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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #125 on: June 21, 2022, 05:37:41 pm »
0

This one might be more common and obvious, but it is simply not sui generis.

How many stalemates have you experienced? I have had exactly one in about 8–10k games so far and that was a 0 VP/turn Possession game.
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Holger

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Re: Prosperity 2E Preview 3
« Reply #126 on: June 24, 2022, 07:29:35 am »
+1

Both of these depend on the state of the board. E.g. a Bish/Fort deck is the maximum VP possible on a board without any net draw. And if the Bish/Fort player sees any tricksy engine building, they can just mill a Bish or three from the pile and still make more than any possible setup.

The Bish/Fort player can't just mill a Bish or three from the pile without temporarily breaking the golden deck. Which is not a huge problem, but it slows down that process since you have to spend a turn trashing a Bishop every time your golden deck gets broken, unless you have good draws.

Not at all. Golden deck is 5 Forts, 4 Bish. You can buy a 5th Bish and lose out only in the event that you bottom deck 2 Forts (i.e. 25% of the time). Unless the other guy is racing you to a golden deck, you still win out.

You can most certainly force endgame by sacrificing expected VP and depleting the Bish pile until they cannot gain enough VP/turn to matter.

Yes, and the sacrifice is extremely small. I've just calculated the odds and VP gains going through all possible cases of deck orderings, and the result is that a deck with 5 Fortresses and 5 Bishops makes an expected value of 11.65 VP, only 0.35 VP less than the golden deck. In 50% of cases, the 5th Bishop is the bottom-most card and even gives you a 13th VP (played with an empty hand). In the other 50% of cases, the bottom-most card is a Fortress and you get between 3 VP (extremely rare, about 0.4%) and 12 VP (>25%) by trashing one Bishop, returning you to the golden deck.
So on average you sacrifice ony 2*0.35 =0.7 VP per extra Bishop you buy and trash, for a golden deck with 5 Fortresses.

I haven't done the math for a deck containing only 4 Fortresses (the minimum number necessary for the 12 VP golden deck) - probably you'll lose a bit more than 0.7 VP for milling a Bishop. 

This means that the B/F golden deck can actually three-pile with only one non-Fortress cantrip costing at most $4 in the kingdom. I don't know the total number/percentage of such cantrips among the kingdom cards, but I'd expect that in the majority of B/F games, you'll have one in the kingdom. (The probability is about (1-(5/6)^8)=77% in a B/F game using only Base, Prosperity and Dark Ages.)

However, even then you can still get a stalemate whenever each player has more VPs than the opponent after their own turn: As the three-piling player wins in this case, neither player will want to buy the penultimate card from the cantrip pile.
« Last Edit: June 24, 2022, 08:29:15 am by Holger »
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Holger

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Re: Prosperity 2E Preview 3
« Reply #127 on: June 24, 2022, 07:40:41 am »
+1

Quote
I'm not very confident any of those will be present in a typical Collection/Stampede game, especially with Stampede (which is always present in a typical Collection/Stampede game, surprisingly enough) taking up half the landscape slots on its own.
The point is that we have many, many other combos that replicate all the major concerns of Collection/Stampede. Highest possible repeatable point total? Not even close. Unable to deplete piles without taking a knock on VP/turn? Not close again. Immune to a lot of attacks? There are far better. Each and every supposed flaw is present somewhere else with some combo of cards.

The fact that one some boards Fort/Bish is utterly dominant is not a sign that the combo is utterly broke.

The difference with Stampede/Collection is one of degree, not kind. There are many, many ways to setup recurring VP loops and many of those are both the most powerful source of points and fragile to buying more cards. What makes Stampede/Collections "unique" is that it is quick and simple.

But we see the exact same dynamics with Collection/Ride. Assuming a 5/5 collection split, your deck can support 7 non-Collections (provided you generate $12 and have no discards) and once you file those slots up you just endless loop or risk missing out on 30 VP/Turn. Supplies generate 25 VP/turn and eat up all your draw slots. They again will have a lot of boards where it cuts into the VP gain to move the game further towards an end state.

Stampede/Collection is not the highest VP/turn possible (that is the unbounded VP from Villa/Butterfly). It is not uniquely prone to seizing it. It is not the only 2 card combo that can degenerate.

AFAICS, Stampede/Collection gives by far the most VP/turn among all "stalemate-prone" 2-card combos, with 50 VP.

Collection/Supplies gives 25VP when both piles split 5/5 (otherwise you can get up to 100 VP/turn, but then there is no stalemate), and Collection/Ride also gives 25 VP in this case (or 30 in an almost golden deck with an extra Silver). Bishop/Fortress gives 12 VP, KC/Monument gives 9 VP, and the other examples given use more than 2 cards to achieve a golden deck.

This matters because a 2-card combo shows up orders of magnitude more often than a combo with 3 or more cards in full random games.
« Last Edit: June 24, 2022, 08:37:42 am by Holger »
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jomini

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Re: Prosperity 2E Preview 3
« Reply #128 on: June 28, 2022, 10:18:43 pm »
0

This one might be more common and obvious, but it is simply not sui generis.

How many stalemates have you experienced? I have had exactly one in about 8–10k games so far and that was a 0 VP/turn Possession game.

Dozens, but IRL we either do a draft to start (alternating choices) or deal up 10 and then make alternating choices to keep 5 for sequential games. We often play a combo until we see something that is stronger or figure out some counter.

We got to the point where the majority of Possession games were stalemates (either that or games where no one would buy Possession at all).

We typically see Fort/Bish become a shuffle race with a sizeable minority going stalemate (this is why I know you can actually safely mill a Bish a turn if the other guy opts to try for an engine).

I realize there is this weird fascination with all random, all sets, but I do not recall that ever being part of the official rules.

In general, stalemates come where one player cannot force an endgame. They will likely become more common as folks get better at Dominion.

I fail to see how the precise point total matters for the dynamics. Exactly which decks can best 30 VP/turn but not 50/turn? I mean, I could be wrong, but Ride/Collections beats the entire Colony pile in 3 turns while Stampede does it in 2. Even Supplies wins out in 4.

And I am not at all convinced that 2-card combos represent the majority of potential stalemates. After all, Kc/Monument is the only "2-card" combo (ignoring the whole, needs trashing thing), but Mastermind/Monument/Cantrip results in the same dynamic (high points/turn, potential game loss if you break the combo). As does Kc/Farmer's market/trash diver (6 VP/turn on average, unless you build out with Necromancer and then get 9 VP/turn). As do a lot of Bish/trash diver options.

My experience is that most people just do not see the combos and fail to play them. We went years without finding the classic Masquerade pins and have yet to find an opponent who ever even considers building out a Cutpurse/Masquerade pin, yet it is possible on a sizeable minority of Masquerade/Cutpurse boards.

Stampede/Collections is quick and easy to spot, but it is categorically not all that different from Collections/Ride or even Collections/Supplies.

We are far from finding all the possible reciprocal zugzwang's and I submit it is far, far too early to note if the community can reliably say that this one particular combo is wildly overpowered compared to stuff that crops up nearly as commonly.
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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #129 on: June 29, 2022, 11:01:18 am »
+2

I realize there is this weird fascination with all random, all sets, but I do not recall that ever being part of the official rules.

It's not a weird fascination, it's the established standard way to play.
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Holger

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Re: Prosperity 2E Preview 3
« Reply #130 on: June 29, 2022, 11:38:06 am »
+1

In general, stalemates come where one player cannot force an endgame. They will likely become more common as folks get better at Dominion.

I fail to see how the precise point total matters for the dynamics. Exactly which decks can best 30 VP/turn but not 50/turn? I mean, I could be wrong, but Ride/Collections beats the entire Colony pile in 3 turns while Stampede does it in 2. Even Supplies wins out in 4.

Sure, any golden deck gaining 20+ VP tokens per turn is usually unbeatable by a deck not gaining a similar amount of VP tokens. All the Collection/horse gainer golden decks mentioned will usually be dominant. Stampede is just the strongest of the group, as the higher VP gain means you need a much larger lede to be able to break the golden deck for a win, and the 5-card limit prevents you from incorporating it into an engine.
 
Quote
And I am not at all convinced that 2-card combos represent the majority of potential stalemates. After all, Kc/Monument is the only "2-card" combo (ignoring the whole, needs trashing thing), but Mastermind/Monument/Cantrip results in the same dynamic (high points/turn, potential game loss if you break the combo). As does Kc/Farmer's market/trash diver (6 VP/turn on average, unless you build out with Necromancer and then get 9 VP/turn). As do a lot of Bish/trash diver options.

I suppose with your method of choosing kingdoms, strong multi-card combos will come up much more often. But in pure random games, it's simple math that 2-card combos come up much more often than 3-card combos (by a factor of about 50 given the current size of the total card pool), let alone combos with even more cards.

Maybe I should clarify that by "n-card combo" I mean a combo requiring n exact cards, i.e. not counting common card types. So Mastermind/Monument/Cantrip would be a 2-card combo rather than a 3-card combo for me, as most random kingdoms contain a cantrip anyway.

Edit: Actually, Mastermind/Monument also gives a 9 VP/turn golden deck on its own, without needing any cantrip (only a "disappearing trasher" to get there, same as with KC):

You build a deck of 3 Monuments and 5 Masterminds. 3 Masterminds will be in play at the start of each of your turns: Two Masterminds are chained so that you can triple-play the 3 Monuments, plus a single Mastermind that triple-plays a new Mastermind from your hand. Then you play the last Mastermind from your hand with your free action to set up an identical next turn. The "completed" chain of 2 Masterminds/3 Monuments will be discarded during clean up, so you draw exactly those 5 cards for your next turn.  :) :)

This golden deck might even be easier to set up than KC/Monument, as MM is cheaper than KC (and can thus be bought with the $ from a single MM'ed Monument).


Quote
Stampede/Collections is quick and easy to spot, but it is categorically not all that different from Collections/Ride or even Collections/Supplies.

I tend to agree; it is somewhat "worse" than the other two in terms of VPs and its engine incompatibility, but not on a completely different level.
« Last Edit: June 29, 2022, 12:44:23 pm by Holger »
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Holger

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Re: Prosperity 2E Preview 3
« Reply #131 on: June 29, 2022, 12:13:19 pm »
0

I don’t see how KC and Monument could every lead to a stalemate. First of all, unless you trashed with Raze, there is a sixth card in your deck which prevents a flat 9VP per turn. Second, building an engine around that combo seems like the natural way to go.
It is highly unlikely that even in a mirror, players will arrive at the same deck situation symmetrically and then whoever was faster has an incentive to, well, yeah actually win the game.

Besides Raze, you can also get down to a 5-card, 9VP golden deck with either of the following: Banish, Donate, Death Cart*, Enhance*, Island, Way of the Butterfly*/Goat/Turtle*/Horse*, pre-Errata Bonfire, and possibly others (those with "*" require another general-purpose trasher in the kingdom, which they can then trash or otherwise remove from the deck).

But I agree that a 9 VP KC/Monument golden deck would come up less often than the other 2-card combos. However, when it does, the mirror should result in a stalemate at least on most boards with no +buy.
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faust

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Re: Prosperity 2E Preview 3
« Reply #132 on: June 29, 2022, 12:17:14 pm »
+2

I don’t see how KC and Monument could every lead to a stalemate. First of all, unless you trashed with Raze, there is a sixth card in your deck which prevents a flat 9VP per turn. Second, building an engine around that combo seems like the natural way to go.
It is highly unlikely that even in a mirror, players will arrive at the same deck situation symmetrically and then whoever was faster has an incentive to, well, yeah actually win the game.

Besides Raze, you can also get down to a 5-card, 9VP golden deck with either of the following: Banish, Donate, Death Cart*, Enhance*, Island, Way of the Butterfly*/Goat/Turtle*/Horse*, pre-Errata Bonfire, and possibly others (those with "*" require another general-purpose trasher in the kingdom, which they can then trash or otherwise remove from the deck).

But I agree that a 9 VP KC/Monument golden deck would come up less often than the other 2-card combos. However, when it does, the mirror should result in a stalemate at least on most boards with no +buy.
I only leads to a stalemate if the board also doesn't have +Cards, since if there is any +Cards it will be better to keep building so you can play more Monuments. Kingdoms that do not have any +Cards are pretty rare.
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jomini

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Re: Prosperity 2E Preview 3
« Reply #133 on: June 29, 2022, 01:45:47 pm »
0

I don’t see how KC and Monument could every lead to a stalemate. First of all, unless you trashed with Raze, there is a sixth card in your deck which prevents a flat 9VP per turn. Second, building an engine around that combo seems like the natural way to go.
It is highly unlikely that even in a mirror, players will arrive at the same deck situation symmetrically and then whoever was faster has an incentive to, well, yeah actually win the game.

Banish, Butterfly, Bonfire ... and that is just the Bs, there are a lot of different ways to get to Kc/Monument. There are many ways to get a trasher out of your deck.

Building an engine requires some form of +cards. If you lack that, then the max per turn is 9 VP. And even if you have it, there is no assurance that greening is not a zugzwang move (e.g. Hireling can let you build out to 12 VP/turn when you play them, but at the risk of slowing your VP gain with bad shuffle luck).

Which is where the stalemate comes in. Even with a dead trasher, 6 VP/turn is dominant over going for greens with only one turn per hand. Big money monument runs will be hard pressed to score 7 VP all that many turns and even if you alternate with 4 VP using duchy, the 6 VP/turn golden deck wins out. If you have Kc/Mon/Banish, forget it, 9VP/turn will overtake provinces very shortly and once you have the setup, there is significant downside to buying more Kc, Mons, let alone something else.

Ending the game requires there to be piles that you can safely buy out before the opponent running the combo overtakes you. Which is not exactly easy. After all, say you get there 3 turns faster. Call it a 15 VP lead. How many turns does it take to pile out? Well, assuming 10 of 20 cards are bought for Kc/Mon, that only leaves you 20 more turns to pile down via three pile. Ending the game then requires you to average <1 VP lost per turn to shuffle concerns.

What stops this from showing up every time is:
1. Boards often have engine potential.
2. People often do not see utterly dominant combos
3. People tend to resign even when they are stalemated if they are unable to win.

Boards without engines are less common, but Stampede/Collections stalemates are not categorically different than something like Kc/Monument/Banish.

Quote
It's not a weird fascination, it's the established standard way to play.
Established by whom?

It is the most popular way to play and the norm for competitions ... but on the former category the overwhelming response I get when I play a stalemating combo is for people to just resign after the first few cycles as my lead grows. On the latter it seems rather trivial to adopt some tournament rule to break the stalemate (e.g. a player who maintains a lead for 50 turns wins the game, with P2 leading in the event of ties) or to prevent whichever combos are deemed too likely to stalemate (e.g. shuffle up a new kingdom if Collections/Stamped comes up, maybe for Stampede/Ride and Stampede/Supplies absent engine enablers).

I mean I could be wrong, and maybe somehow ultracompetitive play with Possession does not become a degenerate mess where you want to instantly tank your own deck and just mass Possess the other guy's deck, but I would suspect that Possession has far, far more stalemates than some once-in-blue-moon two card combo.

Holger:
Any two card combo is more common than any particular 3 card combo, but there are almost always more of the 3 card versions and the question is if there are enough more of the 3-card variety to nonetheless be the dominant possible stalemate trap.

And I am not convinced that perfect play would not find more of the three or more varieties.

After all, those are hard to spot. People here are having trouble even being exhaustive about how to setup a simple 9 VP Monument deck. Yet it can be done with both Kc and Mm (though the latter cannot hit 9 VP/turn in a perfect mirror), but you can also manage similar shots with things like Tr/Mon/Outpost or Tr/Mon/Mission, and of course, Tr can be replaced by Rg or Rc in some circumstances. Even when trying to be exhaustive about something as simple ditching a trasher, people are missing things like Necromancer who can trash the trasher and 3 Mon to setup the 9 VP/turn option.

End of the day, the point is that we have had a LOT of very powerful things that went unnoticed for months or years. Masq pins (pre-errata) were possible from day 1 for Seaside (Minion/Tr/Tr/Outpost/Masq), yet it was years before somebody put the pieces together for Goons/Kc/Masq. Have we found all the stalemates yet? I doubt it. We may well find out that at skilled enough play (maybe some sort of alpha-star-dominion), stalemate is the normal endgame as both players reach a point dancing where buying the Nth kingdom card lowers the odds of winning more than passing and letting the opponent buy it.

Which is my main contention here. The simple errata is to remove Horses from token gaining. The simple solution to stalemates, in general, is just to adopt a 50 turn rule where anyone who leads for 50 rounds (P2 "leading" during ties), wins the game.

Stampede/collections is "solved" by either and nowhere near unique in its function.

Segura:
Even adding in draw does not negate the stalemate. You need two Kc to start the chain absent +actions. This means that roughly 40% of your deck needs to be Kcs to have decent odds of hitting off a chain. That means your deck needs to be <12.5 cards. Maximal VP gain is 15 VP/turn. Kc and Mon take up 10 slots and leave you with ~3 for draw cards before your expected VP total drops. If your opponent goes for 9 VP/turn and you opt for engine, your game ending deck is 7 Kc, 7 Mon, and 10 Draw. Median hand is ~5 VP/turn at that point. And absent additional gains, that means you played for 19 turns after a mirror setup absent additional gains.

Maybe these things are rare on all random, but I would submit that playing them more often gives me a much better feel for how a particular set actually plays to stalemate.

What makes the engine more viable is (+action and +cards) or (+cards and +buy/gains).

And again, it is not like 6 VP/turn is precisely bad on a board with no +buy. It generally wins out against the province piler absent enablers as 7 greens makes for a lot of 5VP losses per round.
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AJD

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Re: Prosperity 2E Preview 3
« Reply #134 on: June 29, 2022, 02:13:22 pm »
+3

(@jomini, I think you're misusing the word "zugzwang". Zugzwang properly is a situation where all options available to you leave you in a worse position than doing nothing; but in Dominion doing nothing is almost always an available option. You're talking about a situation where ending the game leaves you in a worse position than prolonging it, but that's not zugzwang; it's just stalemate.)
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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #135 on: June 29, 2022, 02:45:32 pm »
0

Established by whom?

Probably by Iso, originally. Iso let you automatch for veto mode as well, but IIRC that was somewhat less popular and it was never available on any later online implementation. Nowadays respecting bans and dislikes is included in the established standard because that's the default table setting on ShiT, and a part of that standard is that Possession is on everyone's ban list by default so it's not going to appear unless both players have gone through the steps to remove it on purpose. Of course, ShiT could change its default table setting if people clearly had a preference for something else instead, so the fact that people are happy with it is a part of the establishing process.
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jomini

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Re: Prosperity 2E Preview 3
« Reply #136 on: June 29, 2022, 03:51:22 pm »
+2

Way of the Butterfly Upgrades Actions and Bonfire cannot blow up Estates.
About the other point, as faust pointed out, with draw you want to build up your deck beyond two KCs and three Monuments.

Stalemates basically never occur in Dominion. Unless you play with some funky house rules that let you Butterfly your starting junk. :D

Butterfly works off any general trasher that costs <$4 or where you have a $6 action card. Similarly, Bonfire allows you to burn off the estates with some other trashing and then to get rid of the trasher. More esoteric options include Inheritance/Bonfire (pre-errata), Plan (preferably with a trasher as well), and Dame Anna (where you trash down to Kc/Kc/Anna/Mon, ditch Anna by trashing one of their Knights, and then buying Mon x2 to crank 9 VP/turn).

End of the day Kc/Mon for 9 VP is something like a 2.5 or 2.75 card combo.

Stalemates basically never occur in Dominion because people can only spot the most trivial of them, suck at understanding how to force a stalemate, and are very prone to resigning long before the opponent has a truly insurmountable lead.

People, even high-level players, spent years missing optimal strategies like Countinghouse/Travelling fair or Market square/Hermit or the aforementioned Pins.

And I always find it so odd that folks talk about 2-card combos being a problem (given that, you know the odds that any game will contain the combo rounds down to 0 out to three significant figures.

You can worry about Stampede/Collections as a stalemate. You can dismiss all the other stalemate setups as unlikely. You cannot do both.

I just never will understand people who are concerned about 1/400 events but do not care about ten 1/4000 events.


(@jomini, I think you're misusing the word "zugzwang". Zugzwang properly is a situation where all options available to you leave you in a worse position than doing nothing; but in Dominion doing nothing is almost always an available option. You're talking about a situation where ending the game leaves you in a worse position than prolonging it, but that's not zugzwang; it's just stalemate.)

Zugzwang is just a "compulsion to move" and refers to situations where any change in game state results in a detriment to the player instigating such a choice. It can be used with multiple levels of formalism and I am just using it as shorthand for any state in dominion where changing the game state results in significant (if not insurmountable) handicaps.

If we are going to be precise on the chess terms "stalemate" is incorrect as well as the refers specifically to a player who has not yet lost having no legal moves which never occurs in Dominion.

Awaclus:
Yes, I understand that all-sets, all-random is popular. I just do not understand why Dominion analysis that ever considers any other mode of play (including ones in the literal rulebooks) as illegitimate and worthy of only dismissal. It seems like saying Chess theory should not consider FIDE tournament matches because the overwhelming majority of games played are online Blitzes.

And regardless, it seems quite odd to me that the significance threshold for "too rare to care about" should be fixed right under 0.2% of games. We have what 400-odd cards now? The odds that any two of them happen in the same game are low enough as is that you can safely ignore every "overpowered" Collections setup and not have it impact your rating in a significant fashion.
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Holger

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Re: Prosperity 2E Preview 3
« Reply #137 on: June 29, 2022, 04:53:42 pm »
0

The notion that KC-Monument is a 2.5 card combo when you just pointed out that you need a trasher and an Event to get rid of the trasher is beyond ridiculous.
You need a trasher, a way to get rid of the trasher and no draw (respectively no gain/Buy options). The likelihood for that is smaller than that of 3 card combos.

You mentioned Raze as a disappearing trasher yourself, and I've given you a list of 4 other different cards/landscapes (Banish, Donate, Island, Way of the Goat) which don't require another trasher, making KC/Monument/(one of these 5) already 5 times more likely than a 3-card combo.
 
The fact that there's half a dozen other "disappearing trashers" that do require another trasher doesn't decrease the odds for KC/Monument to work, it increases them even further.

And the presence of draw or +buy does not negate the combo, though the latter may prevent stalemates.
« Last Edit: June 29, 2022, 05:02:15 pm by Holger »
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Holger

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Re: Prosperity 2E Preview 3
« Reply #138 on: June 29, 2022, 05:09:43 pm »
0

You ignored the 4th element, the absence of draw. Chances for those 4 elements to come together are virtually nil. I probably played dozens of games with KC and Monument and none led to a stalemate.

By the way, good luck with getting rid of 20 starting cards with 12 Islands.

Good luck remembering that KC is in the kingdom, so each player can get rid of 12 cards with only 4 Islands.

As jomini said, the existence of draw doesn't negate the combo, as it's risky to increase your deck size above 5. E.g. if you add a draw card together with another KC and another Monument you'll only get 12 VP if you have the draw card and at least 2 KC in your starting hand. Otherwise, unless you've drawn exactly 2 KC and 3 Monument,  you'll only get 3 or 6 VP.
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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #139 on: June 29, 2022, 05:42:42 pm »
0

Awaclus:
Yes, I understand that all-sets, all-random is popular. I just do not understand why Dominion analysis that ever considers any other mode of play (including ones in the literal rulebooks) as illegitimate and worthy of only dismissal. It seems like saying Chess theory should not consider FIDE tournament matches because the overwhelming majority of games played are online Blitzes.

And regardless, it seems quite odd to me that the significance threshold for "too rare to care about" should be fixed right under 0.2% of games. We have what 400-odd cards now? The odds that any two of them happen in the same game are low enough as is that you can safely ignore every "overpowered" Collections setup and not have it impact your rating in a significant fashion.

The thing about nonstandard ways to generate kingdoms is that you are probably the only one playing the game that way, at least out of the people reading your post. That does not make the analysis illegitimate, but it does make it of very little value to everyone reading it, if there are reasons to believe the analysis is not applicable to how people are actually likely to play the game, such as all expansions full random. Some people have e.g. posted analysis on base only full random; while that is not the standard way to play amongst high level players, it is a standard so the analysis is probably valuable to at least some people who read it.

A given 2-card combo is expected to happen to someone in a big tournament, and it is expected to happen to you in particular if you play somewhat actively for like a year. That's not a problem if the combo is merely overpowered while it also outputs a clear winner, and it's probably not a problem if the combo only results in a stalemate a minority of the time, but if it is very likely to result in a stalemate, that is probably a problem for the tournament organizer and at least mildly annoying for you.
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jomini

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Re: Prosperity 2E Preview 3
« Reply #140 on: June 29, 2022, 10:06:30 pm »
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The notion that KC-Monument is a 2.5 card combo when you just pointed out that you need a trasher and an Event to get rid of the trasher is beyond ridiculous.
You need a trasher, a way to get rid of the trasher and no draw (respectively no gain/Buy options). The likelihood for that is smaller than that of 3 card combos.
It would be a three-card combo with something like Donate/Kc/Monument. Or Kc/Banish/Mon. Or Kc/Island/Mon. Or Kc/Necromancer/Mon. Or Kc/WotGoat/Mon. There are five different explicit three-card-combos that all equilibrate to the same end state if the game lasts long enough so it is definitely going to show up more commonly than a single three card combo. There are far too numerous to list four-card combos which also move up the number of boards where the 9 VP version of the combo is possible.

And you can get similar combos without the other pieces. E.g. Mastermind can substitute for Kc in some circumstances. Farmers' market/Necromancer/Kc can score ~7 VP turn.

The precise number is going to lie somewhere between a 2-card combo and a 3-card combo, and will be closer to three than two. But it is just a wee bit non-trivial to calculate out when each makes sense.

You ignored the 4th element, the absence of draw. Chances for those 4 elements to come together are virtually nil. I probably played dozens of games with KC and Monument and none led to a stalemate.

By the way, good luck with getting rid of 20 starting cards with 12 Islands.

That is total nonsense. You get enough Coins to buy whatever you want, like another KC. And chances are extremely high that you actually got a cantrip in your deck (as double splitter plus Lab with KC).

It is not as if the supposed stalemate-inducing golden deck falls from the sky, there is a game before that.

And even if both players mirror, Dominion is not a deterministic game. A small lead in a KC Kingdom easily undos any vague stalemate possibilities. You are ahead, KC enhances the engine potential massively and a normal deck with draw, VP generation and one or two Provinces per turn easily beats the 9VP thingy.

The only nonsense is your inability to realize that:
A. 6VP/turn will eventually outscore all but the most reliable of greening, non-engine decks.
B. A big part of the value in the combo is the reliability which matters a lot more than you think.
C. You have specified 3 cards already for Kc/Mon/draw. The odds that there is any additional +gains in the remaining 7 is below 50%.

Suppose you have Kc/Moat/Mon. You want to build out to maximal points per turn. Okay, your hands will have one of the following outcomes: You have at least Kc/Kc/Moat in hand, draw deck, and get scads of VP; you have Kc/Mon and other stuff in hand and score 3 VP, you have Mon/other stuff and score 1 VP, you have Kc/Moat and other stuff and score zero. Maximum VP/turn in a mirror is 15 VP turn on your good hands. But how big can your deck be and have your deck draw through on ~45% of hands?

Not that big. After all, Kc needs to make up at least 40% of your deck (otherwise you whiff too many turns with only 1 Kc in hand) with 5 Kc & 5 Mons (i.e. the mirror option), you run out of Kc density on the third Moat. As you add Moats, the odds of getting 3, 1, or 0 VP on a turn start going up. So say we both build out to 5 Kc, 5 Mon, and 3 Moats. One of us keeps playing without buying. The one who breaks their engine by having too low of a Kc density can easily lose the game as the other guy more reliably hits more points.

And note this applies even more to decks with a general trashing card in the mix. You can absolutely take 6 VP/turn and call it a day. You can build out to 5 Kc/5 Mon and then hit the wall of unreliable draws that limits 3-piling.

End of the day, draw is not enough to avoid the stalemate. It may make it worthwhile to build past Kc x2/Mon x3. But at some point it becomes zugzwang  where any move towards end state results in lower odds of winning. You need a source of +action.

Beating 9, or even 15 VP/turn is of course quite doable. Colonies, 3 provinces/turn, etc. But assuming that every board, even every Kc board will always have the draw, buys, and time needed for the deadlock to be avoided is just silly. But with that sort of analysis we may as well say that every engine should build toward double provinces - it is after all, the most common engine outcome and is possible more often than not.

Awaclus:
Ahh yes, been here, heard these errors before. The analysis of any card(s) in Dominion is worthless for anyone reading these posts. Most of us have too much noise in our ratings for a single combo to be more than a literal rounding error in our rankings. If you completely ignore Market square/Hermit and lose every time, it manages to drop your rating, what 0.02? The odds that it will determine your tournament standing are exceedingly small and you are far better off just spending the time playing to get a better "feel" for end game play or whatever rather than even bothering to think about any combo.

I am not following why on earth it is a problem for the Tournament organizer or the players. Scrub the game and replay. If you see a stalemateable combo, be it something quick and easy like Collections/Stampede or something convoluted (like Kc/Caption/Monument/Butterfly) any tournament level player should be able to recognize the stalemate and just redo the game.

I avoid the tournament circuit, but unless I missed some setup where everyone gets identical shuffling seeds and kingdoms, it literally just means scrub the kingdom and play again. Marginally annoying.

And the whole thing is most readily avoided by either nerfing all the Horse/Collection stalemates or by just adding in a 50 turn lead rule.

Why exactly people are unable to realize that this is literally nothing more than a specific case of a more general phenomena is beyond me.
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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #141 on: June 29, 2022, 10:22:06 pm »
+1

Why exactly people are unable to realize that this is literally nothing more than a specific case of a more general phenomena is beyond me.

Because we have played thousands of games and the general phenomenon really does not appear to exist to any substantial extent, and there are reasons to believe that Collection/Stampede is different.
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Re: Prosperity 2E Preview 3
« Reply #142 on: June 30, 2022, 12:15:03 am »
+3

Just in case I didn't make this clear: we did not miss Stampede / Collection. We played some games of it to see how they went. And also Ride / Collection and others.

In the end as you can see, how these played did not seem sufficiently bad for me to make Collection worse-to-print in some respect in order to fix them.
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Re: Prosperity 2E Preview 3
« Reply #143 on: June 30, 2022, 10:29:04 am »
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Why exactly people are unable to realize that this is literally nothing more than a specific case of a more general phenomena is beyond me.

Because we have played thousands of games and the general phenomenon really does not appear to exist to any substantial extent, and there are reasons to believe that Collection/Stampede is different.

Oh please, we have empirical evidence that thousands of games were woefully insufficient to find the utterly dominant Pin combos. Pins were viable with Seaside (2009 release), we only found them in 2011. And lest you want to make some silly comment about the number of games being played, the possible game space was orders upon orders of magnitude smaller back then.

It took 9 months for the community to find Hermit/Market square when they were in the same set and had, literally, all the important words like "Trash", "Gain a Gold", "+1 card per" and on the text of the cards. And famously, the championships had Kc/Goons/Masq and neither player even noticed.

Nor is this discussion doing anything to convince me that the community actually knows the game well enough. People are talking about stalemate without mentioning Possession. They do not even know all the ways the create ultra-lean decks. They have no idea about how to go about actually forcing an end game with fragile VP generating deck.

Multiple people have been wrong in this thread about basic stuff: Can Bish/Fort afford to buy and trash extra Bishops? Yes, outside of a mirror. Can you use Necromancer to create an ultra-lean deck with great flexibility (whether or not that is the dominant option, is it possible)? Yes. Will buying non-cantrip draw stall out a Kc/Mon deck? Yes.

But again I ask, how is Stampede/Collections different? A stalemate with Ride/Collections runs into the exact same sort of end state. Bish/Fort can easily have the same limitations where doing anything other than playing the precise combo results in a loss. It is a simpler case, but the difference is strictly of degree, not kind.

Quote
A deck which buys a Province per turn and play a Monument or tripled Monument easily beats your supposed golden deck. Until you actually got to that supposed brilliant, dominating, stale-mate inducing situation, the other dudes and dudettes will have likely build something far better.

A static analysis ignored all the interesting and relevant intricacies of the game like, how fast can I thin and does the ordinary draw deck not deal better with slow thinning?

You can set up a random game with KC, Monument and a disappearing trasher and put your mouth were your money is.
I see, you will have 7 provinces in your deck and you expect to hit a significant number of Kc/Monuments? What is your deck going to look like? Hitting a monument every turn requires over 20% of your deck be Monument. Hitting Kc/Monument with any regularity requires 20% to be Kc. Hitting $8 requires either treasures or hands of Kc x2/Mon x2. I will submit that the treasure option is easier. So you want at least 20% of your deck to be some sort of treasure. That is a lot of buys to support the density needed to buy 8 provinces.

Because at the end of the day, we are talking about some sort of Big Money setup with that much green. End of the day Monument is, at best a silver for buy purposes. Kc/Mon is, at best, a pair of golds. This suggests that your best performance will be something like Big Money, which takes ~17 turns to hit 4 provinces and, if you just flat ignore the duchies, gains a province every other turn thereafter. All told I should expect something like 23 turns for you to hit 8 provinces. You buy your first province around T13 and I can safely say I will setup the combo by then. That means I will generate 90 VP. You get 48 VP from the province pile and assuming we have similar VP on T13 (I am very likely to be ahead if you are buying treasures, but whatever), you need to average 4.2 VP/turn to tie. With a 6 VP/turn setup, and ignoring the fact that I can setup the combo sooner, you will still need to average 1.2 VP/turn from Monuments (you can, of course, buy duchies, but that tanks your deck even more and I gain yet another round of VP.

How fast can I realistically setup the combo? Well Donate is about as fast as it comes. I open Silv/Mon, I buy a silver, I play $4 (below expectation), then have a deck with MonSSC left. I spend a turn paying off $4 debt. I buy a Kc. Then Mon/Mon/Kc in some order. Donate away the treasures. Even if it gets delayed a turn, I have the combo in full T11.

If you play Kc/Mon every turn, you need to pile the provinces by turn 19. If you play an average of 2 Mons/turn, you need to pile the provinces by T18. If you play an average of 1.5 Mons/turn, you need to pile by T17 (again, ignoring the fact that I likely generated a couple of more VP on T3-T10).

As far as why I will not play you:
1. Anyone who offers this sort of thing clearly does not understand Dominion. A single game is not statistically significant. Bottom decking (e.g. T3/T7 Chapel) can flip the win without telling us jack about the strength of the combo or the stalemate.
2. Player skill is a much larger determinant of outcome than strategy strength. Knowing when to trigger reshuffles, how to time buys, and the like will often mean that a strictly inferior strategy in the hands of a skilled player is better than a superior strategy in the hands of a master.
3. I am not convinced that beating you, even repeatedly will do a lick to change your mind.

If you really want to "prove" something, give me an example deck of Kc/Mon/Moat without +buys or other gains that scores an average of 7.5 VP/turn with 5 provinces in deck. Should be easy for you, so how many of each card (Silver, gold, Kc, Mon, Moat) are in your deck?
« Last Edit: June 30, 2022, 11:45:25 am by jomini »
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Awaclus

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Re: Prosperity 2E Preview 3
« Reply #144 on: June 30, 2022, 11:52:41 am »
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Why exactly people are unable to realize that this is literally nothing more than a specific case of a more general phenomena is beyond me.

Because we have played thousands of games and the general phenomenon really does not appear to exist to any substantial extent, and there are reasons to believe that Collection/Stampede is different.

Oh please, we have empirical evidence that thousands of games were woefully insufficient to find the utterly dominant Pin combos. Pins were viable with Seaside (2009 release), we only found them in 2011. And lest you want to make some silly comment about the number of games being played, the possible game space was orders upon orders of magnitude smaller back then.

It took 9 months for the community to find Hermit/Market square when they were in the same set and had, literally, all the important words like "Trash", "Gain a Gold", "+1 card per" and on the text of the cards. And famously, the championships had Kc/Goons/Masq and neither player even noticed.

This evidence does not contradict my claim that the general phenomenon does not appear to exist to any substantial extent. On the contrary, it supports it. What would theoretically happen in games between players playing perfectly is irrelevant because real Dominion is not that. If it ever starts to look like the case that Bishop/Fortress stalemates are a substantial problem in high level play, I will start complaining about it, but until then, I'm not going to care. (I don't also particularly care about Collection/Stampede until it's been demonstrated to be a substantial problem that actually shows up in real games; I haven't e.g. banned Stampede yet.)

Nor is this discussion doing anything to convince me that the community actually knows the game well enough. People are talking about stalemate without mentioning Possession. They do not even know all the ways the create ultra-lean decks. They have no idea about how to go about actually forcing an end game with fragile VP generating deck.

Nobody mentions Possession because nobody plays with Possession anymore because it's on the ban list by default, not that many people remove it, and it only has like a few % chance of appearing in the kingdom when two such players get matched against each other. You can ignore segura, he's a known troll who has had several accounts banned and keeps making new ones.

Multiple people have been wrong in this thread about basic stuff: Can Bish/Fort afford to buy and trash extra Bishops? Yes, outside of a mirror. Can you use Necromancer to create an ultra-lean deck with great flexibility (whether or not that is the dominant option, is it possible)? Yes. Will buying non-cantrip draw stall out a Kc/Mon deck? Yes.

I will admit that I was envisioning a 4-Fortress golden deck and therefore overestimating the chance of having a bad draw compared to a 5-Fortress golden deck; I would normally expect the engine to actually win the Fortress split because it's just a better deck for the purpose of gaining stuff, but if it doesn't, then of course you can have the fifth Fortress and that changes the probability. It is also possible that I'm still overestimating the chance of having a bad draw even assuming only 4 Fortresses because I haven't done the math. However, if you take a look at what I actually said instead of making it up yourself, you might notice that I did specifically say that buying extra Bishops is not a huge problem for the golden deck, and it is unquestionably true that it can temporarily slow it down, so while I may or may not have misestimated the details, I definitely was not substantially wrong on the bigger point.

You are literally the only person who has talked about Necromancer in this thread, and I don't think it has been sufficiently demonstrated to be the case that buying non-cantrip draw stalls out a KC/Monument deck. I can play a KC/Monument cage match if you want a chance to demonstrate that though, or just the general idea that KC/Monument stalemates are a thing that happens at all.

But again I ask, how is Stampede/Collections different? A stalemate with Ride/Collections runs into the exact same sort of end state. Bish/Fort can easily have the same limitations where doing anything other than playing the precise combo results in a loss. It is a simpler case, but the difference is strictly of degree, not kind.

This is how:
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Re: Prosperity 2E Preview 3
« Reply #145 on: June 30, 2022, 04:31:00 pm »
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Awalcus:
I seem to be missing something here. I am saying that Stampede/Collections is just different in degree to other stalemate potentials. A higher percentage of its boards will stalemate at perfect play. Not all of them mind you, as some will be counterable (I have not enough experience to say exactly how small this percentage will be), some will have pile depleting enablers (e.g. Advance/Island is conceptually simple enough to grasp, I hope) that block the stalemate, and perhaps a majority will have a clear 6:4 Collections split thanks to some sort of P1 advantage.

But these are the same kind of things that happen Bish/Fort and the rest. The only difference I see is that the numbers are likely more extreme for Stampede/Collection.

Maybe Stamped/Collection will fall below your concern level, like all the rest. Maybe they will rise above. But fundamentally, the end state is functionally the same, the solutions are the same, and your analysis leaves me utterly unconvinced that this is somehow difference of kind. The fact that it is written on the card just makes it obvious that buying additional cards will lower your expected VP/turn enough to lose. The same dynamic can play out in other boards.

I mean consider something like Dismantle/Donate/Collections. You can open Dismantle/Donate, pop an estate for Copper/Gold, pop the other estate you kept for copper/Gold & pay off most of the debt, and then grab two Collections (one via Dismantle) the next turn. Turn after you can most likely grab 2 again and will certainly be able to do so the following turn if not. 7 Turns, 10 cards and you can Stampede twice per turn for the rest of the game. You need to kill 18 cards (16, if they mirrored on the Dismantle) and your deck supports gaining 6 estates and a Duchy on its final turn. You could gain a card or two instead of a second stampede each turn, but that costs 25 or 30 VP/turn. If your opponent is slow start (e.g. has 5/2 opening, bad shuffle on the post-debt turn) you may hit a 6:4 collection split and can safely build up a 1000 VP lead before you methodically destroy the piles to win. Or you might get an extra 75 VP from them being slow to setup. Can you pile everything out in 3 turns? Maybe

But the determining factors follow the same math. How many VP/turn do you expect to sacrifice to pile down? How many turns will it take you to pile all of that? The difference is that the numbers for Collections/Stamped are much, much bigger than for most other stalemate options. Which is pretty much the exact definition of the phrase "difference of degree".

Again, I can totally buy that the other stalemates will not rise to your level of concern any time soon (if every), I just cannot see Collections/Stampede doing so if they do not.
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