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Author Topic: Coffers Poll Question  (Read 612 times)

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Matt_Arnold

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Coffers Poll Question
« on: November 02, 2018, 02:27:35 pm »
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Ariel and Baz are A.I.s who play Dominion. For thousands of years they will play with different boards of cards, one board at a time. However, all boards will contain a 7-cost purchase, and Coffers. Ariel always saves every Coffer until they spend them on the 7. Baz always spends all Coffers. They will both buy the 7 as soon as possible. Which option is closest to how often Baz will be the first to get to 7?

The recent article about Coffers left me wondering one detail. If a player intends (whether right or wrong) to make a madcap sprint to buy a high-cost purchase as soon as possible, is saving all their Coffers usually getting them to that price-point slower, on most boards? The article makes it clear that immediately saving Coffers is usually losing the game vs spending them early to strengthen one's deck. But let's put a fine point on it: What about a much earlier race than the one for the overall game? For example, the race to be the first one to start using a Forge, Citadel, or Inheritance?
« Last Edit: November 02, 2018, 02:29:01 pm by Matt_Arnold »
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Awaclus

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Re: Coffers Poll Question
« Reply #1 on: November 02, 2018, 02:32:03 pm »
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I would assume saving the Coffers is significantly better.
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faust

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Re: Coffers Poll Question
« Reply #2 on: November 03, 2018, 03:05:14 am »
+1

Let's just consider the Baker Coffers for this, since in general if you want to spike early, I don't think getting any other Coffers cards is helpful.

Then it really depends on what you have available. If you can get Wine Merchant on T1/2 by spending the token, absolutely do. Similar things hold for Swamp Hag and other spiky $5s. But the majority of boards will not have that and then I think even a Silver/Silver (keeping the Coffers) opening would be slightly preferable to -/Gold (spending the Coffers).
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

crj

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Re: Coffers Poll Question
« Reply #3 on: November 03, 2018, 06:03:09 am »
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Let's just consider the Baker Coffers for this[...]
it really depends on what you have available [...]
It feels to me like both these miss the intent of the original question. You have to consider all possible ways Coffers might be in the game, and you have to consider all possible combinations of other kingdom cards. "If you can get Wine Merchant"; OK, now also consider the other 97% of games.

Formalising the original question a little:

Choose kingdoms at random, until you get one that includes both at least one $7-cost and at least one Coffers card.

Now have two AIs play that kingdom, racing to be the first to buy/gain a $7-cost. Both adopt lines of play that are optimal for that objective ignoring longer-term prospects of winning the game. However, A is constrained never to spend a Coffers token except on buying a $7-cost, and B is constrained always to spend every Coffers token at the first opportunity, basically treating +1 Coffers as +$1.

What is the probability that B will gain a $7-cost before A does?
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faust

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Re: Coffers Poll Question
« Reply #4 on: November 03, 2018, 06:45:26 am »
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Let's just consider the Baker Coffers for this[...]
it really depends on what you have available [...]
It feels to me like both these miss the intent of the original question. You have to consider all possible ways Coffers might be in the game, and you have to consider all possible combinations of other kingdom cards. "If you can get Wine Merchant"; OK, now also consider the other 97% of games.

Formalising the original question a little:

Choose kingdoms at random, until you get one that includes both at least one $7-cost and at least one Coffers card.

Now have two AIs play that kingdom, racing to be the first to buy/gain a $7-cost. Both adopt lines of play that are optimal for that objective ignoring longer-term prospects of winning the game. However, A is constrained never to spend a Coffers token except on buying a $7-cost, and B is constrained always to spend every Coffers token at the first opportunity, basically treating +1 Coffers as +$1.

What is the probability that B will gain a $7-cost before A does?
I know what the question is. My point is, if your plan is to race to $7, then the amount of boards where it is optimal to buy a Coffers card along the way is negligible (modulo possible new Renaissance cards). So the only relevant way that either player will even have Coffers is via Baker.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

Holunder9

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Re: Coffers Poll Question
« Reply #5 on: November 03, 2018, 02:09:23 pm »
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There is no way to answer such a question in general. For example if the $7 card is Forge you likely don't want any other trashers whereas if its Expand you most likely will. Also, Baker plays differently than Plaza plays differently than Villain plays differently than the zillion possible cards that yield Coffers.

The intution that it is not always correct so save Coffers is probably correct though.
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Dingan

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Re: Coffers Poll Question
« Reply #6 on: November 04, 2018, 02:21:38 am »
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The recent article about Coffers ...
Maybe I'm blind but where is this?
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Donald X.

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Re: Coffers Poll Question
« Reply #7 on: November 04, 2018, 04:37:05 am »
+1

The recent article about Coffers ...
Maybe I'm blind but where is this?
It's not just some forums! There's a front page. You just drop "forum." from the url.
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crj

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Re: Coffers Poll Question
« Reply #8 on: November 05, 2018, 01:14:29 pm »
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There is no way to answer such a question in general.
Yes there is: answer it for every specific case, then take an average.
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Holunder9

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Re: Coffers Poll Question
« Reply #9 on: November 05, 2018, 01:25:11 pm »
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There is no way to answer such a question in general.
Yes there is: answer it for every specific case, then take an average.
And lose all interesting information in the process. It is obvious that cantrips like Baker and Plaza are better tools to hit $7 than a terminal like Villain. But in addition to that it also depends on which of the 3 $7s you want. With Forge you might not want to thin whereas with Inheritance you only want to trash Coppers.

And then there is the further question of whether the hypothetical AIs only care about quickly hitting $7s or also care about playing well. The quickest path towards a $7 might not be the best one.

Sorry but this question is simply too broad and general to answer meaningfully. Its intent is rather to make you think about whether Coffers hoarding for such a purpose is always leading to its goal.
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timchen

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Re: Coffers Poll Question
« Reply #10 on: November 08, 2018, 01:38:52 pm »
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The argument in the above discussions then point to the probability being close to 50%, since the situations are really rare  where coffers really make a difference to your first purchase of $7. So in most instances the two AIs will do the same thing and it is 50-50.
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