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[WheresMyElephant]

Fun calculation (which is probably obvious to many if they've considered the issue):

Harem-with-Hovel beats Gold, from a totally naive raw money density perspective, as long as your money density is greater than 1. It's like trashing a Copper: one less coin, one less card.

Let's say you have X total cash and Y cards. Money density with a Gold is (X+3)/(Y+1). Money density with a Harem, sans a Hovel is (X+2)/Y. If money density = 1 then X = Y. (X + 3)/(X+1) != (X+2)/(X)

In reality, the choices are equivalent when X = Y - 2; which is actually a good bit sooner - as in turn 2 if you buy a silver (X = 9, Y = 11). The only time you should not take a Hovel trashing Harem over a Gold if you are just looking at money density is if you've been heavily cursed/ruined.

Sorry, I meant the money density AFTER the purchase needed to be greater than 1. (After either purchase; it doesn't matter which option you choose.) Post-purchase money density is described by the formulae you gave, (X+3)/(Y+1) and (X+2)/Y, so we seem to agree.

I didn't want to get too nitpicky about the specifics, since in a real game people probably aren't tracking money density closely enough to tell the difference. Even if they were, if it's that close, they are probably going to decide based on the Harem VP or some other factor.

 But I should've known someone would check my math (and thanks for doing so!)

Edit: To everyone else, yeah this does of course overlook a ton of factors. Including the difference between "raw money density," "effective money density," and "this deck doesn't care about money density."Also including the question of how long that Hovel would have been around anyhow. I don't mean to downplay any of this; it's left as an exercise for the reader, since most of the readers here can probably address it better than I can.

[sandstorm]

I've mentioned this before I think but Great Hall/Silver (Trash Hovel) opening is the first opening in dominion history that has a 100% chance of giving you one hand worth at least 5 coins on turns 3 or 4.

[WanderingWinder]

I've mentioned this before I think but Great Hall/Silver (Trash Hovel) opening is the first opening in dominion history that has a 100% chance of giving you one hand worth at least 5 coins on turns 3 or 4.

If you don't count various multiplayer scenarios or silver/nomad camp/potentially-a-nomad-camp-here-on-exactly$4.

[werothegreat]

I found the edge case!  I found the edge case!

Trash Hovel to Estate on a 5/2 opening when Bishop is on the board, because you'll get more points that way.

[Powerman]

I've mentioned this before I think but Great Hall/Silver (Trash Hovel) opening is the first opening in dominion history that has a 100% chance of giving you one hand worth at least 5 coins on turns 3 or 4.

Silver / Nomad Camp.  Turn 3 you'll hit 3, 4, or 5.  If you hit 3, next 5 cards are copper or silver.  If you hit 4, buy a nomad camp and 3 of the next 4 cards are copper or silver.  If you hit 5... well...

[ConMan]

I think the article isn't looking too shabby at the moment. I would like to suggest opening it with a bit more explanation of the bleeding obvious, though, by explicitly describing the four main ways starting Shelters differ from starting Estates:
1. They have a cost of 1, not 2
2. They're not worth VP
3. 2 of them aren't Victory cards
4. They do stuff

Much of the article then goes on to discuss the effects these differences make alone and in combination, so it would be good to have them spelled out at the start.

[WheresMyElephant]

I found the edge case!  I found the edge case!

Trash Hovel to Estate on a 5/2 opening when Bishop is on the board, because you'll get more points that way.

I'm sure there are edge cases involving Crossroads, Baron, Remake etc. Shelters hurt all these cards but they're all still going to be viable SOMETIMES; even Baron is sometimes your only source of +Buy.

[werothegreat]

I think the article isn't looking too shabby at the moment. I would like to suggest opening it with a bit more explanation of the bleeding obvious, though, by explicitly describing the four main ways starting Shelters differ from starting Estates:
1. They have a cost of 1, not 2
2. They're not worth VP
3. 2 of them aren't Victory cards
4. They do stuff

Much of the article then goes on to discuss the effects these differences make alone and in combination, so it would be good to have them spelled out at the start.

Done.

[theory]

Published.  Other than formatting, the main alteration was a longer explanation of the Hovel/Estate problem. 

[Polk5440]

I will admit that the reason I was drawn into Dominion initially was because of its symmetry. I knew about MTG and in my head it was a sinking hole for money where the player with the best deck and the most money would always win. So Dominion was a fresh experience because it allowed equal access to everything.

I second that.

From playing some games with Dark Ages, though, Shelters do not deviate from the symmetry promise. Everyone still starts with the identical deck. I really enjoy playing with them. Ruins even aren't so asymmetric because they are all so bad. Some are just a little worse than others. Knights, on the other hand, I don't like very much (even though they all attack, they are a close third behind Black Market and Tournament as the worst offenders of equal access). Haven't played more than a few games with them, though.

[Awaclus]

I will admit that the reason I was drawn into Dominion initially was because of its symmetry. I knew about MTG and in my head it was a sinking hole for money where the player with the best deck and the most money would always win. So Dominion was a fresh experience because it allowed equal access to everything.

I second that.

From playing some games with Dark Ages, though, Shelters do not deviate from the symmetry promise. Everyone still starts with the identical deck. I really enjoy playing with them. Ruins even aren't so asymmetric because they are all so bad. Some are just a little worse than others. Knights, on the other hand, I don't like very much (even though they all attack, they are a close third behind Black Market and Tournament as the worst offenders of equal access). Haven't played more than a few games with them, though.

The whole point of Dominion games is asymmetry: you usually don't have unlimited VP available (Monument, Goons + Ambassador and Bishop + a few DA cards aside), so the player who gets the most, wins. If you piledrive, say, Cities or Laboratories, you are the only player who has access to them and then you have quite an advantage there. If it wasn't for asymmetry, every Dominion game would end on a draw. Now, I can see why Black Market isn't everyone's favorite card, because getting the only Mountebank in the whole game can be devastating and is completely luck-dependent, and the same is true for Tournament to a lesser extent (because it depends on luck significantly less), but getting to $5 is a matter of luck only when at least one player opens 5/2 and another player does not. Sure, the player going first always has additional advantage from Knights being on the table, but that's also true for attack cards. While Knights aren't bad cards, they are worse than the power 5 cards, and usually getting a specific Knight is more a matter of choice.

In Dominion, every player has equal chances of winning the game before the first player is decided and Knights, Tournament and Black Market do not change that.

[Polk5440]

I will admit that the reason I was drawn into Dominion initially was because of its symmetry. I knew about MTG and in my head it was a sinking hole for money where the player with the best deck and the most money would always win. So Dominion was a fresh experience because it allowed equal access to everything.

I second that.

From playing some games with Dark Ages, though, Shelters do not deviate from the symmetry promise. Everyone still starts with the identical deck. I really enjoy playing with them. Ruins even aren't so asymmetric because they are all so bad. Some are just a little worse than others. Knights, on the other hand, I don't like very much (even though they all attack, they are a close third behind Black Market and Tournament as the worst offenders of equal access). Haven't played more than a few games with them, though.

The whole point of Dominion games is asymmetry: you usually don't have unlimited VP available (Monument, Goons + Ambassador and Bishop + a few DA cards aside), so the player who gets the most, wins. If you piledrive, say, Cities or Laboratories, you are the only player who has access to them and then you have quite an advantage there. If it wasn't for asymmetry, every Dominion game would end on a draw. Now, I can see why Black Market isn't everyone's favorite card, because getting the only Mountebank in the whole game can be devastating and is completely luck-dependent, and the same is true for Tournament to a lesser extent (because it depends on luck significantly less), but getting to $5 is a matter of luck only when at least one player opens 5/2 and another player does not. Sure, the player going first always has additional advantage from Knights being on the table, but that's also true for attack cards. While Knights aren't bad cards, they are worse than the power 5 cards, and usually getting a specific Knight is more a matter of choice.

In Dominion, every player has equal chances of winning the game before the first player is decided and Knights, Tournament and Black Market do not change that.

I am particularly sensitive to symmetry in availability of cards because of Magic/CCGs, and my tastes reflect that. A card where only one copy is available to "buy" reminds me too much of the negative aspect of CCGs ("rare" cards, I am looking at you). That's all I was trying to say. I was just glad to see Davio felt the same way.