1 Rogue
     1 City Quarter
     2 Black Markets
     2 Scavengers
     S Scrying Pools
     L Liveries
     F Falconers
     G Golems

I have denoted the start and end of the Black Market treasure phases, to indicate where I play action/treasures as treasures.

Turn start:  (Quarry is in hand, Scrying pool has been set aside as the result of the previous turn)

    play Scrying Pool (from Way of the Turtle), draw entire deck (+action)
    play Herbalist as Way of the Seal

<begin outer loop>
    play Black Market
    <begin Black Market treasure phase>
        play all Liveries
    <end Black Market treasure phase>
    <begin Horse gaining loop>
        play Falconer, gain Patron
            Patron is a four coin card so we gain one Horse for every Livery played this turn (not just those currently in play).
            Patron is a card of three types and thus we can react to gaining it by playing another Falconer from our hand.
        repeat this sequence for all Falconers thus playing them all with just one action.
        (each gained action card comes with +action from Academy.  It should be pretty clear by now that we will never run out of actions.)
    <end Horse gaining loop>
    play Black Market
    <begin Black Market treasure phase>
        play Quarry
    <end Black Market treasure phase>
    For all Horses and Patrons we also have in hand,
        play <action> as Way of the Mouse (Hermit), gain Livery
    (Quarry made 5 coin cards affordable to Hermit, but they do not trigger Liveries to produce Horses.)
    (each gained action card comes with +action from Academy.)
    play Scrying Pool, draw Horses, Patrons, and Liveries
    For all Patrons and all Liveries and all-but-one Horse,
        play <action> as Way of the Mouse (Hermit), gain Livery
    play Scrying Pool, draw Liveries
    <begin main Hermit loop>
        For all Liveries,
            play Livery as Way of the Mouse (Hermit), gain Livery
        play Scrying Pool, draw Liveries
        {Exit loop when only 4 Scrying Pools remain, or 5 Scrying Pools if there is only 1 Golem}
    <end main Hermit loop>
    For all Liveries (one final time),
        play Livery as Way of the Mouse (Hermit), gain Falconer
        play Livery as Way of the Mouse (Hermit), gain Squire
    play Scrying Pool, draw Falconers and Squires
    play Vault, draw <two cards>, discard all but Squires, Scavengers, Golem, Mandarin, and <two cards>
    play Scavenger, topdeck Scrying Pool
    play Scavenger, topdeck Count
    play Golem, reveal Count and Scrying Pool
        play Count, discard <two cards>, trash hand which is just Mandarin and a lot of Squires, gain Scrying Pools for trashing Squires
        play Scrying Pool, draw entire deck (only non-action is Quarry which is in play)
    play Rogue, gain Mandarin from trash,
        topdeck treasures (Quarry, Black Markets, Liveries, Patrons, Count, Rogue, Vault, Scavengers, Herbalist)
        put Quarry and a Black Market on top
    play Horse, draw Quarry and a Black Market
    play Scrying Pool, draw entire deck (Quarry already in hand)
    {Exit outer loop when no Golems remain}
<end outer loop>

    play Black Market
        play all Liveries
    For half of your Falconers,
        play Falconer, gain Patron and Horses, convert all to Changelings and discard.
    For the remaining Falconers,
        play Falconer, gain Patron and Horses, topdeck all
    play Scrying Pool.  Draws all of the topdecked Patrons and Horses up to the first Changeling
    play City Quarter.  Draws all of the Changelings.
    play last Scrying Pool as Way of the Turtle.

Buy Phase:

    play all Patrons
    play Herbalist
    DO NOT play Quarry

    buy Travelling Fair for extra buys as needed
    then spend everything on Liveries, gaining a lot of Horses in the process

Night Phase:
    exchange the Changelings for Golems

Cleanup:
    topdeck the Quarry (by way of Herbalist)
    one Scrying Pool has been set aside (by Way of the Turtle)

Proof of finiteness

Liveries in large number are a powerful force.  If Horses are allowed to gain more cards that produce Horses unimpeded, unbounded loops are easy to create even without the presence of Mandarin.  Add Mandarin and Capitalism and now you have a lot of exploits to plug.  The kingdom ended up being very complicated because of it, due to the addition of necessary interlocks.  Here's the reasoning why play is bounded.

The case of not purchasing Capitalism.

We have only one Mandarin and one Rogue.  To gain the Mandarin, we first have to trash it and then gain it back from the trash with the Rogue.  We can trash it easily with Hermit.  When we gain the Mandarin back, the only thing going back onto the deck will be the Quarry, so the Rogue cannot be played again and we cannot gain the Mandarin back again.  After that, the playing of all cards will be final.  Unbounded play must therefore be predicated on gaining more cards during play.
The only gainers are Hermit and Falconer.
Without the Quarry in play, the Hermit is limited to gaining three coin cards and Falconers are limited to gaining four coin cards.  The Falconers can therefore produce more Horses.  But the number of Falconers in our deck is finite and will run out.  After which we can play actions as a Hermit and only gain cards that cost up to three coins which will not produce any more Horses.
With the Quarry in play, five coin actions are reduced to a cost of three coins and can be gained with Hermit, but they will not produce more Horses.  We can gain more Falconers, but they are limited to gaining cards which cost less than themselves, and their cost has been reduced to three coins.  Eventually we will not be able to gain any more cards.
There is one final way to gain a card; trashing a Squire.  The Rogue is an attack card, but it is not in the supply, so we can only gain Scrying Pools.
Any action played as a Hermit can gain a Squire and trash a Squire and gain a Scrying Pool.  That seems like a gain, but it isn't.  You are losing two cards and  gaining two cards.  It just makes waiting for the end take a lot longer.

The case of purchasing Capitalism.

Hermit can no longer trash the Mandarin, nor the Squires.  The gaining situation is the same as above.  We can gain Horses only when the Quarry is not in play, but we cannot gain any really useful cards unless the Quarry is in play.  Gaining the Mandarin from the trash will return the Rogue and a lot of other useful action/treasures to the stack to be played again but most importantly, it removes the Quarry from play.  The only card that can trash the Mandarin is the Count and only by trashing the entire hand.  That obviously ends play unless triggered by a Golem.  This is limited because Golems are not treasures and they cannot be returned from play and they cannot be gained, only acquired in the Night phase or bought in the final Buy phase.

Analysis

If we play L Liveries and then F Falconers gaining F Patrons, we will gain L*F Horses.
We then turn those L*F Horses and F Patrons into (L+1)*F more Liveries,
and then turn those Liveries into more Liveries, S-4 more times for O(L*F*S) Liveries.
The final Hermit loop converts O(L*F) Liveries into O(L*F*r) Falconers and O(L*F*(1-r)) Squires.  The Squires are converted to Scrying Pools by the Count.
For the next playing of Falconers, L' = O(L*F*S), F' = O(L*F*r), and S' = O(L*F*(1-r)).
To maximize Liveries gained next iteration, we need to maximize L'*F'*S'= O(L*F*S) * O(L*F*r) * O(L*F*(1-r)) = O(L^3*F^3*S*(1-r)*r).
That at least tells us that we should gain Falconers and Squires in equal number so F = S, and that equates to O(L^3*F^4).
The number of Liveries appears to cube itself each time we play a Golem, but not really since the other components do not grow nearly as fast.
Empirical data suggests that the actual exponent of growth for Liveries is ~2.4 (though my spreadsheet could only do 7 iterations before blowing up).

This is repeated for each Golem, with the number of Golems for the next turn equal to half the number of Horses gnerated in the last iteration.
Empirically, G' = ~(L^(2.4*G)^1.7.  That means that overall growth per turn = L^(2.4*[(L^(2.4*G)^1.7]) or thereabouts not even counting the Liveries we end up buying.
The problem is that the exponents aren't in a favorable place.  I believe, overall, it surpasses 2 up-arrows.

For those that are new to up-arrow notation:

If f(x) = x*2, then f(f(f(2)))) = 2*2*2*2 = 2^4 = 2↑4 = 16  "exponentiation"
If f(x) = x^2, then f(f(f(2)))) = ((2^2)^2)^2 = 2^8 = 256
If f(x) = 2^x, then f(f(f(2)))) = 2^(2^(2^2)) = 2↑↑4 = 65536  "tetration"
If f(x) = 2↑↑x, then f(f(f(2)))) = 2↑↑(2↑↑(2↑↑2) = 2↑↑↑4 = ?  "pentation"

Mathematicians have not blessed that second row with a name that I could find.  Bankers would call it "compounding", and if applied to finance, "amortization".

EDIT:  Forget what I said about amortization.  It's just another form of exponentiation.  I don't have any label for that second row.

5
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: November 11, 2020, 05:11:56 pm »
I'm saying this on the basis that exchanging a card that is being gained from the Black Market deck shouldn't work, and you'll be forced to take the card you were originally gaining. So in our case, our Fairgrounds would get removed from the Black Market deck and we'd stop being able to buy it.

Though, I'm remembering that gaining Horse can be exchanged with Changeling, and that's not from a supply pile, so maybe it does work after all. I've yet to test this with the Black Market / Trader situation on the client.

Exchanging just requires a pile, it doesn't have to be a Supply pile, so Horses work. Black Market cards do not have a pile, you can't upgrade Page/Peasant from the BM for instance.

The dominionstrategy.com wiki seems to have some contradictions.  The rules given for exchanging are as you have stated, but is the Black Market deck a pile or not?

Their rules clarifications for Black Market include:

"If you buy a card from the Black Market deck and then use Trader to prevent yourself from gaining it, the bought card goes back on top of the Black Market deck."

I wonder what ShuffleIT has implemented?

6
Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: November 08, 2020, 11:47:38 am »
I believe that the latest Trader change kills the triple up arrow solution. It had a good run.  :'(

I believe it still works exactly as it did.
Fairgrounds does not have any on-gain ability.
The only difference in the new rules for Trader is that you can process the on-gain of the card you buy before exchanging it for a Silver.  Before, you didn't have that option.  I just tested this in a kingdom with Trader and Ducat.  Now buying a Ducat with Trader and Copper in hand allows you to choose whether to react to the Ducat or Trader first.  If you do Ducat, you can trash the Copper from your hand and then still elect to react with Trader, thus returning the Ducat to the kingdom and gaining a Silver.

7
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.

8
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


9
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.


10
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.)

11
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.


12
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.

13
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.

14
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.

15
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.

16
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).

17
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.


18
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.


19
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.

20
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.



21
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.

22
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.

23
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)

24
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.
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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.

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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.
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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.
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  • 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.
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  • 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.
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  • Delve
Yes.  I only took it out to simplify things.
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  • 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.
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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.
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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.

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