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Varsinor

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Re: Mine
« Reply #50 on: August 07, 2012, 09:38:55 am »
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Silver/silver means that in any hand where you hit 5 other coin (e.g. silver/silver/copper/curse), you have a 0% chance of making province. In the same hand, but with gold/copper you have a 50% chance of hitting 8 (and getting the province) and a 50% chance of hitting 6.

Sure, but you have already made arbitrary assumptions there. If you change your example of the first four cards to Silver/Silver/Silver/Curse, than additional Silvers are the cards you want because both a Copper and a Gold would waste money by netting you $7 or $9.
If you change it to Silver/Copper/Copper/Curse, than you'd probably also rather want Silvers than Golds or Coppers for your fifth card (unless you prefer a $5 card to Gold/Goons/Harem/Nobles in which case it doesn't really matter or there is a card for $7 you want).

Silver/silver is a narrower spread and depending on your deck this can be bad (e.g. when it gives you more 7 coin hands; fewer 6s and 8s) or good (more 8s; fewer 7s and 9s).

As you say it depends on the deck. So as long as you don't have an argument for why the narrower spread should be better in more decks, I maintain that there is no reason that cursing *alone* makes Gold+Copper more desirable than Silver+Silver.
In fact, now that I think about it, there may even be a case for the narrower spread being better in more decks (in the absence of the special factors like discard attacks, sifters and trash for benefit of course) - because most games are Province games and most decks a) don't have an abundance of +buys and b) have 3 or more Gold at some point. Which means the deck with the narrower spread will have less risk of wasting money with $9 or more while on the low end of the distribution, at the end of the game the difference between an Estate for $4 and a Duchy for $5 can be quite important.
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jomini

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Re: Mine
« Reply #51 on: August 07, 2012, 11:08:13 am »
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Silver/silver means that in any hand where you hit 5 other coin (e.g. silver/silver/copper/curse), you have a 0% chance of making province. In the same hand, but with gold/copper you have a 50% chance of hitting 8 (and getting the province) and a 50% chance of hitting 6.

Sure, but you have already made arbitrary assumptions there. If you change your example of the first four cards to Silver/Silver/Silver/Curse, than additional Silvers are the cards you want because both a Copper and a Gold would waste money by netting you $7 or $9.
If you change it to Silver/Copper/Copper/Curse, than you'd probably also rather want Silvers than Golds or Coppers for your fifth card (unless you prefer a $5 card to Gold/Goons/Harem/Nobles in which case it doesn't really matter or there is a card for $7 you want).


Cursing has several affects:
1. It lowers the expectation value of your hand. Decks should virtually never have an expectation value of more than 8 coin without +buys. In a cursing game you rarely have useful +buy so we don't have too many cases where the expected other hand ever gets all the way up to silver x3, curse. More often we start tapping provinces and duchies (thus bringing down our expectation value). You normally want to green before your expectation value crests 8.
2. It makes combos harder. Lining up villages and power 5's is a lot harder in a bloated curse deck. This tends to devalue 5's and 4's meaning that in addition to VP buying, we also want to have a wide distribution earlier so we get more 3's and 6's and fewer 4's and 5's. The less coin "wasted" at 4 and 5 before greening the better. So when your expectation value gets to be 4.5 coin, you want more variance so you can pick up more "lucky" golds. Obviously the exact value of 4/5 coin actions depends on the board, but generally cursers lower the value of complicated/terminal stuff compared to silver.
3. It depletes a pile. This can lead to duchy rushing (perhaps with other cards like great hall) and the odd "lucky" province can let you control end game. For instance if the duchies are split 3/3 and you grab a province, the other player must get both the other duchies while you whiff at an estate to win. If you do grab an estate, he cannot end the game until he breaks ahead on the estates (while you can) or until he gets "lucky" and hits a province.

So for your specific examples: silver/silver/silver/curse/x is a way higher expectation value than I tend to see in cursing games. I will normally have already started greening before I get to an expectation value of 8 coin per hand. Silver/copper/copper/curse/X means that I have an expectation value of 6 coin; here it is not clear cut, but I would lean more towards variance, as I'm likely very close to greening and I'd much rather have slightly better odds at province than slightly better odds of gold.

Which I think is the bigger point. For most BMish decks you want to start greening before your expectation value gets to 8 coin. Once you start greening, you want more variance because there is nothing at 6 or 7 you want. You'd much rather have a really good hand followed by a "bad" hand.

Silver/silver is a narrower spread and depending on your deck this can be bad (e.g. when it gives you more 7 coin hands; fewer 6s and 8s) or good (more 8s; fewer 7s and 9s).

As you say it depends on the deck. So as long as you don't have an argument for why the narrower spread should be better in more decks, I maintain that there is no reason that cursing *alone* makes Gold+Copper more desirable than Silver+Silver.
In fact, now that I think about it, there may even be a case for the narrower spread being better in more decks (in the absence of the special factors like discard attacks, sifters and trash for benefit of course) - because most games are Province games and most decks a) don't have an abundance of +buys and b) have 3 or more Gold at some point. Which means the deck with the narrower spread will have less risk of wasting money with $9 or more while on the low end of the distribution, at the end of the game the difference between an Estate for $4 and a Duchy for $5 can be quite important.
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9's are you least likely concern. 7 is a much bigger concern because it "wastes" 2x as much coin in the greening stage, and it allows the other player to pull ahead and control the end game. Two 7s means that you nab two duchies and if he gets a single province & duchy, he gets a 3 VP lead and you can now be forced to waste an 8 on a duchy because you can't end the game.

In short dominion likes variance when you are above 5 and below 8 coins in expectation value and greening. It likes high variance above 3 and below 6 when you are cash buying. It dislikes variance when you are near 5 or near 8 coins and greening. It dislikes variance when you are near 3 or near 6 and cash buying. I submit that most curse games spend most of the time in the 3-6 range for cash buying and most of the greening stage is spent in the 5-8 range.
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Varsinor

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Re: Mine
« Reply #52 on: August 08, 2012, 02:35:10 pm »
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Sparked by a game I played yesterday, I did some simulations with Geronimoo's simulator on the question of Hunting Party + Mine in a Province game and it turned out that it is considerably stronger than pure Hunting Party on a 5/2 start, but a little bit weaker on a 4/3 start. (In a Colony game, the strategy with Mine is undoubtedly way stronger regardless of the start.)

Buying a Mine with the first $5 and only then Hunting Parties (and never buying Gold but mining it) beats pure Hunting Party by 45% to 43% with a random start. If you start 5/2, then Mine+HP beats pure HP by a clear 50% to 37%. But on the other hand, if you start 4/3, then pure HP narrowly beats Mine+HP by 44% to 43%.

The reasons for the substantial difference between the two starts should be
a) that Mine considerably profits from the fact that in can be played one reshuffle earlier and
b) Hunting Party isn't a very good starting buy on a 5/2 start because of the considerable risk to draw only one card with it on its first play - especially when there is no $2 card you want to buy (and could draw with the HP). (If you are really unlucky, you may even have to play it twice (or more) for only one card.)

If an additional buy in the form of Market is in the supply, the Mine strategy profits from it (as the additional buying power it creates can better be used with an additional buy).
According to the simulations, it is optimal to buy one Market after Mine and four Hunting Party (and further HPs after that with money below $8). Such a Mine+HP+Market deck beats pure HP by 50% to 40% (55% to 35% on 5/2 and 48% to 42% on 4/3) and HP with one Market (after the fourth HP) even by 52% to 39% (60% to 32% with 5/2 and 51% to 41% with 4/3, in other words: don't buy a Market when you don't have a Mine). (Mine+HP+Market beats Mine+HP without Market with 49% to 41% on a random start.)

Here is an argument in favor of the Mine that I think has not been mentioned so far:
When you buy a Mine, you do not need to spend a $6 buy on a Gold to have one (you can mine it instad). So in other words, you can spend just as many $5+ buys on Hunting Party as you would without the Mine - you just replace one early buy of Gold with one early buy of Mine.

Sure, you can get those copper changed into silvers and those silvers into golds, but the nature of the Hunting Party searching means that the additional card's diversity represents a significant slowdown.

You have one Silver and one Gold in any case, so there is no slowdown at all by getting additional of them - especially as you don't get additional treasure cards that might bloat your deck, but replace treasure cards of lower value.
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Varsinor

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Re: Mine
« Reply #53 on: August 08, 2012, 02:36:20 pm »
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Here is the game I played yesterday as an example (which also had Market which made me include that in the simulations above). I had a 5/2 start and there was no $2, which made me start nothing/Mine:

http://councilroom.com/game?game_id=game-20120807-174707-2ca8d694.html

I got to play the Mine 7 times in 17 turns (on turns 3, 6, 8, 9, 11, 13 and 16).

Comments on my play:
- I think it was a mistake to buy Wishing Wells with my extra buy from the Market on turns 10 and 12 and it was definitely a mistake to play a Wishing Well before a Hunting Party on turns 13 and 15 (although on turn 15 it didn't turn out to be relevant).
- The simulations suggest that it was a mistake to buy my fourth Hunting Party at all on turn 10 with $9 (and two buys) instead of a Province. After all, my opponent had already bought two Provinces.
- I bought the Market too early (between the second and the third Hunting Party). According to my simulations above I shouldn't have bought it until after the fourth Hunting Party (although those simulations did not include Wishing Well).
« Last Edit: August 08, 2012, 03:15:44 pm by Varsinor »
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