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Author Topic: Big hands [lol]  (Read 7416 times)

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jimjam

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Big hands [lol]
« on: August 30, 2011, 03:42:26 am »
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The objective here is to obtain the largest hand (or attempt to draw as many cards as possible) in a turn possible without playing any actions on that turn. Duration cards are an obvious contributor, what else? How many can you get? The game will still end on 3-piles, but for simplicity assume if you have no cards you may add infinite blank cards to your deck at any time. It is a 2 player game and your opponent will help you achieve your goal.
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kn1tt3r

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Re: Big hands [lol]
« Reply #1 on: August 30, 2011, 05:24:27 am »
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It has to include:
- Caravans
- Wharfs
- Tacticians (all 10 played by Golem/Lab trick)
- Opponent's Torturors
- Opponent's Council Rooms

- something I've missed...?

However, I just got nearly insane calulculating how many TRs and KCs you need yourself to play 10 Wharfs and 10 Caravans 3x each (including whatever combinations of KC>TR>KC or TR>KC>KC> ...).  Or in other words: How man TRs are left for your opponent to play double Council rooms (for Torturers it doesn't matter because you can only get 10 curses anyway)? 

Do you have the solution yourself btw?
« Last Edit: August 30, 2011, 06:30:40 am by kn1tt3r »
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Zem

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Re: Big hands [lol]
« Reply #2 on: August 30, 2011, 05:51:06 am »
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another thing are 9-10 horse traders in your hand after the council rooms and before the last torturer of your oppenent

if the goal is just to draw as many cards as possible without playing actions then 9-10 adventures and 9-10 loans

of course in that case a single adventure and infinite blank cards would be be enough to draw infinite cards

edit: had an idea! your opponent could use masquerade to take your king's courts and throne rooms after you have played them, and pass you horse traders instead. That way you can use them on your previous turn for the durations, and he on his turn for the council rooms.

So now it depends on the exact rules used for KC/TR + duration, how many stay in play with the duration, and how many can you draw again next turn. Calculating this with the old official rules would be even harder and you would have to use some tricks to avoid having all of them stay in game, but i think the rules have been amended in that only the last KC/TR stays. Still pretty hard.

The most important cards are probably kc and tactican, so all other cards are only available 9 times at most to avoid ending the game.

edit2:
another trick to get a very small gain:
- start your turn with 4 horse traders and a secret chamber
- opponent plays a spy, you reveal and set aside the 4 horse traders and then reveal  the secret chamber, drawing 2 horse traders, revealing them.
- Now you have to return 2 cards to the deck but  have only the secret chamber in your hand. you return it.
Net gain-->1 card

- opponent plays a council room, you draw the secret chamber
- he plays a spy, you reveal SC to draw 2 horse traders, reveal them, return SC to deck
net gain -->1 card

You could do it again but you would need 10 horse traders for that.

You can use the secret chamber in conjunction with an opponents spy/pirate ship/tribute/thief/etc to pass all your king' courts and throne rooms to your opponent without him having to pass you the horse traders:
- he plays a thief, you reveal the secret chamber, draw two KCs, return two other cards, the cards are removed by the thief
- he plays 2 masquerades, you pass the KCs, receive 2 coppers.
- he plays a thief, you draw two KCs, return 2 coppers, the coppers are removed by the thief,
- repeat

definitely to hard for me to calculate
« Last Edit: August 30, 2011, 07:54:14 am by Zem »
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ghostofmars

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Re: Big hands [lol]
« Reply #3 on: August 30, 2011, 07:51:03 am »
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Cards in the Kingdom
King's Court
Wharf
Laboratory
Torturer
Tactician
Golem
Horse Trader
Caravan
Throne Room
Black Market
Haven (bane card for Young Witch in Black Market)

I didn't manage to put the Council Room in

Your deck consists of
10x Tac, 10x Wha, 9x KC, 9x HT, 9x TR, 9x Car, 9x Hav, 9x Gol
Opponents deck consists of
cards which give +2 actions (from BM), 9xTor, 1x Council Room(from BM)

I play
TR - TR - KC - KC - Wha
and then more KC as long as I've cards and then a single Wha to draw more cards. When all KC are played I play all the remaining Wha. I still have 8x "play three times" left afterwards, which I use for Car.
Then I play the remaining TR on the branch of the 2nd TR which gives 8x double actions which I use for 1 Car and 7 Hav. The remaining 2 Hav are played as single actions.
Now I start playing Gol which draws into Lab, Tac. Playing the Tac first and then the Lab I play all Tac.

My opponent then plays 1 Council Room and 9 Torturer for 6 of which I set aside a Horse Trader and gain a Curse for all of them.

In the next round I get:
50 = 10x5 cards from the Tacticians
60 = 10x3x2 cards from KC+Wharf
24 = 8x3 cards from KC+Caravan
2 cards from TR+Caravan
14 = 7x2 cards from TR+Haven
2 cards from the Havens
12 = 6+6 cards from the Horse Traders
9 Curses
---
173 cards
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Fangz

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Re: Big hands [lol]
« Reply #4 on: August 30, 2011, 08:20:12 am »
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What about having played (multiple) KC-possessions on your last turn? That seems like the most efficient way of using the KCs, to get as many uses of council room as possible. Also doesn't require cooperation from the opponent :)

Let's say you play all the possessions KC'ed. Your opponent then has 31 turns to play TR (or KC)-council rooms, drawing you a minimum of 40 cards per turn, assuming he has the necessary villages to chain all those up, and is using outpost to get an extra turn after each. So the maximum hand has to exceed 1240.
« Last Edit: August 30, 2011, 08:34:47 am by Fangz »
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Zem

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Re: Big hands [lol]
« Reply #5 on: August 30, 2011, 08:29:08 am »
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173 cards


using ghostofmars solution i cannot find much room for improvement:



opponent has 1 masquerade, 1 secret chamber, 1 spy, 1 minion (from black market)

I start the turn with 4 horse traders, 1 KC,

opponent plays masquerade, he passes 1 secret chamber, i pass 1 KCs

he plays spy, i reveal 4 HT, set aside; reveal 1 SC, draw 2 HT; reveal 2 HT, set aside; return 1 SC to deck ( +1 card due to SC)

he plays KC+council room, i draw 1 SC + 2 HT (+2 cards, compared to only council room)

he plays minion, i reveal 2HT, reveal SC, draw 1 HT + x, reveal 1HT, return SC+x (9 HTs revealed)


The previous turn could perhaps be improved:
I can start with 6 cards (opponent has played the council room), I can play trusty steed/wishing well/hunting party from black market to increase hand size, so I could perhaps chain KCs differently


edit:
of course Fangz idea beats that by a mile.
« Last Edit: August 30, 2011, 08:45:08 am by Zem »
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ghostofmars

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Re: Big hands [lol]
« Reply #6 on: August 30, 2011, 12:11:50 pm »
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I think, I've optimized the solution further :)
I play cards to give me 10 Possessions, 3 TR, 4 KC, 1 Outpost in hand, furthermore I have two remaining actions
TR+TR+TR+KC+KC+KC+KC => 2x 2xPossession + 8x 3xPossession = 28x Possession
+Outpost
In my Outpost turn I manage to draw again 10 Possessions, 3 TR, 4 KC and get another 28x Possession turns.

Now the second player has 56x possessed turn + 1x original turn. In each of these he plays
Village+TR+KC+KC+KC+KC+KC => 10x 3xCouncil Room
+Outpost
where he again plays 30x the Council Room.

This amounts to a total of 57x2x30=3420 cards


PS: I found a infinite card solution
(1)I play KC+Possession
(2)He plays Possession
back to (1) until infinite future Possession turns are accumulated. Then he plays the KC+CR+Outpost combination (see above) and I gain 60xinfinite cards :)
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DStu

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Re: Big hands [lol]
« Reply #7 on: August 30, 2011, 12:31:16 pm »
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PS: I found a infinite card solution
(1)I play KC+Possession
(2)He plays Possession
back to (1) until infinite future Possession turns are accumulated. Then he plays the KC+CR+Outpost combination (see above) and I gain 60xinfinite cards :)


That's not (countable) infinte but "only" arbitrary large I think as you have to stop somewhen. But ignoring this small techicality, you can improve your countable infinite to uncountable by


(1) Play TR+Posession
(2) For each of the Posessions, he play TR+Posession, goto (1)

in depth infinite you have 2^\N Posessions played, for each one play a CR, which adds an uncountably many cards to your deck.

PS: Think Possession does not work this way, as I think you don't end up with a Breadth-first-search but depth-search, so even when you do it infinitely often the CR at the end goes to the next Posession-branch and does not accumulate to infinitely many carddraws. But so it's more fun...


« Last Edit: August 30, 2011, 01:44:08 pm by DStu »
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jimjam

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Re: Big hands [lol]
« Reply #8 on: August 30, 2011, 08:00:00 pm »
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It would only be countable because you can associate each time you play a card with a number.

You guys got a lot of the tricks. I still have to put it together, but this is my game plan...

If you play possession on your opponent's turn then it will not give you more turns to play council room, it will cause him to possess you, which will not help you, but not hurt you either. So 62 turns (POPPPPP.....N), where P=possessed, O= outpost, and N=normal is the best.
Use TR on the first KC in order to get the full 30 possessions; the other 4-5 can be used on Wharf (the tradeoff is such that you can either go with 10 KC or 10 Tactician and I think you will get the same yield).

Possession/CR is the main trick.

Masquerade is useful for several reasons:
-Move the KCs over, which is efficient.
-Grab the possessions so you can ambassador 2 (or use moat with 1), so that you can grab 10 CR without ending the game before your final turn
-If you can empty your hand with Horse Traders you can get an additional free card by masquerading, attacking, masquerading, etc.

Golem/Tactician/Caravan is the other part.

1 Torturer is fine, since you only need to play it 9 times throughout the 62 turns.
The 10 kingdom card restraint is kind of annoying because then we have to budget actions and cards (cards is less of an issue with scrying pool).
Off the top of my head:
You need many of:
Tactician
KC
Caravan
Golem
Council Room
Masquerade (can be bane card)
Wharf
Possession
Black Market (well, you need 1)

Horse Traders and TR are probably the best to put in. Unfortunately you might have trouble using all of the TR since you might not get to hit all Caravans if you're comboing with Tactician/Golem, and Haven is not listed.
Some cards that are helpful in the BM deck are:
Outpost (2 would be nicer, but you can masquerade it)
Scrying pool (2 would be nicer to help draw everything for both players)
Villages/Tourney
YW (Bane)
Haven (Would like more, but not enough piles)
Ambassador (Possession/Council Room changeover)
Torturer
Some attacks that don't give curses
« Last Edit: August 30, 2011, 08:02:54 pm by jimjam »
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DStu

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Re: Big hands [lol]
« Reply #9 on: August 31, 2011, 01:13:17 am »
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It would only be countable because you can associate each time you play a card with a number.

It is if you don't ignore the "techicality" that you can't "really" follow the scheme to infinity. Once you ignore this you are uncountable, because with the counting you are somehow "stucked"* in the first branch, but there are infinitely many more branches left.

Of course, one should not take my post too serious, there should be no way how you can really achieve this in RL, as as you said, you should really stay countable there. Ignoring "techicalties" when dealing with infinities is seldomly a good idea...

* Of course you can count more cleverly and get out to some more branches, but as Cantor told us we will never get all.
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jimjam

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Re: Big hands [lol]
« Reply #10 on: August 31, 2011, 04:15:02 am »
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Not really. This is a bijection to the natural numbers: 1-30 are the first 30 possession plays. 31-60 are the 30 possession plays of your first possession, 931-960 are the 30 possession plays of your first possession of your first possession play.
ie in base 30, the first(rightmost) digit is the root, the second digit is its children, the third digit are their children, etc.

In fact if you could play an infinite amount of possessions per turn, but only sequentially, it would still be countable.
Here's an inefficient ordering: count the first possession to depth 1. Then count 2 possessions per turn to depth 2.
1,4,27,256... For any finite depth or possession plays per turn eventually you will count it.

Edit: There's no good way to get uncountable turns, except something like "Take an extra turn for every subset of the natural numbers".
« Last Edit: August 31, 2011, 04:34:03 am by jimjam »
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jimjam

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Re: Big hands [lol]
« Reply #11 on: August 31, 2011, 04:55:59 am »
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Ignoring 10/11 piles rule:


First turn
-30 Possession(using a TR and 5KC)
-outpost
Outpost turn
30 Possession (TR, 5KC)
10 Tacticians gives 50 cards
9 Caravans gives 9 cards
TR->4 KC on 8 wharves gives 48 cards
TR->1 more wharf gives 4 cards
5TR on havens gives 10 cards
4 more havens gives 4 cards

First Possession turn (the hardest)
masquerade 5 KC, giving 5 HT,
attack, which gives 10 cards. Their hand is empty.
masquerade a HT/attack 3 times, giving 6 cards.
university the last CR.
TR->5KC->30 CR. They draw the last HT and a moat, and a possession.
ambassador away the possession; play HT to get 2, use moat to keep the possession in the supply.
play outpost

29 cards in hand,+30*61 more turns gives 1859 cards, + 9 tortures at some point.
=
2011 cards.

Choice points: An extra tactician gets you 5, a TR wharf gets you 4, and two havens gets you 2. Instead, an extra KC will get you 6 on the last wharf, 3 on one haven, and the saved TR use on a different haven, yielding 2.
Using one less TR on the havens allows you to do the masquerade trick for the last HT, which again is a tie.


Edit: There is one more trick I just realized. Hint: It is almost as good as CR.
« Last Edit: August 31, 2011, 05:03:10 am by jimjam »
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kn1tt3r

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Re: Big hands [lol]
« Reply #12 on: August 31, 2011, 05:13:45 am »
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This number is too high, because it is all limited by the amount of cards available.

Usually it's:

60 Coppers, 40 Silvers, 30 Golds, 12 Platinums, 16 Potions => 158
14 Estates, 8 Duchies, 8 Provinces, 8 Colonies, 10 Curses => 48
10x10 Kingdom cards, maybe 11 due to Young Witch => 110
BM is in supply => 1310 additional BM cards, if all the rest is in there (if I'm not mistaken)

=> 1626 cards in total

But you can only draw them all if your opponent can get rid of them all (without trashing them). Don't know how or to what degree that's possible...
« Last Edit: August 31, 2011, 05:16:13 am by kn1tt3r »
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jimjam

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Re: Big hands [lol]
« Reply #13 on: August 31, 2011, 05:23:41 am »
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Yeah, in the beginning I removed that constraint.
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DStu

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Re: Big hands [lol]
« Reply #14 on: August 31, 2011, 05:58:36 am »
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Not really. This is a bijection to the natural numbers: 1-30 are the first 30 possession plays. 31-60 are the 30 possession plays of your first possession, 931-960 are the 30 possession plays of your first possession of your first possession play.
ie in base 30, the first(rightmost) digit is the root, the second digit is its children, the third digit are their children, etc.

In fact if you could play an infinite amount of possessions per turn, but only sequentially, it would still be countable.
Here's an inefficient ordering: count the first possession to depth 1. Then count 2 possessions per turn to depth 2.
1,4,27,256... For any finite depth or possession plays per turn eventually you will count it.

Edit: There's no good way to get uncountable turns, except something like "Take an extra turn for every subset of the natural numbers".


Not sure if I should really argue further, as as I said earlier there are some unrealistic and false assumptions, and under correct play of the rules (of the game and the universe) uncountability should not occur. But under the wrong assumptions above, which are
A) "After infinitely many turns", you play an CR. And more importantly:
B) You resolve TR+Possession in a Breadth-first-like manner, which is wrong from my understanding of the rules.

this should work. Because with (B) Breadth-first, you play 1TR+Possession, then he plays 2xTR+Possession, then I 4xTR-Possession etc. pp. So we have a binary-tree with (A) infinite depth. Evey path of this tree you can map 1to1 to the space {0,1}^\N of all infinitely long sequences of zeros and ones. Which is uncountable.

But if
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jimjam

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Re: Big hands [lol]
« Reply #15 on: August 31, 2011, 02:14:27 pm »
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Depth/Breadth first doesn't change anything. Even a number like 1.01010101.... doesn't correspond to any Possession play because each Possession play has a finite distance from the root. A binary tree is completely countable. The number of different branches are uncountable, but not Possession plays. However, many branches do not correspond to a Possession play (all the ones that continue infinitely).
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guided

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Re: Big hands [lol]
« Reply #16 on: August 31, 2011, 02:57:04 pm »
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My intuition is that cards are drawn one at a time, so it is meaningless to speculate on the cardinality of uncountable sets that one might wave one's hands to loosely associate with the process of drawing cards :P
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jimjam

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Re: Big hands [lol]
« Reply #17 on: September 16, 2011, 02:04:49 pm »
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my original solution was incorrect, however a revised one gets over 3000 cards without using any duration cards besides outpost
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