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Subject: Probability of getting a Gold on the 3rd turn - Part I rss

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Greg Jones
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I think getting Gold early is usually an important tactic. So I decided to calculate the probabilities of getting Gold on the 3rd turn (the first turn your new cards come into play) based on what two cards you buy in your first and second turn. None of the probabilities are very high. I think the probabilities for getting Gold on the 4th or later turn should be comparable, but these are really difficult to calculate as in some cases they depend on the way you play your action cards and even on buys in the 3rd turn. So I think the probabilities should give you an idea of how fast you can expect to get Gold with a given starting combination.

This post covers the 3/4 coin start. The 2/5 coin start report is now up here: http://www.boardgamegeek.com/thread/370808. This analysis doesn't take into account any attack cards being played before your 3rd turn.


Here are the combinations that give 10% or better.

Silver x Smithy = 35 / 792 + 25% = 29%

If you get the Smithy in your hand, you're going to be looking at seven cards. If one of them is the Silver, you've got six coins as long as you don't also draw all three of your Estates. That gives this combination the best initial chances. One problem is that it could tend to get weaker as you buy more action cards. If you play the Smithy as your first action, any of those action cards you draw are dead weight

Silver x Silver = 168 / 792 = 21%

If you draw two Silver and two Copper, or either one of your Silvers and four Copper, you can buy a Gold.

The next several buys also have the same probability, because the action cards they use each net you two coins, the same value as Silver. Since you have only one action card in these combinations, you can always play it if you draw it.

Silver x Moneylender = 168 / 792 = 21%

The Moneylender nets two coins, since you discard a Copper worth one coin and get three coins to use this turn. This has one of the highest probabilities to buy Gold, and it has the added benefit of streamlining your deck while you do it.

Silver x Militia = 168 / 792 = 21%

The same chances to get Gold, this time with an added attack benefit.

Silver x Woodcutter = 168 / 792 = 21%

The Woodcutter doesn't give you any special benefit if you succeed in buying the Gold, but it might otherwise or as part of your greater strategy.

Silver x Chancellor = 168 / 792 = 21%

The added benefit of this combo is that if you are lucky enough to buy a Gold in your third turn using the Chancellor, you can discard your remaining draw pile and reshuffle. Now you have a chance to draw the same cards and do it again, or better yet, draw your just-purchased Gold immediately.

Chancellor x Throne Room = 133 / 792 = 17%

The idea is to draw these together along with two Coppers. You double the Chancellor's two-coin bonus, and you can buy Gold. Like the above, you can discard your remaining draw deck and try to do it again. You should only buy this combo instead of the above if you want to have the Throne Room for later use (or not to have the Silver). When I buy this combo, if I draw the Chancellor without the Throne Room on my third turn, I usually choose to use the option to discard my draw deck. If not, I'll likely draw my Throne Room without another action card on the fourth turn, which is no good.

Woodcutter x Throne Room = 133 / 792 = 17%

The Woodcutter is quite similar to the Chancellor, so this combo has the same probability. Again, the Woodcutter doesn't especially benefit you if you buy the Gold.

Silver x Moat = 35 / 792 + 12% = 16%

The Moat is almost as good as the Smithy, if you think about it. Draw two cards instead of three. So this combo is half as strong as the best one. You would probably only buy this if the Smithy was not available.

Copper x Smithy = 12%

Smithy is so good, it even breaks 10% in combination with buying a Copper. Of course, why would you ever do that? Just buy Silver x Smithy. Skipping further down the list, Smithy x Village is a popular buy. Only 6.6% though. It has some better future potential, though, as you buy more action cards. Smithy x no buy actually fares better at 8.3%. When you have the Village, if you draw the Smithy first, there's a chance that you draw the Village as a dead card. At best the Village is a no-op, since you have only one other action card. Cellar x Smithy also does better than Smithy x Village at 7.4%.


These have less than a 10% chance:

Copper x Silver = 70 / 792 = 8.8%
Copper x Chancellor = 70 / 792 = 8.8%
Copper x Militia = 70 / 792 = 8.8%
Copper x Woodcutter = 70 / 792 = 8.8%
Copper x Moneylender = 70 / 792 = 8.8%
Chancellor x Chancellor = 70 / 792 = 8.8%
Chancellor x Militia = 70 / 792 = 8.8%
Chancellor x Woodcutter = 70 / 792 = 8.8%
Chancellor x Moneylender = 70 / 792 = 8.8%
Woodcutter x Moneylender = 70 / 792 = 8.8%
Smithy x no buy = 8.3%
Chancellor x Smithy = 35 / 792 + 3.7% = 8.1%
Woodcutter x Smithy = 35 / 792 + 3.7% = 8.1%

The Village works as a no-op when you have only one other action card. The Spy is also a no-op if you have no other action cards that draw cards. So all these Spy, Village, and no-buy combos with Silver equivalents have the same probability.

Silver x Spy = 7.6%
Silver x Village = 7.6%
Silver x no buy = 7.6%
Chancellor x Spy = 7.6%
Chancellor x Village = 7.6%
Chancellor x no buy = 7.6%
Militia x Village = 7.6%
Militia x no buy = 7.6%
Woodcutter x Spy = 7.6%
Woodcutter x Village = 7.6%
Woodcutter x no buy = 7.6%
Moneylender x Village = 7.6%
Moneylender x no buy = 7.6%

Cellar x Smithy = 7.4%*
Smithy x Village = 6.6%
Moat x Moneylender = 35 / 792 + 0.63% = 5.1%
Chancellor x Moat = 35 / 792 + 0.63% = 5.1%
Militia x Moat = 35 / 792 + 0.63% = 5.1%
Woodcutter x Moat = 35 / 792 + 0.63% = 5.1%
Silver x Cellar = 35 / 792 = 4.4%
Silver x Throne Room = 35 / 792 = 4.4%
Cellar x Chancellor = 35 / 792 = 4.4%
Cellar x Militia = 35 / 792 = 4.4%
Cellar x Woodcutter = 35 / 792 = 4.4%
Cellar x Moneylender = 35 / 792 = 4.4%
Moat x Smithy = 4.3%
Moat x Throne Room = 3.4%
Copper x Moat = 2.5%
Moat x Spy = 1.7%
Moat x no buy = 1.5%
Moat x Moat = 1.3%
Moat x Village = 1.3%
Cellar x Moat = 0.63%

* With the Cellar, sometimes there are non-obvious decisions to make. As far as getting Gold, it only matters in combination with the Smithy. The Cellar reduces your hand size to four when you play it, and that gets you at most five coins with these cards. The Moat can then draw up to five cards, but then the rest of your cards are at best Copper, so that's not enough either. The Smithy can get you back to six cards after playing the Cellar, and that's just enough if your luck is just right.

I figued the probability of drawing Gold with every sensible way to play the Cellar, and reported the best. It's mostly straightforward. If you draw a Cellar and four Coppers, you have to drop at least one. Exactly one turns out to be the right number. With a Cellar, more than one Copper, and some Estates, drop all the Estates. If you have a Cellar, one Copper, and all three Estates, the choice is a little counterintuitive. Drop all four cards including the copper. Nothing remains in your deck worse than a Copper. At worst you get four Coppers. At best you get the Smithy, and then you are guaranteed to get six Coppers after playing it. If you have the Cellar and Smithy in hand at the start of your turn, just drop any Estates you have.


These remaining options have no chance of getting Gold:

Copper x Copper, Copper x Cellar, Copper x Spy, Copper x Throne Room, Copper x Village, Copper x no buy, Cellar x Cellar, Cellar x Chancellor, Cellar x Militia, Cellar x Woodcutter, Cellar x Spy, Cellar x Throne Room, Cellar x Village, Cellar x no buy, Spy x Village, Spy x no buy, Throne Room x Village, Throne Room x no buy, Village x Village, Village x no buy, no buy x no buy


Here's the methodology. I compiled a reduced set of cards you can buy. I excluded any cards that don't help you buy Gold. These might be good buys in some games, but they certainly won't be part of a top-ranked combination to increase your odds of buying Gold in turn 3. It might still be interesting to see what your odds would be if you bought one of them. I might post those results later.

Estate
Duchy
Province
Curse
Bureaucrat
Chapel
Feast
Gardens
Remodel
Thief
Workshop

I excluded any that can help you, but help you the same amount as another card that costs the same or cheaper. In combinations when you can afford the more expensive one, I relist the more expensive one with the same odds.

Militia (Chancellor)
Witch (Moat)
Woodcutter (Chancellor)

I excluded any cards that cost 6 or more. You can't afford these in turns 1 and 2.

Gold
Adventurer

There are 16 cards left plus the no-buy option.

Copper
Silver
Cellar
Chancellor
Council Room
Festival
Laboratory
Library
Market
Mine
Moat
Moneylender
Smithy
Spy
Throne Room
Village
no buy

That means 17x16 / 2 + 17 = 153 combinations. However some are too expensive. There are 6 5-cost cards, 4 4-cost cards, 3 3-cost cards, and 4 options for 2 or less.

6 5-cost cards with 4 for 2 or less for 24 combinations.
4 4-cost cards with 7 for 3 or less for 28 combinations.
The 7 for 3 or less can combine freely with the other 6 for 3 or less for 42 / 2 = 21 combinations plus 7 of picking the same choice twice.

So there are only 80 possible combinations.

The technique I find most intuitive for solving these probabilities is permutations with duplicates. If there are l of one kind of card, m of another, and n of a third, then the number of unique ways these can be ordered is given by this formula: (l + m + n)!/(l! x m! x n!). With two new cards, there can be four kinds of cards in your deck. If you buy the same card twice, my method works if you consider them to be different anyway. The number of different shuffles of the deck is 12! /(7! x 3! x 1! x 1!) = 15840.

To find the probability of any particular initial hand combination, we want to find out how many shuffles have those cards as their first five. You can calculate the permutations of the hand itself. Given these cards, there is also some number of independent ways to permute the cards not drawn. Multiply these together to get the number of shuffles that get that combination, and divide by 15840 to get the probability.

I reduced the results with their least common denominator, 792.

5 Copper
5! / (5!) x 7! / (2! x 3! x 1! x 1!) / 15840 =
420 / 15840 = 21 / 792 = 2.7%
4 Copper, 1 Estate
5! / (4! x 1!) x 7! / (3! x 2! x 1! x 1!) / 15840 =
2100 / 15840 = 105 / 792 = 13%
3 Copper, 2 Estates
5! / (3! x 2!) x 7! / (4! x 1! x 1! x 1!) / 15840 =
2100 / 15840 = 105 / 792 = 13%
2 Copper, 3 Estates
5! / (2! x 3!) x 7! / (5! x 1! x 1!) / 15840 =
420 / 15840 = 21 / 792 = 2.7%
1 new card, 4 Copper
5! / (1! x 4!) x 7! / (3! x 3! x 1!) / 15840 =
700 / 15840 = 35 / 792 = 4.4%
1 new card, 3 Copper, 1 Estate
5! / (1! x 3! x 1!) x 7! / (4! x 2! x 1!) / 15840 =
2100 / 15840 = 105 / 792 = 13%
1 new card, 2 Copper, 2 Estates
5! / (1! x 2! x 2!) x 7! / (5! x 1! x 1!) / 15840 =
1260 / 15840 = 63 / 792 = 8.0%
1 new card, 1 Copper, 3 Estates
5! / (1! x 1! x 3!) x 7! / (6! x 1!) / 15840 =
140 / 15840 = 7 / 792 = 0.88%
2 new cards, 3 Coppers
5! / (1! x 1! x 3!) x 7! / (4! x 3!) / 15840 =
700 / 15840 = 35 / 792 = 4.4%
2 new cards, 2 Coppers, 1 Estate
5! / (1! x 1! x 2! x 1!) x 7! / (5! x 2!) / 15840 =
1260 / 15840 = 63 / 792 = 8.0%
2 new cards, 1 Copper, 2 Estates
5! / (1! x 1! x 1! x 2!) x 7! / (6! x 1!) / 15840 =
420 / 15840 = 21 / 792 = 2.7%
2 new cards, 3 Estates
5! / (1! x 1! x 3!) x 7! / (7!) / 15840 =
20 / 15840 = 1 / 792 = 0.13%

Then I just chose for each combination, which of these draws would let you get a Gold. It's more complicated when there are action cards that let you draw additional cards. Generally, I considered cases when you have those in your hand separately. I just figured the total number of cards you would have after playing the extra draw card, and recalculated as if you had that size hand out of an 11 card deck.
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Jeremiah Lee
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That's intense!
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Erik Boyko
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That's great, thanks! I'm reminded of a question I've been meaning to ask: has anyone ever found it to be a bad idea to purchase a province card [6 vp] instead of an action card or a gold? I had a game recently where I got really lucky with the chancellor and bought three consecutive province cards very early on in the game. I think my only other cards besides the starting deck at that point were a gold and a silver. I then fell behind with some bad draws, but came back later in the game for the win.
 
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Johan Eriksson
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I´d say if you get to 8 gold, always go for the province!
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Andrew Mitchell
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Well done on the stats, Greg...
I spot checked a few of them [eg smithy+silver] using a different method and they are all correct :)
I did a 10,000 game simulation on my computer a couple of weeks ago and I'll try to post that later today.
Andrew
 
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Juho Snellman
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morningstar wrote:
I think getting Gold early is usually an important tactic. So I decided to calculate the probabilities of getting Gold on the 3rd turn (the first turn your new cards come into play) based on what two cards you buy in your first and second turn. None of the probabilities are very high. I think the probabilities for getting Gold on the 4th or later turn should be comparable, but these are really difficult to calculate as in some cases they depend on the way you play your action cards and even on buys in the 3rd turn. So I think the probabilities should give you an idea of how fast you can expect to get Gold with a given starting combination.


One thing to note is that the smithy / non-smithy versions aren't directly comparable due to different deck cycling speeds. A silver + silver opening has a >40% chance of buying a gold before the second reshuffle, since it doesn't matter whether the gold is bought in the 3rd or 4th hand. On the other hand, for a silver + smithy buying the gold in the 4th hand almost certainly means losing it into an empty discard pile.

And of course there's the opposite effect that a player with a smithy will on average see the gold more quickly after a reshuffle.
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Scott Mayer
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xxeyes wrote:
I'm reminded of a question I've been meaning to ask: has anyone ever found it to be a bad idea to purchase a province card [6 vp] instead of an action card or a gold?
I'm fairly certain that it's often better to buy a gold or action card than a province early in a game. However, buying a province is never that bad, and I don't really have anything more than gut instinct and a couple of anecdotes to support my position.

My rule of thumb: if I'm setting up to be able to consistently buy a victory card per turn, without much chance of obtaining multiples in a turn, I want the early province. If I'm setting up to go broken and buy multiple victory cards in consecutive turns, I want the gold/action card.

t~
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tiornys wrote:
xxeyes wrote:
I'm reminded of a question I've been meaning to ask: has anyone ever found it to be a bad idea to purchase a province card [6 vp] instead of an action card or a gold?
I'm fairly certain that it's often better to buy a gold or action card than a province early in a game. However, buying a province is never that bad, and I don't really have anything more than gut instinct and a couple of anecdotes to support my position.

My rule of thumb: if I'm setting up to be able to consistently buy a victory card per turn, without much chance of obtaining multiples in a turn, I want the early province. If I'm setting up to go broken and buy multiple victory cards in consecutive turns, I want the gold/action card.

t~

My rule of thumb -- and this is more gut instinct over 300 games than analysis -- is to start buying provinces after I have 8 gold for the third time, or if my opponent has bought one. The reason is that my deck may not yet be tuned to make a 4-5 province run the first time I have 8. But if I pass on the province and improve my deck, it improves my later chances of running out the province deck in straight turns, or at least getting an insurmountable lead.
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Greg Payne
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As much as I like this, you are still missing parts of the full story, namely that $5 is still a useful "milestone" if you started with 4/3, and less so (although still generally not bad) with 5/2. Is there any chance that you can revisit 4/3 with Part 3 to analyze $5 on turn 3?
 
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Mark McEvoy
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Looking forward to part 2, and curious to see how Library, Council Room, Laboratory, and the like figure into this. Though given that they can't pair with a Silver, I don't expect any of them fare too well. Cellar-Library can likely slightly best Cellar-Smithy... but I wonder if the best odds in the 5-2 break (after Silver-Moat) are Council Room-Nothing.
 
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Mark McEvoy
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Oh! Oh! Could you also add Envoy to the mix for Part I? How would Envoy-Silver compare to Smithy-Silver? I can't figure out in my head if it's better or worse.
 
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David desJardins
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thatmarkguy wrote:
How would Envoy-Silver compare to Smithy-Silver? I can't figure out in my head if it's better or worse.


Envoy-Silver gives you the following chances for gold on turn 3:

Silver 4 Copper = 7c4/12c5 = 4.42%

Envoy* 7 Copper 2 Estate = 3c2/12c10 * 5/10 = 2.27%

Envoy* Silver 7 Copper Estate = 3c1/12c10 * 5/10 = 2.27%

Envoy* Silver 6 Copper 2 Estate = 7c6*3c2/12c10 * 5/10 = 15.91%

Envoy* Silver* 5 Copper 3 Estate = 7c5/12c10 * 5/10 * 4/9 = 7.07%

(*) must be in first 5 cards drawn

So that adds up to 31.94%, slightly better than Smithy-Silver.
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Hey David, do you have to account for the card your opponent makes you discard? So it's 9 cards kept instead of 10?

So any Silver used would also need the Asterisk (must be in first 5 drawn), right?
 
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Mark McEvoy
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He already accounted for that.

Envoy* 7 Copper 2 Estate = 6 copper after opponent makes you discard one.
Envoy* Silver 7 Copper Estate = 7 copper after your opponent makes you discard silver
Envoy* Silver 6 Copper 2 Estate = 6 copper after your opponent makes you discard silver
Envoy* Silver* 5 Copper 3 Estate = 1 silver 4 copper after your opponent makes you discard a copper (because your silver was in your first 5 and thus never in question)

Thanks for doing the math for me, David.
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Aha! I see it now. I knew there was something I was missing. That's why I asked, I know he's smarter than me and I was just missing it. (And you are too, obv.)


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Greg Jones
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Lardarse wrote:
As much as I like this, you are still missing parts of the full story, namely that $5 is still a useful "milestone" if you started with 4/3, and less so (although still generally not bad) with 5/2.


Yes, I agree. I recently got whupped on a set where Festivals were critical. They were almost all gone before I could get 5 coins.

Lardarse wrote:
Is there any chance that you can revisit 4/3 with Part 3 to analyze $5 on turn 3?


Yes, as soon as I get a new job and a new house.
 
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Greg Jones
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thatmarkguy wrote:
Looking forward to part 2, and curious to see how Library, Council Room, Laboratory, and the like figure into this. Though given that they can't pair with a Silver, I don't expect any of them fare too well. Cellar-Library can likely slightly best Cellar-Smithy... but I wonder if the best odds in the 5-2 break (after Silver-Moat) are Council Room-Nothing.


Preview: Part 2 is probably coming this weekend.

There are some 2/5 combos that do quite well. 28% is the best odds.
 
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Greg Jones
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The 2/5 coin start report is now up here: http://www.boardgamegeek.com/thread/370808.
 
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Greg Jones
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thatmarkguy wrote:
Oh! Oh! Could you also add Envoy to the mix for Part I? How would Envoy-Silver compare to Smithy-Silver? I can't figure out in my head if it's better or worse.


By popular demand:

Envoy x Silver = 32% = 35 / 792 + 28%
Envoy x Copper = 20%
Envoy x no buy = 14%
Envoy x Cellar = 12%*
Envoy x Village = 11%
Envoy x Chancellor = 9.0% = 35 / 792 + 4.5%
Envoy x Moat = 5.2%

Compare to the Smithy:

Smithy x Silver = 29% vs. 32%
Smithy x Copper = 12% vs. 20%
Smithy x no buy = 8.3% vs. 14%
Smithy x Cellar = 7.4% vs. 12%
Smithy x Village = 6.6% vs. 11%
Smithy x Chancellor = 8.1% vs. 9.0%
Smithy x Moat = 4.3% vs. 5.2%

In most cases, the Envoy does about 50% better than the Smithy. An unfortunate exception is the strongest Smithy x Silver combination. That's because if you draw the Silver with the Envoy, it's going to be discarded. So in that case, the Envoy just performs slightly better.

Thanks to DaviddesJ for inspiring the solution for these. It's easy to solve them when you just assume that you'll need to draw 7 Coppers. It doesn't matter which are drawn with the Envoy and which are not - at least some of them must be, and so one of those could be discarded by an opponent. Only when the Silver is in play does that matter, and David already solved that one for us.

* Cellar tactics:

If you start with a Cellar and four Coppers, it's impossible to get a Gold. You're going to end up with eight cards before the opponent discards one. You need to get seven Coppers, since one will be discarded. That means drawing 2 Estates will block your chance of getting a Gold. There are only three more Coppers left in your deck, so when you draw five cards you'll get at least two Estates. So you might be better off not to use the Cellar, and buy something for 4.

If you start with the Cellar, the Envoy, and three Estates, you can guarantee you'll get a Gold. Discarding two Estates and playing the Envoy will draw the rest of your deck, which contains seven Coppers. Discarding three Estates will draw the rest of your deck and reshuffle the three Estates and redraw one. You're better off not to do that, because your next hand will start with two Estates.

With any other hand, your best chance is completely intuitive. Discard all your Estates and none of your Coppers.
 
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Greg Jones
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Adding cards that don't help you get a Gold on turn 3, but have other useful purposes. The most likely one you'll consider is the Chapel, for its arguably underpriced incredible early-game value.

Silver x Chapel = 35 / 792 = 4.4%

Surprisingly, this choice does a little better than Chapel x Smithy. Still, with little chance to get a Gold, I think it's too early for the Chapel. I'd rather buy Silver x Smithy or one of the other top combos and buy a Chapel and a Gold in turns 3 and 4.

Same odds: Silver x Estate, Silver x Curse, Silver x Bureaucrat, Silver x Feast, Silver x Gardens, Silver x Remodel, Silver x Thief, Silver x Workshop

I think the value of these buys depends mostly on what you think of the action card included. In my opinion, these would only be good buys in particular setups.

Chancellor x Chapel = 35 / 792 = 4.4%
Moneylender x Chapel = 35 / 792 = 4.4%

These Silver equivalents have the same odds as a Silver. I don't like these combos any more. The Chancellor's not much use as you want to draw your bad cards to put in the Chapel. The Moneylender is a bit redundant when you have the Chapel, because you can quickly get rid of your Coppers with the Chapel.

Same odds: Chancellor x Estate, Chancellor x Curse, Chancellor x Bureaucrat, Chancellor x Feast, Chancellor x Gardens, Chancellor x Remodel, Chancellor x Thief, Chancellor x Workshop, Moneylender x Estate, Moneylender x Curse, Moneylender x Bureaucrat, Moneylender x Feast, Moneylender x Gardens, Moneylender x Remodel, Moneylender x Thief, Moneylender x Workshop

I wouldn't recommend any of these combos, because if you draw both action cards in the same hand, you can only play one.

Smithy x Chapel = 3.7%

I'm really not liking this combo. Your chances of getting Gold are really low. On top of that, chances are good if you play your Smithy, you'll draw your Chapel and miss your chance to play it. In that case, you may as well have bought it in turn 3 or 4.

Same odds: Smithy x Estate, Smithy x Curse, Smithy x Workshop

Moat x Chapel = 0.63%

Same odds: Moat x Estate, Moat x Curse, Moat x Bureaucrat, Moat x Feast, Moat x Gardens, Moat x Remodel, Moat x Thief, Moat x Workshop


In conclusion, I would say buying a Chapel in your first two turns with a 3/4 start is not very strong. If you do, I would say a Silver is the best thing to pair it with in most sets. If you're going for a specialty strategy, a different buy could be good. Chapel x Remodel comes to mind.
 
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David desJardins
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morningstar wrote:
Silver x Chapel = 35 / 792 = 4.4%

Surprisingly, this choice does a little better than Chapel x Smithy.


That doesn't seem surprising. Buying Chapel-Smithy gives you 7 money in 12 cards, so the average value of drawing 3 cards is 3*7/12 = 1.75, so it's not surprising that a Silver is better.

Quote:
In conclusion, I would say buying a Chapel in your first two turns with a 3/4 start is not very strong.


I would say that basing this decision on the probability of buying a Gold on turn 3 is missing the forest for the trees.
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Greg Jones
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DaviddesJ wrote:
morningstar wrote:
In conclusion, I would say buying a Chapel in your first two turns with a 3/4 start is not very strong.


I would say that basing this decision on the probability of buying a Gold on turn 3 is missing the forest for the trees.


I wouldn't say so. It's not a good idea to trash a lot of your Coppers until you have a different source of money. Sure, if you're lucky, you can trash several Estates. Otherwise, I'd rather buy something good in one of my 3rd and 4th turns and buy the Chapel in the other. Then start using the Chapel in turn 5 or later. It only delays streamlining your deck a couple turns, but you have a lot more momentum when you do.
 
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Kirkwb
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Basic Chapel Strategy is to rid yourself of your first 10 starting cards asap, picking up silver in the process. Then you work on filling your nicely thinned deck with Gold.

If you put it off your lowering your chances of drawing 4 of the initial 10 cards with a chapel.

A hand where I draw Smithy and Chapel is worthless to the chapel strategy, the Smithy is getting in the way.

Some boards I want to wait to buy Chapel, but most I want to open with it. Trashing your coppers is exactly what you want to do (get 2 silver first of course).

Forrest for the Trees is right.
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Greg Jones
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DaviddesJ wrote:
morningstar wrote:
Silver x Chapel = 35 / 792 = 4.4%

Surprisingly, this choice does a little better than Chapel x Smithy.


That doesn't seem surprising. Buying Chapel-Smithy gives you 7 money in 12 cards, so the average value of drawing 3 cards is 3*7/12 = 1.75, so it's not surprising that a Silver is better.


The reason it surprised me is that without the Chapel, buying a Smithy alone outperforms buying a Silver alone (by about double). In that scenario the average value of 3 cards is 1.9, still less than 2. Average value doesn't tell the whole story when you're shooting for a particular target.
 
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