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RobF

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Impossible score, version two
« on: August 01, 2011, 10:45:38 am »
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In a 2 player game, that lacks any kingdom cards that give VP chips (Monument etc), what is the smallest positive total score (sum of both players) that is impossible to achieve?

Edit: variable VP victory cards are allowed. 
Edit 2: you might also want to think about the solution in the case variable VP cards are NOT allowed.  This variation will probably be easier.
« Last Edit: August 01, 2011, 10:54:58 am by RobF »
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Fangz

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Re: Impossible score, version two
« Reply #1 on: August 01, 2011, 10:49:12 am »
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Are gardens, vineyards, etc allowed?
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Agrisios

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Re: Impossible score, version two
« Reply #2 on: August 01, 2011, 10:51:59 am »
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Are gardens, vineyards, etc allowed?

Do they give VP chips? If not ...
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Thisisnotasmile

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Re: Impossible score, version two
« Reply #3 on: August 01, 2011, 10:52:42 am »
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At first I thought "Okay, let me just think about this for a second". Then I thought about it. The answer is Very very very very very high unless I've missed something and it's going to involve a lot more calculations than I originally thought.
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Thisisnotasmile

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Re: Impossible score, version two
« Reply #4 on: August 01, 2011, 10:58:12 am »
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Double post yay.

I'm probably not going to calculate the exact solution, but this might help other people who do want to:

Are we allowed to buy VP chip cards (from the Black Market) and not use them for VP chips for the purpose of bumping up the value of Gardens and/or Vineyards? Or are they just banned altogether?

I assume the latter but it's better to know for sure than to calculate it all only to find out you've missed off stuff because you weren't sure.
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Davio

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Re: Impossible score, version two
« Reply #5 on: August 01, 2011, 11:04:06 am »
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Double post yay.

I'm probably not going to calculate the exact solution, but this might help other people who do want to:

Are we allowed to buy VP chip cards (from the Black Market) and not use them for VP chips for the purpose of bumping up the value of Gardens and/or Vineyards? Or are they just banned altogether?

I assume the latter but it's better to know for sure than to calculate it all only to find out you've missed off stuff because you weren't sure.
Don't forget insane Fairgrounds VPs due to BM.

Even calculating Gardens could take multiple pages in my notebook.

If we do the Fairgrounds, Gardens and Vineyards hard mode, we must take into account that EVERY pile could be emptied due an ultimate mega-turn with a gazillion buys, money, etc...
« Last Edit: August 01, 2011, 11:08:12 am by Davio »
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Agrisios

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Re: Impossible score, version two
« Reply #6 on: August 01, 2011, 11:06:25 am »
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Indeed a lot of calculations. To start with: I think you can gain 58 points per Fairground, I guess, if you put all cards into Black Market. It's only 56 without Goons, Monument, Bishop. This is only true for one player though, because of the prizes. Making the puzzle for both players is insane.

Treasures should be only in Black Market to maximize Vineyard score. For the same reason Young Whitch should be in the supply.

Important question for Gardens: Do you use money from both Base and Intrigue?

Another question is: Can you legally empty all piles to get maximum garden/vineyard score? Probably yes.
« Last Edit: August 01, 2011, 11:20:37 am by Agrisios »
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Davio

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Re: Impossible score, version two
« Reply #7 on: August 01, 2011, 11:10:37 am »
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I would like to add:

With Gardens, it's better for 1 player to have 120 cards and all Gardens (12 * 8 = 96 VP) and the other player to have 0 than 2 players with both 60 cards and 4 Gardens each (6 * 4 * 2 = 48 VP)

This is an example, but you get the drift.
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Thisisnotasmile

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Re: Impossible score, version two
« Reply #8 on: August 01, 2011, 11:19:41 am »
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You obviously want Gardens, Vineyard, Duke, Harem, Nobles, Great Hall, Island, Fairgrounds and Black Market out. That leaves you space for only one other Kingdom card... Although, would it be more worthwhile to ditch Harem and put another action card in for the sake of Vineyards? (yes)... What other adjustments do we need to make to have optimal VPs available? This is a 3-part problem. Part 1 is figuring out the optimal Kingdom, then part 2 would be to calculate the max VPs you can get from that. Part 3 will be to see if there are any scores lower than the max VP that can't be scored? I don't really know if we can say either way without checking it, and if there are, then calculating the max VP didn't really achieve much. Maybe we can get those lower values, but not with our 'optimal' kingdom?

This just gets harder and harder the more I think about it...
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Thisisnotasmile

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Re: Impossible score, version two
« Reply #9 on: August 01, 2011, 11:26:14 am »
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Anyhow, easy mode (No variable VP):

Colony = 80
Province = 48
Duchy = 24
Estate= 14
Harem = 16
Nobles = 16
Island = 16
Great Hall = 8
Total = 222 (I think)

+1 to make it impossible is 223


I'm pretty confident there are no lower numbers because lower scores can be achieved just by adding curses to this solution or any subset of it.
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Agrisios

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Re: Impossible score, version two
« Reply #10 on: August 01, 2011, 11:29:01 am »
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You obviously want Gardens, Vineyard, Duke, Harem, Nobles, Great Hall, Island, Fairgrounds and Black Market out. That leaves you space for only one other Kingdom card... Although, would it be more worthwhile to ditch Harem and put another action card in for the sake of Vineyards? (yes)...

Yes, no Harem. Young Whitch is a must. The other one is probably King's Court to legally empty as many piles as possible. Otherwise you can only get 9 from each pile.
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WanderingWinder

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Re: Impossible score, version two
« Reply #11 on: August 01, 2011, 11:29:36 am »
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It's pretty clearly 169 with the basics (ambassador), and off the top of my head, isn't it 223 with the extra non-variable VP cards?
Ninja'd, but anyway....


Also, if you want to be cruel, allow Goons (but not bishop or monument, which can give infinite VP)

Agrisios

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Re: Impossible score, version two
« Reply #12 on: August 01, 2011, 11:34:22 am »
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Also, if you want to be cruel, allow Goons (but not bishop or monument, which can give infinite VP)

Goons can give infinite VP too (Ambassador).
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ghostofmars

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Re: Impossible score, version two
« Reply #13 on: August 01, 2011, 11:43:20 am »
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I get 1515 in the hard mode as highest possible score:

+60 copper
 40 silver
 30 gold
 12 platinum
 16 potions
 5 curses
 14 estate
  8 duchy
  8 province
  8 colony
  8 garden
  8 GH
  8 island
  8 duke
  1 harem
  8 nobles
  8 vineyard
  8 fairgrounds
 10 Ambassador
 10 YW
 10 BM
 10 Bridges
122 further cards

---
420 cards, 172 action cards, 144 differently named cards
42*8(garden) + 57*8(vineyard) + 57*8(fairgrounds) + 8*11(duchy/duke) + 8*10(colony) + 8*6(province) + 8*(2+2+1)(island,GH,nobles) + 2(harem) + 14(estate) - 5(curses) = 1515
The opponent gets an Ambassador to put all his cards back in the supply. Then I play Masquerade to exchange his Ambassador with a Curse.
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RobF

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Re: Impossible score, version two
« Reply #14 on: August 01, 2011, 11:47:18 am »
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I agree with the above solutions (Timeisnotasmile, WanderingWinder) to the non-variable version.
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RobF

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Re: Impossible score, version two
« Reply #15 on: August 01, 2011, 11:56:59 am »
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The opponent gets an Ambassador to put all his cards back in the supply. Then I play Masquerade to exchange his Ambassador with a Curse.
Remember it's total score between both players, although your method does maximize that.  You may not have to give him a curse if you somehow drew and played all your cards before playing the last Masquerade, but I don't think that would ever be necessary since the max score will never want all the curses anyway (-10 is worse than +1 on 8 gardens).  I have to think a little more about whether there could be impossible scores below this max if you have to use some curses in your solution, but it seems unlikely.
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Deadlock39

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Re: Impossible score, version two
« Reply #16 on: August 01, 2011, 06:09:10 pm »
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I found a couple of errors in ghostofmars' solution, so maybe I can take a stab at the right answer.

The Fairgrounds calculation isn't quite right.  They cannot be worth 57.  They are worth 144/5 = 28.8, round down = 28, x2 = 56.
This would make his final number 1507.

However, we are at 172 actions for Vineyards.  Swapping a BM action out for GH gains us 2 more actions up to the next Vineyards break point of 174.  We gain 8 VP on Vineyards, and only lose 7 on Great Hall because we still get one from the BM deck.  This also increases our total card count by 2, so we can lose 2 curses.
This bumps us up to 1510.

I did this assuming his Black Market numbers are correct. (There are 108 actions and 14 non-actions in the BM in his solution.)

With your opponent's Curse, the combined total is 1509, and the impossible score is 1510.

I think it is feasible that the interactions between total cards and total actions with Gardens/Vineyards could create a impossible score at a lower point total, but it seems unlikely.

Jimmmmm

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Re: Impossible score, version two
« Reply #17 on: August 18, 2011, 11:13:54 am »
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I think the next question has to be: how big a score can you get with VP tokens included? Obviously we need to either exclude Monument or limit the number of turns, but either way there must be some finite limit.

I'm not going to do any maths right now, but a starting point would be buying 10 Goons and 9 Village types, and getting 10 VP per card remaining, then Bishoping them away...

Actually, on second thoughts, Bishoping your cards would probably lose more Garden points than it would gain, and there's also the possibility of playing a Bishop with nothing else in your hand, which should probably not be allowed for the sake of this question...
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Thisisnotasmile

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Re: Impossible score, version two
« Reply #18 on: August 18, 2011, 11:33:02 am »
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Goons + Ambassador allows an infinite score too.
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WanderingWinder

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Re: Impossible score, version two
« Reply #19 on: August 18, 2011, 11:40:04 am »
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Goons + ambassador can lead to infinite, as can bishop (you eventually bishop nothing but gain 1 VP).

Deadlock39

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Re: Impossible score, version two
« Reply #20 on: August 18, 2011, 12:00:46 pm »
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That problem would have to exclude Ambassador as well or you could return your cards to the supply and buy them again with Goons.  That will keep you from getting your opponents Coppers and Estates, but we can drop Goons into Ambassador's place in the kingdom.

I think the real puzzle there is what is the max number of points you can get while obtaining your 10 Goons and 9 Villages (gaining the least number of cards) because after that, you just get 10VP x the number of cards left.

I think you could do it without buying any other cards if you use Shanty Town.  The question is, do we need to prove we can buy the last card of every pile on the last turn without 10 Bridges.  If you can, you can swap Bridge for Shanty Town.

We get 1 Shanty Town first, then use it to draw 6 coppers and buy a Goons.
Then play Goons and buy another. (+1VP)
Play 2 Goons and buy another Goons and another Shanty Town (+2VP * 2)
With these, cards, we can always play all of our Goons.  (Start with ST and 4 coppers, draw ST+Goons, play Goons, repeat.)
Repeat until you have all the Goons and 9 STs.
Total VP is 89. (1 + 2*2 + 2*3 + 2*4 + 2*5 + 2*6 + 2*7 + 2*8 + 2*9 = 89VP)

We cannot gain VP tokens for the BM cards, so we are left with:
 46 copper
 40 silver
 30 gold
 12 platinum
 16 potions
 10 curses (we want 5, but can buy and trash 5 before ending the game)
  8 estate
  8 duchy
  8 province
  8 colony
  8 garden
  8 GH
  8 island
  8 duke
  8 nobles
  8 vineyard
  8 fairgrounds
 10 YW
 10 BM
  1 Shanty Town

If I didn't screw up, this is 263 cards to gain for 10VP each.  Total Goons points are 2630 + 89 = 2719VP.

Anyway, while writing this up, I just realized that Great Hall shouldn't be in there at all based on my most recent response to ghostofmars.  Also, Island can be swapped out for a different action, because that would now gain us 20 extra Goons points.

I might try to finish figuring it out later.


WanderingWinder

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Re: Impossible score, version two
« Reply #21 on: August 18, 2011, 12:43:39 pm »
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Also, you should add a black market which contains EVERY OTHER CARD IN THE GAME and from which you should be able to buy all those cards for 10 points each from having all goons in play before you play that black market. That's going to up it A LOT

Deadlock39

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Re: Impossible score, version two
« Reply #22 on: August 18, 2011, 03:24:39 pm »
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Hmmm, we already had BM, but for some reason, I had it in my head that you could not gain Goons tokens from BM buys, but that wouldn't be the case.  If I get back to this, I will make sure I include those.

Deadlock39

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Re: Impossible score, version two
« Reply #23 on: August 18, 2011, 10:48:22 pm »
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Okay, so with Goons allowed, but no Monument, Bishop or Ambassador to prevent infinite scores.  Here is a first attempt.

...Wow, this is crazy long.  (It is a bad habit of mine I suppose.)

If my counts are correct, there are currently 135 different cards in the game, and 119 of them are actions.

Our Kingdom is:
1. Gardens
2. Duke
3. Vineyards
4. Fairgrounds
5. <Any Action>
6. Goons
7. Shanty Town
8. Bridge
9. Black Market
10. Young Witch
B. <Any Action Bane>

In my previous post, I came up with 89VP tokens max in the process of buying 9 Shanty Towns and 10 Goons.

Since there are only 8 cards in VP piles, we have excluded Island, Nobles, and Great Hall from the Kingdom, because we get 20VP from buying 2 more cards with Goons which is more than the 16 (or 8) they provide.

We have 7 action cards in the Kingdom for a total of 70.
There is a total of 119 actions 4 are prizes and 108 are in the Black Market for a total of 182 actions for Vineyards.

There are 135 total Kingdom cards.
5 treasures, 4 Victory cards, and Curse add 10 to the total unique cards for Fairgrounds to make 145. 

There are 7*10 action and 4*8 victory cards in the Kingdom. 
Since we can't use Ambassador, we can't get our opponents cards.  There are 53 Coppers and 11 Estates to be had.
There are 40 Silvers, 30 Golds, 12 Platinum, 8 Duchies, 8 Provinces, 8 Colonies and 5 Prizes.   
135+70+32+53+11+40+30+12+8+8+8+5
This totals 412 cards for Gardens.  We need at least 1 Curse for the Fairgrounds break point, so we should grab 8 to hit 420 so the Gardens break point offsets all the negative points.
Total of 420 cards for Gardens.

The easiest is 8 Duchies for Duke.

Starting with the 420 cards that we will ultimately have from Gardens, we have 5 prizes that we can't buy and 9 Shanty Towns, and 10 Goons that we buy before we get 10VP per buy.  This drops us to 396 cards to buy with Goons, but we can buy two Curses we don't want to finish with at some point, and then Trash them, so that puts it back up to 398.

That should be all the pieces. The score is:
2VP * 4    (Island, Great Hall, Nobles, Harem)      8
1VP * 11  (Estate)                                              11
3VP * 8    (Duchy)                                              24
6VP * 8    (Province)                                           48
10VP * 8  (Colony)                                             80
8VP * 8    (Duke)                                               64
42VP * 8  (Gardens)                                           336
58VP * 8  (Fairgrounds)                                      464
60VP * 8  (Vineyards)                                        480
-1VP * 8  (Curse)                                               -8
10VP * 398 + 89VP (Goons)                               4069

Total: 5576VP
(To make it like the original problem was, we add our opponent's 3 points, and then 1 to get the impossible score of 5580VP)

Now... I did this all with the 3 forbidden cards still in the Black Market, but just not allowed to be played.  That probably isn't right, so if we actually take them out:
We lose 3 actions -8 Vineyards VP
We lose 3 unique cards -16 Fairgrounds VP
We lose 3 cards -8 Gardens VP
We only need 1 Curse to reach our Gardens break point -(-7) Curse VP
We buy 3 less cards -30 Goons points.

The new total is 5521VP (and an impossible score of 5525VP)

Doing this makes me think there were a few mistakes in ghostofmars numbers (possibly done before Walled Village?), so I might try to re-run the original problem later. 
The OP never did confirm a solution he thought was correct for the second question.

WanderingWinder

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Re: Impossible score, version two
« Reply #24 on: August 18, 2011, 10:53:54 pm »
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We're going to have to revise, methinks, 'cause I didn't see you take out the cards/actions for bishop, ambassador, and monument which must not be in the black market.
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