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[Nimmy]

Hi,

I am trying to come up with a strategy for Big Money + (one) Village.
The idea is that the Village gives you the possibility not to draw the next card, which in some circonstances is actually the good play.
Can you think of any good strategy that will work ?
I tried something like this:
  - Wait until you have (say) 5 silver/golds before buying the village
  - Each time you get the village, compute the exact probability to draw each card (this information you can have easily), then
      - If you have a large probability to have a VP card, draw it (better for it to hurt you this hand rather than the next)
      - If you don't have 8 but have a large probability of getting 8 drawing the next card, then draw it. Otherwise, don't.
      - If you have 5 and you have a high probability to get 8 in your next hand, then don't draw (this is an example, I didn't code this actually)

You can find the exact details in attachment. This strategy did not work (it loses 35%/58% to BMU), and I can't think of clever rules (or good thresholds for the probabilties) that would make it better. Can you ?

A few notes:
- You cannot choose how to play village in Geronimoo's simulator, so I wrote my own. It is very raw and a bit^W^Wcompletely broken, but if you really want to play with it, it's in attachment (launch python game.py, linux guy here)
- I don't have that much time to code strategies, so don't expect me to test them daily.

i don't think you can do way better than BMU with one village, but I hope it's possible not to do worse.
It is quite possible, especially given the strategy, that it would work way better with Walled Village. Maybe it's something interesting to try.

[WanderingWinder]

By the time you can even think about getting some kind of advantage, the game will be long, long, long over.

[Nimmy]

Actually, I think the problem would be better suited with a $2 cantrip, the big problem with buying a village being that you didn't buy a silver. So you can try the same reasoning with, e.g., the Pearl Diver. So now, I think BMU + pearl diver is strictly better than BMU, but how to play it ?

[ARTjoMS]

The idea is that the Village gives you the possibility not to draw the next card, which in some circonstances is actually the good play.

uh.huh.puh.

Silver also gives you ''possibility not to draw card'' and increases average money per card (unless it is bigger than 2, so this is way more likely to work in colony games).

Village gives you possibility to draw card. This could work if you have bad cards in hand and want to force reshuffle (no cards in draw pile),

[rinkworks]

Is BMU itself as sophisticated as that?  I wonder how much BMU would be improved by strategically not playing the Smithy.  I assume it's already understood that you don't play it if you're at 8 without it, but, as you describe, there are other reasons you might not want to play it.

Back to the original question, I second the idea of using Pearl Diver instead of Village.  If you want to be purer still, use Hamlet (never taking its discarding options).  In a BM+x strategy, Pearl Diver will be strictly better than Hamlet (how often do you get to start sentences with "Pearl Diver is strictly better than..."?), but Hamlet will be cleaner to simulate.

[WanderingWinder]

On a pearl diver, it's obviously going to be better to take it that nothing (or, most of the time, estate or copper) on $2. Whether to buy it with 3+... eventually it'll be better than silver, but I think that would come a little after you're going to be getting that chance (or at least maybe estates will be needed) in a non-colony game. With colonies, I think this would happen reasonably often; village maybe occasionally rarely with colonies, hamlet quite often indeed (assuming you can use its buy option).

[DG]

For every game where you get the minor advantage in card play you'll have many games where you lose through lack of money. The only advantage of not drawing a card is when you're trying to delay a reshuffle.

If you're not convinced, consider a situation where you already have 5 to spend and a village in hand. Through good memory you can also deduce the last six cards of your draw deck - estate, gold, silver, copper, copper, copper (in any order). The use of the village doesn't change the chances of a province next turn at all. Not playing the village only denies you the chance of a province this turn.

[Nimmy]

Basically, what I want to know is if we can use some advanced strategy about shuffling (force reshuffle, knowing what is in your deck) to have better strategies for an AI in a basic scenario.

As an exemple, BMU + Chancellor, when you reshuffle every time the average money in your deck is less than your total average money is way better that BMU (59/34). (BTW,question for Geronimoo: the Single Chancellor strategy in your simulator is worse than this, what is the strategy you used to play it ?)

For rinkworks: BMU, as far as Geronimoo's simulator is concerned, does not use Smithy, and does not use any action cards at all, hence its strategy cannot be sophisticated.

[rinkworks]

For every game where you get the minor advantage in card play you'll have many games where you lose through lack of money. The only advantage of not drawing a card is when you're trying to delay a reshuffle.

If you're not convinced, consider a situation where you already have 5 to spend and a village in hand. Through good memory you can also deduce the last six cards of your draw deck - estate, gold, silver, copper, copper, copper (in any order). The use of the village doesn't change the chances of a province next turn at all. Not playing the village only denies you the chance of a province this turn.

I get what you're saying, but the thing is, if we humans can analyze a situation and come to a conclusion like that, a computer ought to be able to do that too.  In that particular case, where playing the Village is calculably the right one, an algorithm ought to be able to recognize that it should play it.  In other situations, though, playing the Village may be calculably wrong.

[rinkworks]

For rinkworks: BMU, as far as Geronimoo's simulator is concerned, does not use Smithy, and does not use any action cards at all, hence its strategy cannot be sophisticated.

I thought BMU (Big Money Ultimate) was, by definition, Big Money + Smithy.

[WanderingWinder]

For rinkworks: BMU, as far as Geronimoo's simulator is concerned, does not use Smithy, and does not use any action cards at all, hence its strategy cannot be sophisticated.

I thought BMU (Big Money Ultimate) was, by definition, Big Money + Smithy.

Nope. It's just the "optimized" version of playing with only the basics.

[rinkworks]

Well.  Now I know.

[DG]

In that particular case, where playing the Village is calculably the right one, an algorithm ought to be able to recognize that it should play it.  In other situations, though, playing the Village may be calculably wrong.

There are however far fewer situations than you probably think where the right choice is not to play the village. Playing the village does not change the random distribution of the remaining draws of the deck (except through changing the reshuffle).

[timchen]

No it doesn't. But there is an obvious case where this kind of consideration would work: suppose your remaining deck has higher-than-average money density. If you have $8 already, then not playing the village is certainly a good idea. I

Also, in the case you mentioned, there is actually a 2-1 advantage to play the village, if you consider the chance of buying a Province between the two shuffle.

[Davio]

You could still make a case for playing Village with $8.

Imagine you have 5 cards left in your draw deck and they are: Estate, Estate, Estate, Silver, Gold

If you don't draw, you're 100% guaranteed of a shitty next turn.
If you draw, there's a 2/5 chance of drawing dead money - 40%.
This means there's 60% chance of drawing an Estate, which may be good, because you get to reshuffle.

All in all, it's not so clear cut.


I think that buying that Village instead of a Silver is a mistake. You may use that card only a couple of times and I'd rather use that Silver than have to decide whether to draw or not.