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[JThorne]

I've been mulling this one over, waiting, but what the heck, I'll do it. Someone said "start a new thread" so I'm starting a new thread.

I was shocked to see that anyone would even bother to argue this, but to review: You open Chapel/Silver.

Question: With a hand of Chapel-Silver-Copper-Copper-Copper, do you trash three coppers or buy a key power-$5?

Answer: You trash three coppers.

Trash down/build up is such a fundamental principle it's hard to imagine why there would even be an argument. You're going to have at least another $3 hand before your next shuffle, and if you want to be sure to hit $5 you can always buy another Silver. Your odds of colliding two Silvers increases dramatically with three fewer coppers in your deck.

I tried to imagine any situation in which it would be beneficial to buy the $5, and I had a really hard time doing so. If you're worried about losing the split, well, you'll probably lose it anyway to the player who builds correctly and can buy $5s reliably every turn. I've seen many people make this mistake, and inevitably, they build up their drawing capability while their deck is still half-full of junk and then start complaining about how they never draw their Chapel with their junk cards, or draw their Chapel dead.

It's even worse with Steward. The number of times I've seen Steward used for money early in a Steward, Copper, Copper, Copper, Estate hand because they wanted that power-$5 so badly is astounding. Or even Steward-4C being used to buy Gold. (Ick. Yellow cards.) The beauty of Steward is that you can trash Coppers even more aggressively than with Chapel because it can switch to giving economy for the build phase.

There's nothing like the audible "click" you hear when an engine snaps into place and starts humming because you've draw a tiny deck into your hand. The world is your oyster. You've made your own shuffle luck. Anyone who has bought a Donate on turn three or four and trashed down to five cards or less knows what I'm saying. Did you really need a power-$5 first, or are you just going to start getting them by the handful starting now?

It would be nice to have some clarity about this, if nothing else for the benefit of newer readers.

[LastFootnote]

If you get Chapel-Silver-Copper-Copper-Copper against a similarly skilled opponent, haven't you basically already lost?

[McGarnacle]

This is interesting. I never thought of this. What if, on the other hand, you really wanted a $4? Trash only 1 copper and buy it, or trash down all the way? What about a $3. I would think you want to do the same as with a $5, but I could be wrong.

[Deadlock39]

If you get Chapel-Silver-Copper-Copper-Copper against a similarly skilled opponent, haven't you basically already lost?

Perhaps in most cases... but what if they got that hand too? There may also be worse things that could happen to them later if the board lends itself.

[werothegreat]

but what if they got that hand too?

What if we both buy the exact same cards, and our shuffles are completely identical in every way?

[Deadlock39]

but what if they got that hand too?

What if we both buy the exact same cards, and our shuffles are completely identical in every way?

First player advantage becomes even more relevant?

[Chris is me]

If you get Chapel-Silver-Copper-Copper-Copper against a similarly skilled opponent, haven't you basically already lost?

Here's a shitty idea I'm just theorycrafting - what if you buy another Chapel on that hand?

The idea is, you're BEHIND. You are gonna hit, GENEROUSLY, $3 on the other hand that shuffle (presumably another Silver), and you are one card less thin. If you bought another Chapel, you could potentially trash as many as 7 cards next shuffle, or as few as 1 card (in the nightmare Silver Silver Chapel Chapel Junk hand).

You always trash the one Chapel with the other if able. This just gives you that outside chance of thinning it all out in turns 6-7 and clawing your way back into it. Even if both Chapels land on 1 silver, that's still six more junk cards out in that shuffle, leaving just 1 Copper (and the other Chapel) left. Even if the Chapels collide, it's not significantly worse than just being behind with 1 Chapel (you'll have trashed 4-6 junk cards + the Chapel, which is not much different than the position you'd be in if you bought nothing)

Thoughts?

This is bad, right? Thoughts?

[4est]

If you get Chapel-Silver-Copper-Copper-Copper against a similarly skilled opponent, haven't you basically already lost?

Here's a shitty idea I'm just theorycrafting - what if you buy another Chapel on that hand?

The idea is, you're BEHIND. You are gonna hit, GENEROUSLY, $3 on the other hand that shuffle (presumably another Silver), and you are one card less thin. If you bought another Chapel, you could potentially trash as many as 7 cards next shuffle, or as few as 1 card (in the nightmare Silver Silver Chapel Chapel Junk hand).

You always trash the one Chapel with the other if able. This just gives you that outside chance of thinning it all out in turns 6-7 and clawing your way back into it. Even if both Chapels land on 1 silver, that's still six more junk cards out in that shuffle, leaving just 1 Copper (and the other Chapel) left. Even if the Chapels collide, it's not significantly worse than just being behind with 1 Chapel (you'll have trashed 4-6 junk cards + the Chapel, which is not much different than the position you'd be in if you bought nothing)

Thoughts?

This is bad, right? Thoughts?

My gut instinct is to say, yes, this is definitely bad. 

It seems like it's probably worse than buying nothing most of the time (especially in the case of collision, "nightmare hand" or not, since the extra Chapel could have been another junk card to trash).  I'd assume that only VERY rarely will this result in efficient enough trashing during the second shuffle to "catch up" with a more efficient-trashing opponent (at the cost of an extra junk card, Chapel, which you'll have to trash later), but it's hard to say how rare that best case scenario is, and thus how worth going for it is if you're behind.

Sounds like a job for the simulators. 

[xyz123]

Interesting that this thread has been created as over the weekend I played a board where this edge case may have cropped up. I made a note of the kingdom for that very reason. The board was:

- Provinces/Estates
- Obelisk (Wishing Well)

- Chapel
- Fool's Gold
- Ratcatcher
- Settlers/Bustling Village
- Wishing Well
- Golem
- Count
- Embassy
- Royal Carriage
- Tribute

I know that Fool's Gold and Chapel usually don't mix but that is because the Chapel buy and trashing turns means passing up opportunities to gain FGs. Here there is no way to gain more than 1 FG per turn so that disadvantage is minimised. I think that opening Chapel/FG and on early Chapel turns keeping 2 to spend so you can still buy a Fool's Gold can work. Even if you do lose the split 4-6 being thin and picking up an Embassy still gives you a good chance of lining up your FGs.

If I am mistaken about this I would be interested in hearing why.

[Cave-o-sapien]

If you get Chapel-Silver-Copper-Copper-Copper against a similarly skilled opponent, haven't you basically already lost?

Here's a shitty idea I'm just theorycrafting - what if you buy another Chapel on that hand?

The idea is, you're BEHIND. You are gonna hit, GENEROUSLY, $3 on the other hand that shuffle (presumably another Silver), and you are one card less thin. If you bought another Chapel, you could potentially trash as many as 7 cards next shuffle, or as few as 1 card (in the nightmare Silver Silver Chapel Chapel Junk hand).

You always trash the one Chapel with the other if able. This just gives you that outside chance of thinning it all out in turns 6-7 and clawing your way back into it. Even if both Chapels land on 1 silver, that's still six more junk cards out in that shuffle, leaving just 1 Copper (and the other Chapel) left. Even if the Chapels collide, it's not significantly worse than just being behind with 1 Chapel (you'll have trashed 4-6 junk cards + the Chapel, which is not much different than the position you'd be in if you bought nothing)

Thoughts?

This is bad, right? Thoughts?

I'd like to see the simulations, too.

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

[AJD]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

In this game ages ago I opened Chapel/Silver and drew EEECC turn 3, so I shrugged and bought another Chapel, and I think the slightly quicker trashing helped me get my engine off the ground first.

[O]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling. It only assumes that you want it for some future theoretical engine (it even goes into talking about 5$ splits as if I was suggesting buying a minion). This is true for none of the examples i listed

It also still fails to present the fact that once you open CCC-CH-S you are at a significant disadvantage and need some substantial luck to catch up to a player with a more optimal chapel hand. You would have to demonstrate that the "comeback odds" versus a deck is ahead is less with the 5$ than with chapelling. It is not merely sufficient to show that if two players open CCC CH S, the one who chapels has a better win % than the one who buys the 5$. If you know for certain your opponent starts turn 3 with 4 golds in their deck to your none, you would open Treasure Map/Treasure map (say bakers on the board) over silver/silver, despite it probably being a far inferior opening in the head to head.

I could very well be wrong. But the OP here is entirely irrelevant to the posts in the original thread because of this, in fact it doesn't even attempt to make an argument.

[Awaclus]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

[O]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

Archive and Hunting Party both set up your next chapel to hit more estates. Mountebank substantially hampers the enemies trashing as soon as it hits.  You are a full shuffle of chapel tempo, which is incredibly different than a shuffle full of tempo unless your gameplan is "trash into pure copperless engine", in which case yea I would not be considering the 5$.

Your comparisons fall short because they keep trying to oversimplify the situation way too much.

[Awaclus]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

Archive and Hunting Party both set up your next chapel to hit more estates. Mountebank substantially hampers the enemies trashing as soon as it hits.  You are a full shuffle of chapel tempo, which is incredibly different than a shuffle full of tempo unless your gameplan is "trash into pure copperless engine", in which case yea I would not be considering the 5$.

Your comparisons fall short because they keep trying to oversimplify the situation way too much.

Archive and Hunting Party set up your next Chapel to hit 1 extra card. Trashing three coppers now sets up your Chapel to hit 3 extra cards immediately. The Mountebank isn't going to hit until your next shuffle, at which point your opponent has already gotten in 2 Chapel turns most likely, which makes it pretty trivial for him to trash the rest of his junk too, and if he gets a Mountebank at that point, you're screwed because you spent your early game gaining more stop cards instead of trashing junk so you're going to have a very hard time even connecting the Chapel efficiently (also he's playing the Mountebank much more often than you're playing yours because his deck is thinner).

[O]

Trashing three coppers now sets up your Chapel to hit 3 extra cards immediately.

this is immediately and obviously misleading, since it removes those from the chances to chapel for the next shuffle aswell. It's not the same as setting up future shuffles.

[Awaclus]

Trashing three coppers now sets up your Chapel to hit 3 extra cards immediately.

this is immediately and obviously incorrect.

It is not in comparison with skipping that trashing and buying something like Hunting Party.

[Kirian]

So OK, let's consider a very simple scenario in which both players' first four hands are identical, and the only action cards of interest in the early game are Chapel and Lab, but there's a Market and enough other stuff to make a killer engine.

They both open Chapel/Silver on 3/4.  T3, both draw CCCEE and buy Silver.  T4, both draw Chapel-SCCC.

Turn 4:
P1 Chapels 3 Coppers.
P2 buys a Lab

Turn 5:
P1 draws CE and 3 of Chapel-SSCCCEE (8 cards)
P2 draws CE and 3 of Chapel-Lab-SSCCCCCCEEE (12 cards)

One thing we see immediately is this:  P1 will get to play Chapel again on either T5 or T6.  Their deck has 10 cards.  P2... might not see their Chapel until T7.  But hey!  Let's just assume best-case scenario for P2 and worst-case for P1.  So:

Turn 5:
P1 draws CCEEE and buys nothing
P2 draws Chapel-CEEE and dumps four cards.

Turn 6:
P1 draws Chapel-SSCC, dumps the Coppers.  Buying another Silver would be counterproductive at this point.
P2 draws Lab-SCCC, then draws CC and buys a Gold (or, say, a $5 with +Buy, like Market).

At this point, our status is this:

P1's deck is Chapel-SSCCEEE
P2's deck is Lab-Chapel-GSSCCCCCC, and is guaranteed to draw SC plus three other cards next turn.

P2 likely has an edge here because they got rid of all their Estates and P1 failed to get rid of any, but the chance of P1 not getting rid of some in the next few turns is pretty low.

So if we give our trasher the worst possible outcome and our buyer the best possible outcome, the buyer comes out ahead.

What about the reverse?

Turn 5:
P1 draws Chapel-CEEE and trashes it all.
P2 draws SCCCE and buys another Lab, or a Market perhaps.

Turn 6:
P1 draws SSCCC and buys a Lab
P2 draws SCCEE and... probably should skip another Silver buy.

P1's deck is now Lab-Chapel-SSCCC
P2's deck is now Lab-Chapel-Market-SSCCCCCCCEEE

P2 is guaranteed to draw Lab-Chapel-CC and will definitely finally get to trash some cards on T7.  But their deck is 15 cards thick, and P1's deck will hit $6 or better until they start greening.

P1's best case scenario is hugely better than P2's best case for moving into an engine.
P1's worst case scenario is certainly better than P2's worst case, though likely not by as much.

P1's average case, then, is better than P2's average case.

[O]

So OK, let's consider a very simple scenario in which both players' first four hands are identical, and the only action cards of interest in the early game are Chapel and Lab, but there's a Market and enough other stuff to make a killer engine.

They both open Chapel/Silver on 3/4.  T3, both draw CCCEE and buy Silver.  T4, both draw Chapel-SCCC.

Turn 4:
P1 Chapels 3 Coppers.
P2 buys a Lab

Turn 5:
P1 draws CE and 3 of Chapel-SSCCCEE (8 cards)
P2 draws CE and 3 of Chapel-Lab-SSCCCCCCEEE (12 cards)

One thing we see immediately is this:  P1 will get to play Chapel again on either T5 or T6.  Their deck has 10 cards.  P2... might not see their Chapel until T7.  But hey!  Let's just assume best-case scenario for P2 and worst-case for P1.  So:

Turn 5:
P1 draws CCEEE and buys nothing
P2 draws Chapel-CEEE and dumps four cards.

Turn 6:
P1 draws Chapel-SSCC, dumps the Coppers.  Buying another Silver would be counterproductive at this point.
P2 draws Lab-SCCC, then draws CC and buys a Gold (or, say, a $5 with +Buy, like Market).

At this point, our status is this:

P1's deck is Chapel-SSCCEEE
P2's deck is Lab-Chapel-GSSCCCCCC, and is guaranteed to draw SC plus three other cards next turn.

P2 likely has an edge here because they got rid of all their Estates and P1 failed to get rid of any, but the chance of P1 not getting rid of some in the next few turns is pretty low.

So if we give our trasher the worst possible outcome and our buyer the best possible outcome, the buyer comes out ahead.

What about the reverse?

Turn 5:
P1 draws Chapel-CEEE and trashes it all.
P2 draws SCCCE and buys another Lab, or a Market perhaps.

Turn 6:
P1 draws SSCCC and buys a Lab
P2 draws SCCEE and... probably should skip another Silver buy.

P1's deck is now Lab-Chapel-SSCCC
P2's deck is now Lab-Chapel-Market-SSCCCCCCCEEE

P2 is guaranteed to draw Lab-Chapel-CC and will definitely finally get to trash some cards on T7.  But their deck is 15 cards thick, and P1's deck will hit $6 or better until they start greening.

P1's best case scenario is hugely better than P2's best case for moving into an engine.
P1's worst case scenario is certainly better than P2's worst case, though likely not by as much.

P1's average case, then, is better than P2's average case.

We've already established that 1: There are cards that help way more than lab and 2: average case comparison is not quite relevant when you already need a swing in luck.

[Chris is me]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

Archive and Hunting Party both set up your next chapel to hit more estates. Mountebank substantially hampers the enemies trashing as soon as it hits.  You are a full shuffle of chapel tempo, which is incredibly different than a shuffle full of tempo unless your gameplan is "trash into pure copperless engine", in which case yea I would not be considering the 5$.

Your comparisons fall short because they keep trying to oversimplify the situation way too much.

Okay what board are you buying Chapel on that you don't want to transition to a "pure copperless" deck? That's every Chapel board. That's the whole point of Chapel.

Trust literally everyone posting here - even the swingy outside Chance crazy luck scenarios at best barely benefit the player skipping Chapel trashes. It's just the wrong move. There's no single $5 buy that immediately undoes trashing 3-4 cards or enables trashing 3-4 more cards.

[O]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

Archive and Hunting Party both set up your next chapel to hit more estates. Mountebank substantially hampers the enemies trashing as soon as it hits.  You are a full shuffle of chapel tempo, which is incredibly different than a shuffle full of tempo unless your gameplan is "trash into pure copperless engine", in which case yea I would not be considering the 5$.

Your comparisons fall short because they keep trying to oversimplify the situation way too much.

Okay what board are you buying Chapel on that you don't want to transition to a "pure copperless" deck? That's every Chapel board. That's the whole point of Chapel.

Trust literally everyone posting here - even the swingy outside Chance crazy luck scenarios at best barely benefit the player skipping Chapel trashes. It's just the wrong move. There's no single $5 buy that immediately undoes trashing 3-4 cards or enables trashing 3-4 more cards.

Do you think you are achieving productive discussion by removing the word "engine" from "pure copperless engine?

You are buying chapel in many, many games that don't involve straight engines. Copper has varying negative utility, and in games without straight engines copper often has less negative utility. I am not trying to suggest that copper has positive utility in chapel games. 

I'd be more likely to "trust the majority" of you here if you didn't try and treat this as some "gotcha" rhetorical contest instead of a discussion.

[drsteelhammer]

This "analysis" (it's really just stating is as some kind of incontrovertible answer) ignores any and all possibilities that your 5$ buy 1) Speeds up your future chapelling in itself or 2) slows down your enemies chapelling.

Trashing three Coppers speeds up your future Chapeling three times as much as Laboratory does, plus it also speeds up your current Chapeling by three Coppers. There is no card in the game that comes even close in that regard — Chapeling as much as you can is always better than buying a $5.

As far as luck is concerned, sure, you're behind if you draw that hand, but that's not a reason to put you almost another full shuffle worth of tempo behind by not taking full advantage of the Chapel when you draw it.

Archive and Hunting Party both set up your next chapel to hit more estates. Mountebank substantially hampers the enemies trashing as soon as it hits.  You are a full shuffle of chapel tempo, which is incredibly different than a shuffle full of tempo unless your gameplan is "trash into pure copperless engine", in which case yea I would not be considering the 5$.

Your comparisons fall short because they keep trying to oversimplify the situation way too much.

Okay what board are you buying Chapel on that you don't want to transition to a "pure copperless" deck? That's every Chapel board. That's the whole point of Chapel.

Trust literally everyone posting here - even the swingy outside Chance crazy luck scenarios at best barely benefit the player skipping Chapel trashes. It's just the wrong move. There's no single $5 buy that immediately undoes trashing 3-4 cards or enables trashing 3-4 more cards.

Do you think you are achieving productive discussion by removing the word "engine" from "pure copperless engine?

You are buying chapel in many, many games that don't involve straight engines. Copper has varying negative utility, and in games without straight engines copper often has less negative utility. I am not trying to suggest that copper has positive utility in chapel games. 

I'd be more likely to "trust the majority" of you here if you didn't try and treat this as some "gotcha" rhetorical contest instead of a discussion.

O, have you ever opened Chapel/Banquet? Or t3 Banquet on an Engine board?

[O]

no, probably respectively

unfortunately example 1 is still well within the realm of "comparisons that really don't work"

[drsteelhammer]

i think it's as close as we can get. gaining additional Coppers and refusing to trash your own is more similar than our intuition suggests.

[O]

shuffle 1 vs shuffle 2 and 7-4  coppers vs 7-9 coppers, greatly increasing the chance of chapel missing the shuffle for your second shuffle to 4/15.

[Awaclus]

shuffle 1 vs shuffle 2 and 7-4  coppers vs 7-9 coppers, greatly increasing the chance of chapel missing the shuffle for your second shuffle to 4/15.

Banquet on T3 is 6-4 vs 7-4 Coppers (assuming the other hand is the S/C/C/C/Chapel and you trash when you buy Banquet and don't when you don't).

[O]

was talking about t1 t2 banq chapel

[aku_chi]

Okay what board are you buying Chapel on that you don't want to transition to a "pure copperless" deck? That's every Chapel board. That's the whole point of Chapel.

Not so.  There are definitely situations where it's correct to keep some Coppers around with Chapel and even more situations where it's correct to defer trashing some Coppers.  Sometimes you need the Coppers to reach a high price point and the tempo loss from trashing and adding additional economy would be costly.
Example 1: Tournament.  With Chapel + Tournament, it's super important to be the first person in the matchup to buy a Province.  Potentially, you can block the opponent's Tournaments (and subsequent Province buy) and snowball into an easy victory.  So, it will probably be correct to keep 2-3 Copper to afford your first Province (even if this increases your stop card count above 4).
Example 2: Pathfinding.  For an extreme example, add Magpie.  There are situations where keeping some extra Coppers around to buy Pathfinding will not compromise your ability to draw your deck, but will enhance your economy.

That being said, it's (almost?) always correct to trash as many Copper as possible with Chapel the first time you use Chapel.  I can't think of an example where it makes sense to buy a $5 over trashing 3 Coppers with S/C/C/C/Chapel on turn 3 or 4.

[GendoIkari]

but what if they got that hand too?

What if we both buy the exact same cards, and our shuffles are completely identical in every way?

First player advantage becomes even more relevant?

Well it depends on the board. If double-Province (or some sort of megaturn) isn't really a thing that you can expect to do, then the game will just end in a draw the vast majority of the time. If 2 Provinces can be bought at once, then it just depends on how the parity works out; how many times only a single Province had been purchased.

But it does indeed become very difficult for player 2 to ever win the game. The only way it is possible is if player 1 3-piles on any pile that isn't VP.

[Limetime]

Really the only card that helps you trash more than trashing those 3 coppers is donate. Why you have chapel in a game with donate is beyond me.

[faust]

but what if they got that hand too?

What if we both buy the exact same cards, and our shuffles are completely identical in every way?

First player advantage becomes even more relevant?

Well it depends on the board. If double-Province (or some sort of megaturn) isn't really a thing that you can expect to do, then the game will just end in a draw the vast majority of the time. If 2 Provinces can be bought at once, then it just depends on how the parity works out; how many times only a single Province had been purchased.

But it does indeed become very difficult for player 2 to ever win the game. The only way it is possible is if player 1 3-piles on any pile that isn't VP.

Edge case is something like Chariot Race. When player 1 plays it as their first action, it will flip the same card in both decks. But when player 2 plays it, player 1's deck state has already advanced and it's possible to gain VP.

[trivialknot]

In my rankings I put Banquet dead last, after Chancellor even.  That might be hyperbole, but it's pretty weak.  And what if Banquet cost $2, and gained you 3 copper?

The one thing I could imagine buying in place of trashing, is Storyteller.  Because buying a Storyteller is about as good as trashing 3 copper immediately, and might be better than that later on.  But chapel/storyteller don't seem like such a great combo.  Storyteller prefers a large money-dense deck.

[Kirian]

We've already established that 1: There are cards that help way more than lab and 2: average case comparison is not quite relevant when you already need a swing in luck.

(1) OK, what card would you substitute in there?  Mountebank?  I'm game for that.
(2) If you need a swing in luck, average case is extremely relevant; that's the whole point of the notion of expectation value.  Unless there's a situation where your worst case is better than their best case (i.e. you get to open Chapel/Mountebank vs their Chapel/Silver), the average case is what matters.  (And if your worst case is better than their best case, guess what, your average is better too!)

Example 2: Pathfinding.  For an extreme example, add Magpie.  There are situations where keeping some extra Coppers around to buy Pathfinding will not compromise your ability to draw your deck, but will enhance your economy.

I'm pretty certain with Pathfinding and Magpie on the board you ignore Chapel altogether.

[GendoIkari]

(2) If you need a swing in luck, average case is extremely relevant; that's the whole point of the notion of expectation value.  Unless there's a situation where your worst case is better than their best case (i.e. you get to open Chapel/Mountebank vs their Chapel/Silver), the average case is what matters.  (And if your worst case is better than their best case, guess what, your average is better too!)

I think you're missing his point on this one. He's saying that it doesn't matter which option is stronger or better. He's saying it matters which option has the outside chance of being good enough.... For example:

Let's say we play a game where we both roll a die, and the higher roll wins. I would rather roll a d6 than I would roll a special d20 where 19 of the sides are 1 and the last side is 20. The expectation is that the d6 will win most of the time, so it's a smarter move.

But, let's change the rules of the game so that you need to role 10 or better to win. Suddenly, the d20 is the better option, even though it has a lower average.

O's example of the Treasure Maps also illustrated this well. Even if option B only wins 10% of the time against option A, it still could be the right pick when both option A and B are expected to lose against C.

[Cave-o-sapien]

P1's best case scenario is hugely better than P2's best case for moving into an engine.
P1's worst case scenario is certainly better than P2's worst case, though likely not by as much.

P1's average case, then, is better than P2's average case.

I enjoyed this analysis and found it instructive.

However, I'm not sure your concluding claim is accurate based on the best/worst case scenarios without knowing how the case values are distributed for each player. If the distributions are skewed in opposite directions it's possible to contradict your claim.

[trivialknot]

Risky vs safe strategies were described in Stef's classic article.  It's not just a great guiding principle in Dominion, but in life in general.

But really, T3 is way too early to go all out for a risky strategy.  There's so much up to chance still.  Anyway, Ch-SCCC is definitely not the worst thing that can happen.  The worst thing that can happen is if you draw Chapel turn 5.

[Deadlock39]

The worst thing that can happen is if you draw Chapel turn 5.

With your other opening buy, your T3 buy, your T4 buy and a Copper.

[jomini]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

I have done a few (note some of these were non-random kingdoms so I have played way more on Pin boards than random would give you):
1. Gaining excess Chapels so I can Masq them over for a Possession Pin with opponent draw (Gov I think).
2. Beggar/Chapel/Tomb. Village (of some sort), Chapel x2, Beggar x3; around 7 VP per turn in a no net-draw game.
3. Market square/Hermit - get 5 Madmen & still be able to trigger two shots of mass gold.
4. B-Crat pins - force my opponent to top deck 5 green, draw & kill 5 silvers.

Boring price only stuff like getting it off a $3 Develop play because it is better than an estate or fodder for Forge are of course common enough.

[Sharajat]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

The link is lost to the mists of Goko, but I remember a game where my opponent opened Chapel/Saboteur and Sabbed my Chapel. 

Unsurprisingly I won that.

[DG]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

Theoretically you could be playing a game with goons where you are be buying and trashing a lot of copper each turn. I'm pretty sure I've seen actually games where you take a extra chapels knowing you can trash them for something better with a card like graverobber. Chapel/Chapel might even be a good opening in some kingdoms, perhaps one with alms and procession.

[LastFootnote]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

The link is lost to the mists of Goko, but I remember a game where my opponent opened Chapel/Saboteur and Sabbed my Chapel. 

Unsurprisingly I won that.

Saboteur can't hit Chapel.

[Limetime]

In the correct kingdom double chapel might be better with alms + something that rewards you for getting thin(maybe windfall)

[Gherald]

One of the few cards I'll buy with Chapel - Silver - CCC is Hunting Party.

HP doesn't just give you +1 card to play Chapel on, it also seeks out the Chapel and cycles your deck more, meaning you can then play Chapel more often to offset the no trashing on turn 3/4

I'm not sure whether it's most often better than trashing the coppers, but it's close enough that it's how I choose to play on boards where an HP engine is the way to go.

[Sharajat]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

The link is lost to the mists of Goko, but I remember a game where my opponent opened Chapel/Saboteur and Sabbed my Chapel. 

Unsurprisingly I won that.

Saboteur can't hit Chapel.

Huh, I distinctly remember something like that happening.  But you're right.

[Cave-o-sapien]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

The link is lost to the mists of Goko, but I remember a game where my opponent opened Chapel/Saboteur and Sabbed my Chapel. 

Unsurprisingly I won that.

Saboteur can't hit Chapel.

Huh, I distinctly remember something like that happening.  But you're right.

Maybe it was Swindler instead? Turning a Chapel into an Estate is worse than if Saboteur could hit it.

[Sharajat]

Related question: I'd love to see the games where the winning player purposefully gained more than one Chapel (not counting Landmark effects such as Obelisk). Is it ever something other than a case of desperation by the losing player?

The link is lost to the mists of Goko, but I remember a game where my opponent opened Chapel/Saboteur and Sabbed my Chapel. 

Unsurprisingly I won that.

Saboteur can't hit Chapel.

Huh, I distinctly remember something like that happening.  But you're right.

Maybe it was Swindler instead? Turning a Chapel into an Estate is worse than if Saboteur could hit it.

That would make sense.  I distinctly remember he opened Sab+Chapel and I bought at least 2 chapels that game, and it went on forever.   That doesn't mean Swindler wasn't out though (Swindler+Chapel is an actual good opening since you don't get much mileage out of that Silver if you draw it with chapel anyway).  This was back in the Goko era when animations took a while to play out.