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[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.