1851

**Tournaments and Events / Re: 1 Day Cup 5th May**

« **on:**April 29, 2012, 07:38:03 am »

When would be too late to de-register if something comes up?

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1851

When would be too late to de-register if something comes up?

1852

It's... beautiful.

I was very interested to see what other approaches there were. I particularly liked that you can end the game with Mining Village for the final buy rather than Harem, and the idea of using Scheme to protect your engine parts. Mazwa's use of Quarry as the only cost-reducer, so that Colonies and Provinces had to be bought the hard way, was nice too.

I started thinking about this when the scoring criterion was turns - VP/2, which made it more obvious that the thing to focus on was maximising score. With that in mind my first idea was was KC/KC/Workshop/NV/(Highways), which lets you put away 3 cards a turn indefinitely. There are (at least) two ways to set that up: you can either dispose of the Chapel via Farmland/Island, or you can observe that you have an extra play of KC hanging around, and use it on a Highway. The second option makes you wonder if you can pull the same trick on a bigger deck, which leads to the set-up in the log.

Why three Workshops? I think because it didn't stall too badly the first time I tried it, and 4 felt like it would slow down the trashing at the end more than it was likely to speed up the middle section. I settled on 7 KCs, 7 Highways, 3 Workshops and 3 NVs (and a single Chapel) which is what you need to be able to draw your deck and put 9 cards on the mat, and also happens to have enough slack that you can afford to open your turn with a single KC/Highway if necessary.

I think up to turn 8 is as tight as possible if you're trying for this engine. Turns 9-11 are completing the set-up. Turns 12-24 are the business turns, of which 6 were lost due to failing to draw the deck (so the gains from better luck here are greater than any potential gains from upping the Workshop count). It then takes 5 turns to trash 20 cards, which is followed by the final Farmland purchase.

Can anyone tighten this up, or find a more efficient method that doesn't rely on too much shuffle luck? In particular, this needs 5 Kingdom cards (trash, cost reduction, gaining, stashing, drawing and KC, with Highway counting twice). Can you gain arbitrarily many cards with less set-up? My feeling is that increasing the points gained is unlikely to be cost-effective, as the big three of Silk Road, Duke and Gardens are already in.

A huge thanks to allfail for the fascinating challenge.

1853

I should think so.

Specifically buying?

buying out the Colonies

Specifically buying?

1854

Is there any way on Iso to dictate what cards are in the BM deck?

There is not.

1855

Potentially interested, and timing isn't a problem.

1856

Someone recently posted a 6 PileDriver game to the game reports forum.

*moderator edit: fixed link, good guy greg style*

1857

No entries by far... is the criterion too painful to work with? Or maybe I shouldn't offer the prizes

I think it's a fascinating challenge, and will submit something before the deadline.

The VP/10 change does make a huge difference.

1858

Game 1: Shanty Town/Smithy is not a great draw engine. The main feature of this set that your ignored but your opponent took advantage of is Peddler, which when paired up with Salvager in the late game enables a double Province turn, and earlier in the game provides the +Buy to allow you to purchase Peddlers. Had you noticed that Hodor never bought any Treasure at all?

Game 2: Crossroads for $4 on turn 4 looks surprising, but perhaps you were worrying about Feast collision. It should probably have been Black Market. The Wharf should have been your second Tactician, and that would have got your combo going faster. I'd also have looked to pick up a second BM at some point, although you only seem to have missed one once, and that was on a Wharf rather than Tactician turn. BM buys: I think you should have taken Province over both Torturer and Highway. If you'd also bought Hoard instead of Gold then you'd have picked up a free Gold each time too.

DStu's Wharf/Hoard suggestion is good, especially in the presence of Crossroads.

Game 2: Crossroads for $4 on turn 4 looks surprising, but perhaps you were worrying about Feast collision. It should probably have been Black Market. The Wharf should have been your second Tactician, and that would have got your combo going faster. I'd also have looked to pick up a second BM at some point, although you only seem to have missed one once, and that was on a Wharf rather than Tactician turn. BM buys: I think you should have taken Province over both Torturer and Highway. If you'd also bought Hoard instead of Gold then you'd have picked up a free Gold each time too.

DStu's Wharf/Hoard suggestion is good, especially in the presence of Crossroads.

1859

Are you only counting points from Victory cards?

1860

Ah, Hamlet. The extra discard shaves off a turn compared to Oasis once you hit 5 or 6 cards.

1861

Here are some possibly less popular ones. I take full advantage of my freedom to not be comprehensive, particularly on the indifferent section.

Contraband: + Apprentice, Salvager, Upgrade, Remodel, Expand, Remake, Colony, Platinum, Harem, Nobles ? Monylender, Spice Merchant - [Cost==5 && Cards >= 3], Wharf, Merchant Ship, Governor

Philosopher's Stone: + Ambassador, Platinum, Colony ? Coppersmith, Warehouse - [Cards>=1], [Trash>=1], [Duration], Governor

Explorer: + Duke, Gardens ? - [Cost==5 && Cards >= 3], Wharf, Merchant Ship, Governor

EDIT: inserted missing colons

Contraband: + Apprentice, Salvager, Upgrade, Remodel, Expand, Remake, Colony, Platinum, Harem, Nobles ? Monylender, Spice Merchant - [Cost==5 && Cards >= 3], Wharf, Merchant Ship, Governor

Philosopher's Stone: + Ambassador, Platinum, Colony ? Coppersmith, Warehouse - [Cards>=1], [Trash>=1], [Duration], Governor

Explorer: + Duke, Gardens ? - [Cost==5 && Cards >= 3], Wharf, Merchant Ship, Governor

EDIT: inserted missing colons

1862

In a 4/3 opening it's unclear whether you will buy an ambassador on your second hand after the first round.

Although you can buy Silver/X over X/Silver with a 4/3 start for any 3-cost X, it is particularly strong when you don't like Ambassador but suspect that your opponent will be tempted.

1863

If it's a game where you want your deck to be small, then the trashing and attack aspects are both important. If it isn't, then the attack aspect is pretty weak: the presence of a few extra coppers and estates in your deck is not a huge issue if you're playing BM, especially given the time your opponent will be spending dismantling their own economy. So it feels more like a trasher than an attack to me.

1864

I wrote a program to calculate the distribution of effective hand sizes when you draw from a deck with a specified number of labs, under the assumption that there aren't enough labs that you can run out of cards to draw. It's in Haskell. For the uninitiated, you can run it here (although I don't know how long that link will stay valid). Change the top line ("main = print $ distribution 10 2") to run the program with different parameters. I'll explain what they are and how it works below.

The model is that we draw cards from the top of the deck until we see 5 more non-Labs than Labs. The function g counts the number of times we have 0, 1, 2, ... Labs left in deck if we try to do this all possible ways. The weights function gives the number of possible arrangements for the rest of the cards in deck (the remaining Labs and n-5-(# played Labs) non-Labs) for each number of remaining Labs. The distribution function multiplies the frequencies from g by the weights, then turns the list round to get it in order of increasing hand size. The parameters to distribution are the numbers of non-Labs and Labs (in that order). The linked example calculates distribution 10 2 which returns [21,25,20], meaning that in a deck containing 2 Labs and 10 other cards the probabilities of an effective hand size of 5, 6 or 7 are 21/66, 25/66 and 20/66 respectively.

Code: [Select]

`-- i = number of labs left in deck`

-- j = number of cards left to draw to make up hand

g 0 _ = delta 0 -- when i gets to zero there are no labs left

g i 0 = delta i -- when j gets to zero we've drawn enough cards so stop and record that we had i labs left in deck

g i j = zipWith (+) (g i (j-1)) (g (i-1) (j+1)) -- either draw a non-lab, or draw a lab

-- number of ways to arrange remaining cards for each possible number of remaining labs

weights nonLabs labs = [choose (nonLabs - 5 - labs + 2 * labsLeft) labsLeft | labsLeft <- [0,1..labs]]

-- distribution of hand sizes

distribution nonLabs labs = reverse $ zipWith (*) (weights nonLabs labs) (g labs 5)

-- infinite list of zeroes except for 1 at ith position

delta i = replicate i 0 ++ [1] ++ repeat 0

-- binomial coefficient n choose k

choose n k = rows !! n !! k

rows = iterate f (1 : repeat 0) where

f r = zipWith (+) r (0:r)

The model is that we draw cards from the top of the deck until we see 5 more non-Labs than Labs. The function g counts the number of times we have 0, 1, 2, ... Labs left in deck if we try to do this all possible ways. The weights function gives the number of possible arrangements for the rest of the cards in deck (the remaining Labs and n-5-(# played Labs) non-Labs) for each number of remaining Labs. The distribution function multiplies the frequencies from g by the weights, then turns the list round to get it in order of increasing hand size. The parameters to distribution are the numbers of non-Labs and Labs (in that order). The linked example calculates distribution 10 2 which returns [21,25,20], meaning that in a deck containing 2 Labs and 10 other cards the probabilities of an effective hand size of 5, 6 or 7 are 21/66, 25/66 and 20/66 respectively.

1865

For the specific Lab/Moneylender example, it's easy to calculate the probability that you match Copper with Moneylender on any given turn given the composition of the deck: you know the probability of drawing a Lab in your first 5 cards, and the probabilities of matching Copper with Moneylender from 5 and 6 card hands, which is enough. Up to awkwardness with the reshuffle, that will give you an expected number of matches, which in this case (only one Moneylender) is the same as the probability of a match.

With more Labs or Moneylenders, things would get more complicated. For more Labs you get a greater variety of effective hand sizes, with a not too simple distribution. It would be easy to calculate the distribution for a given number of Labs and cards in deck exactly using a computer (think roughly of splitting the non-lab cards into 5 card hands, then throwing down extra cards from the labs at random, with the probability of a card landing in a particular hand proportional to its size, except that you can do it deterministically). You can then use this distribution and the fixed hand size probabilities to get an expected number of collisions.

This relies heavily on the fact that we can ignore actions. Adding in cantrips wouldn't cause any more difficulties, but something like Village/Smith would be much harder.

With more Labs or Moneylenders, things would get more complicated. For more Labs you get a greater variety of effective hand sizes, with a not too simple distribution. It would be easy to calculate the distribution for a given number of Labs and cards in deck exactly using a computer (think roughly of splitting the non-lab cards into 5 card hands, then throwing down extra cards from the labs at random, with the probability of a card landing in a particular hand proportional to its size, except that you can do it deterministically). You can then use this distribution and the fixed hand size probabilities to get an expected number of collisions.

This relies heavily on the fact that we can ignore actions. Adding in cantrips wouldn't cause any more difficulties, but something like Village/Smith would be much harder.

1866

Avin, that works for strategies of the form "wait until there are n cards left, then guess", but there are more complicated strategies that you could follow (you can take into account the number of black cards seen so far, or make a choice randomly if you like). The easiest way to sidestep these problems is to observe that the problem doesn't change if you switch to betting on the last card instead of the next card, as mentioned above.

The hardest thing about the question as presented is that it comes after three basic calculations, which primes you to calculate rather than look for a more elegant solution.

The hardest thing about the question as presented is that it comes after three basic calculations, which primes you to calculate rather than look for a more elegant solution.

1867

I had the same experience with Ambassador. When Seaside first came out it looked laughably bad. Then there was the phase of every game with Ambassador turning into Copper/Estate tennis. It's now usually worthwhile only when you have a reason for wanting a tiny deck: it's a lot like Chapel in both when it's strong and how I've perceived it over time.

1868

But the clever proof he's remembering shows that you can't actually take advantage of this extra information to win more than 50% of the time, and the reasoning is, because you need the bottom card to be a particular color to win.

The extra small observation you need is that while in the original game you were betting on the the next card being black, it's entirely equivalent to be betting on the bottom card being black, as it's just one of the remaining cards chosen uniformly at random. Formally it's a simple coupling argument.

It's slightly embarrassing that this is the topic that gets me to register for such excellent forums.