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Author Topic: The Myth of Big Money Choking  (Read 10416 times)

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ragingduckd

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The Myth of Big Money Choking
« on: September 25, 2013, 09:34:33 pm »
+46

Here's how we usually think of the life-cycle of a Big Money deck: after building up its money density, BM gains Provinces quickly for a while, but soon it begins to choke on its green and slows down. Somewhere around 5-7 Provinces, it stalls out hard and has a very difficult time buying any more.

For evidence of this claim, just look at some simulation results. Here Big Money Unimproved stalls out around 38 VP; Big Envoy around 44 VP:



Of course, this doesn't matter much for a matchup between them. Either BM deck will have essentially secured the win by the time it stalls hard. But it's very relevant if you're playing an alt-VP engine against BM. If you're running a little behind with Goons or Vineyards, then you'd be mad to help your opponent end the game by buying even one or two Provinces for him.

Right?

As it turns out, this stalling is a myth. The claim that BM chokes on its own green is wrong. The apparent simulator evidence comes from the way the bots handle late game strategy and from the way humans naturally misinterpret the average VP graph.

BM simulator strategies start buying Duchies and Estates like crazy when Provinces run low. That's the right play against another BM opponent, but it's no way to buy all 8 Provinces quickly. If we're contemplating an alt-VP only strategy, these sims don't really tell us anything about how quickly our BM opponent will be able to end the game.

Here's a version of BMU that never buys Duchies or Estates. I've matched it against a deck that just sits there:



Without Duchies or Estates, BMU gets to 5 Provinces around T19 and keeps right on going. There's no choking at that point at all. It still appears to be slowing towards the end though. Maybe BMU's hard stall comes around 8 Provinces instead of 5?

Nope. This is a misinterpretation of the average VP curve. We can't think of it as the performance of a single "average" deck. It's actually the average performance of a large number of decks, and the decks that make up that average are changing over time.

While all 1000 simulated decks are contributing to the average at T15, some of the luckiest ones drop out by T25 because they've bought all 8 Provinces and ended the game. The remaining decks are the ones that have been less lucky. That sample bias pulls the average VP curve down. The later it gets, the larger the bias gets.

BMU actually keeps buying Provinces at the same average rate indefinitely. It doesn't stall out at 5 Provinces, nor at 8, nor even much later. To demonstrate this, I altered dominiate to run with 80 Provinces instead of 8. Even the luckiest decks won't be removed from the average in 60 turns, so we can see what BMU does in the long run without that sample bias:



Et voilà. BMU gains at a constant rate up to 20 Provinces and beyond, a little more than two turns per Province.

So don't believe the myth that BM chokes in the long run and don't assume that you'll have tons of extra time against BM if you just keep your hands off the Provinces. Instead, expect your BM opponent to pick up another Province every two turns or so right up to the end.
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ftl

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Re: The Myth of Big Money Choking
« Reply #1 on: September 25, 2013, 09:50:25 pm »
+5

That makes sense, I suppose. A province every two turns will be roughly alternating province/gold buys. That buy sequence produces a value of $1.5/card - to buy provinces you need $1.6/card, to buy gold you need $1.2/card, so that's indefinitely self-sustaining. Well, some of those non-province hands will be silvers, so you're getting a little less than $1.5/card as you go on buying a province every other turn.
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dondon151

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Re: The Myth of Big Money Choking
« Reply #2 on: September 25, 2013, 10:18:02 pm »
+3

I have to say that this was sort of expected. I mean, if you don't hit $8, you'll be increasing your money density, and if you do hit $8, you'll be decreasing your money density. Over a functionally limitless supply and over thousands of trials, of course the VP graph is going to be linear.

I don't think that most (at least, good) players who commit to building an engine vs. a BM alternative are deterred by this at all. Perhaps their way of justifying their commitment to an engine is a bit of a fallacy, as AI pointed out here, but the takeaway is that a strong BM strategy is still going to require 21-23 turns to empty out all 8 Provinces and end with exactly 51 (or 48 if Shelters) VP.

EDIT: I have a feeling that people are going to be reading this post and getting the impression that I'm blowing off AI's article. That is not the case. The article is helpful. It just spins something that we already knew in a way that is easier to visualize and understand.
« Last Edit: September 26, 2013, 01:43:56 am by dondon151 »
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Kirian

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Re: The Myth of Big Money Choking
« Reply #3 on: September 25, 2013, 10:46:58 pm »
+4

This isn't a myth, it just requires a really large banana.
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SCSN

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Re: The Myth of Big Money Choking
« Reply #4 on: September 26, 2013, 05:18:43 am »
+6

The main take-away from this is that if you're up against a viable engine that goes for some form of alt-vp, you should probably have gone for that yourself keep your hands of the Duchies almost entirely; since your opponent is winning the long-game, those extra Duchy points are unlikely to matter and they hurt you a lot if your best chances of winning are to empty the Provinces as fast as possible.

Also, in practice, if you're going for the alt-vp engine, you'll find your opponent very often buying those Duchies anyway, thus making the myth effectively true (he won't be able to sustain 1 Province/2 turns and will in fact choke), which can be important to recognize because knowing that you have that extra time gives you more flexibility and less pressure to take risks.
« Last Edit: September 26, 2013, 05:30:34 am by SheCantSayNo »
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Re: The Myth of Big Money Choking
« Reply #5 on: September 26, 2013, 05:47:31 am »
+1

I think it's more complicated than just buying Provinces and Provinces only - the opponent can stall too, there's PPR to consider, and denial.

If your opponent buys 8+ Alt-VP cards, there's a definite possibility their deck is in a worse state than yours, such that they're ahead but are improving by less than 3VP per turn - e.g. a Duchy beats an Estate+Copper turn, even vs. all 8 Gardens.

If the game is close, against a deck which has a considerable chance to buy (or remodel into) the last Province for the win, you have to Duchy dance. It depends what kind of alt-VP - Vineyards upgrade too quickly, but Fairgrounds usually max out at 6.

Some types of alt-VP mean you just can't let your opponent get the whole pile - BM has to deny Duchies to a Duke player, and you have to be careful about an opponent with 8 Silk Roads, as their Estates are 3VP each. In that case, BM needs to buy other green cards than just Provinces.
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DG

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Re: The Myth of Big Money Choking
« Reply #6 on: September 26, 2013, 09:14:09 am »
+1

25 turns is still a long time to buy eight provinces though. If you can't execute an alternate strategy in that time then it just isn't viable to start with.
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HiveMindEmulator

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Re: The Myth of Big Money Choking
« Reply #7 on: September 26, 2013, 10:51:53 am »
0

Very nice article. Thanks for putting in the time to make this and present it so well.

As far as the conclusion goes, I'd say it's all relative. You could plot in log scale and get a decay. The curve is convex from 5-10 then merely linear after that... Pure Big Money doesn't choke because it was never running that fast to begin with. If you have action cards, however, you're losing out on their density if you're not buying them in proportion with the Provinces. And in reality, this is something people have a hard time with.

SCSN hit the nail on the head with the important take-away. I see a lot of people not adapt to their opponent at all. If your opponent isn't buying Provinces, you don't need Duchies. You need things that will help buy more Provinces.
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popsofctown

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Re: The Myth of Big Money Choking
« Reply #8 on: September 26, 2013, 11:04:20 am »
0

I always thought of Big Money as being the deck that doesn't choke..
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zporiri

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Re: The Myth of Big Money Choking
« Reply #9 on: October 01, 2013, 11:32:29 am »
0

I think the main question this brings up is, is it still worth it to buy duchies after 4 provinces are gone in a BM 2 player mirror? I would think that the player who buys duchies is getting 3pts/turn and the player who alternates province/gold is also getting 3pts/turn, but the player who gets buys duchies will eventually get a lucky hand and buy a province which is a 3 point increase, and sometimes get an unlucky hand where he buys an estate which is 2 point decrease. So is buying duchies ~4 provinces remaining still the best move?
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ftl

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Re: The Myth of Big Money Choking
« Reply #10 on: October 01, 2013, 12:12:46 pm »
0

Yes, you still want duchies in a BM mirror.
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Warfreak2

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Re: The Myth of Big Money Choking
« Reply #11 on: October 01, 2013, 12:42:17 pm »
+4

Gold is only better than Duchy if you'll see the Gold at least twice - having $8 to buy a Province is the same as having $5 with another Duchy in your hand, so if you only use the Gold once, it's at best neutral to your score. But even if you do see the Gold twice, it could still be worse than a Duchy - for example, the second time you see it, you have $8 but have to obey PPR, or you draw it in a $4 hand and have to buy an Estate.
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SCSN

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Re: The Myth of Big Money Choking
« Reply #12 on: October 01, 2013, 12:58:05 pm »
+6

Your omitting the other side of the coin: it can also be better than a Duchy, even if you only see it once. The Duchy might not end up mattering points-wise, whereas the Gold might enable you to end the game with a win when your opponent breaks PPR, or to break PPR yourself when you think it's advantageous to do so. What's best really depends on your deck and that of your opponent, where you are in your shuffle, where he is, etc. To give an example: if your opponent's deck is more resilient to greening and you're just before a reshuffle, getting the Gold to hopefully steal the game on Provinces might well be your best chance of winning a game where Duchy-dancing would lead to a certain loss.
« Last Edit: October 01, 2013, 12:59:14 pm by SheCantSayNo »
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blueblimp

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Re: The Myth of Big Money Choking
« Reply #13 on: October 01, 2013, 11:09:17 pm »
0

BM mirrors have been studied extensively in simulators so there's not a lot of room for disagreement there about how to play them. (If there is, it's simple enough to go try it in a simulator and see whether it does better.)
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ftl

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Re: The Myth of Big Money Choking
« Reply #14 on: October 02, 2013, 01:07:09 am »
+3

Well, sort of. Real play is more nuanced than the simulators - you typically care about "how close you are to a reshuffle" more than the simulators track. If you're about to reshuffle, you're more likely to lean to get a gold, if you've just shuffled, grab that duchy. Simulators typically approximate this via "number of provinces remaining" which isn't perfect, it's just easier to think about than reshuffles.
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blueblimp

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Re: The Myth of Big Money Choking
« Reply #15 on: October 02, 2013, 01:08:54 am »
0

That's not an inherent limitation of even the existing simulators. Dominiate could definitely take into account reshuffles. Not sure about Geronimoo's (I can't remember the available conditions off the top of my head), but maybe.
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sudgy

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Re: The Myth of Big Money Choking
« Reply #16 on: October 02, 2013, 03:28:30 am »
0

That's not an inherent limitation of even the existing simulators. Dominiate could definitely take into account reshuffles. Not sure about Geronimoo's (I can't remember the available conditions off the top of my head), but maybe.
You could -maybe- use number of cards in deck...
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Davio

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Re: The Myth of Big Money Choking
« Reply #17 on: October 02, 2013, 03:55:47 am »
+1

What I've always found with BM is not that it chokes by itself, but that it's real easy to throw a wrench into it. Even a Bureaucrat can cause big problems for a BM deck. :)
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Re: The Myth of Big Money Choking
« Reply #18 on: October 03, 2013, 01:43:09 pm »
0

I'd never considered this, since in practice I always see BM choking (by buying duchies/estates).  Excellent post!

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Re: The Myth of Big Money Choking
« Reply #19 on: October 04, 2013, 06:26:32 am »
+5

The opening post tells us that BM and BM-Envoy both stall around the 40 VP-mark.

As you all know, 4 Provinces + 4 Duchies + 7 Estates = 43 VP.
This means that if you have at least 44 VP in a regular Province game, you've mathematically won.
Games without Colonies, alt-VP, VP tokens or trashing/Cursing can thus simply be seen as a "race to 44 VP".

Games like these are essentially solitaire optimization games and key is not to try to actually stay ahead of your opponent, but to maximize your chances in surpassing that VP threshold while limiting your opponent to do the same.

Say your opponent has 3 Provinces, 7 Duchies and 3 Estates for 42 VP.
You have 2 Provinces, 0 Duchies and 11 Estates for 23 VP.
There are 3 Provinces, 1 Duchy and 0 Estates left.
Granted, this is a bit of a weird situation for a standard BM game, but bear with me.

Even if you have $8, the correct move here is to always buy the last Duchy, because you need both the Duchy and the Provinces to win. If you allow your opponent to grab that last Duchy (which he is more likely to be able to than grab a Province), it's all over, he has 45 VP. I engineered this weird case to show that there is no "penultimate Province rule" in effect as there are 3 Provinces left.

Sometimes, even buying an Estate over Province is the right call...

Say your opponent has 3 Provinces, 7 Duchies and 4 Estates for 43 VP.
You have 2 Provinces, 1 Duchy and 9 Estates for 27 VP.
There are 3 Provinces, 0 Duchies and 1 Estate left.

Don't allow your opponent to get that Estate!

Bots don't take into consideration these special cases. They don't occur very often so that's not a big deal, but still, always keep the VP barrier in mind if there is one.

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XerxesPraelor

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Re: The Myth of Big Money Choking
« Reply #20 on: October 04, 2013, 06:42:46 am »
+3

They don't stall at 40 VP, it's just that they've probably won by then already, since normally the estates aren't all taken. The graph forgets about the ones that have won already, and so it looks like it's stalling, when actually it's already won.
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Tables

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Re: The Myth of Big Money Choking
« Reply #21 on: October 07, 2013, 06:15:49 am »
0

Say your opponent has 3 Provinces, 7 Duchies and 3 Estates for 42 VP.
You have 2 Provinces, 0 Duchies and 11 Estates for 23 VP.
There are 3 Provinces, 1 Duchy and 0 Estates left.
Granted, this is a bit of a weird situation for a standard BM game, but bear with me.

Even if you have $8, the correct move here is to always buy the last Duchy, because you need both the Duchy and the Provinces to win. If you allow your opponent to grab that last Duchy (which he is more likely to be able to than grab a Province), it's all over, he has 45 VP. I engineered this weird case to show that there is no "penultimate Province rule" in effect as there are 3 Provinces left.

Perhaps this is just a semantic point, but I disagree that the correct move is *always* to buy the last Duchy. Essentially if you take a Province, you're saying: I think it's more likely that I will hit $5 on another hand before you hit $5 and then $8 twice more before you hit $8 than it is that I will hit $8 on three more hands before you hit $8." I think that is a perfectly reasonable statement, especially if you've been tracking deck contents somewhat and know your opponents remaining cards this shuffle are relatively weak, and/or you're very likely to hit $5-7 on your next hand.

This also ignores the point Xerxes makes above, but in reality the situation described here is not really related to the big money stall (or lack thereof)

Edit: Also the second situation you describe is similar but more extreme. How likely is it that your opponent will hit $2 on his next hand? Probably pretty high. But then what's the chance you'll get $8 once more before he finally gets to $8? Probably pretty low. Which gives better odds of winning? Probably the latter, but it depends.
« Last Edit: October 07, 2013, 06:17:41 am by Tables »
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meandering mercury

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Re: The Myth of Big Money Choking
« Reply #22 on: October 07, 2013, 10:50:33 am »
0

Another basic question on choking:

On a typical BM-vs-BM matchup, the conventional wisdom is to usually buy a Gold if you spike to $8 early (and in the sim, I think you need $18 total in your deck, or something like that).

Suppose you're playing a very slow engine and you have to buy out all 8 Provinces yourself. Obviously, as SCSN points you, you shouldn't touch the Duchies -- but how much money should you build up before buying Provinces? Since you're in it for the long haul, doesn't it make sense to build up some more?
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Re: The Myth of Big Money Choking
« Reply #23 on: October 07, 2013, 11:42:37 am »
0

Another basic question on choking:

On a typical BM-vs-BM matchup, the conventional wisdom is to usually buy a Gold if you spike to $8 early (and in the sim, I think you need $18 total in your deck, or something like that).

Suppose you're playing a very slow engine and you have to buy out all 8 Provinces yourself. Obviously, as SCSN points you, you shouldn't touch the Duchies -- but how much money should you build up before buying Provinces? Since you're in it for the long haul, doesn't it make sense to build up some more?
You should build up enough money to get double Province turns. This depends on the engine, but I'd say this is a good rule of thumb.
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meandering mercury

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Re: The Myth of Big Money Choking
« Reply #24 on: October 07, 2013, 12:09:49 pm »
0

My bad -- I meant "playing against" a very slow engine. That is, you're the BM player, and you're trying to decide how much money to get before turning over to Provinces.

I think it's been said that if you're going for Duchy+Dukes solo, you should also build up $$ because you're in it for the long haul.
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