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Making Luck Episode 47: Menagerie

In this episode, Adam and Jake discuss Menagerie from the Cornucopia expansion.

https://www.youtube.com/watch?v=wLtjnGnuKo0

Kingdom at the end: Overlord, Develop, Ghost Town, Menagerie, Swindler, Workshop, Ironworks, Militia, Courtier, Ghost Ship, Pilgrimage, Orchard

Menagerie does not look very strong here.
-The only copper trashing is Develop.
-Most of the cards in the kingdom are terminal, so what are you going to do with that menagerie draw, put a bunch of terminals you can't play into your hand?
-The only village is Ghost Town, which is just about the worst village for Menagerie.  If you want more than one extra action per turn, then you had to draw duplicate Ghost Towns on your previous turn.  It's also hard to draw a hand full of uniques when Ghost Town gives you a larger starting hand size.  And Menagerie even stops being a good defense against Ghost Ship when Ghost Town just redraws the cards you topdecked.
-Swindler could mess up any delicate balance of uniques that you try to set up.

I'd still get Menageries with the goal of defending against Ghost Ship/Militia, but I wouldn't build my deck around it, or expect to do much more than defend.  I'm not especially convinced by Ghost Town/Ghost Ship either, they aren't exactly stellar draw cards.  I'd play more of a good stuff deck, and probably avoid Ghost Town entirely.

I think Overlord is the star of the set.  Hitting $5 is hard early on, so Overlord is crucial to play early Ghost Ship.  Overlords help you play attacks consistently while avoiding terminal collision.  I could see Swindler or Militia being better than Ghost Ship in some situations, and Overlord gives you that option.  It can be used as a tactical Menagerie.  Finally, it's immune to Swindler.

So I actually agree with most of what you're saying about Menagerie. I envision a deck that thins aggressively for a while with exactly two Ghost Towns, and then at a certain point probably turns for more Ghost Towns at the cost of activating all of the Menageries 100% of the time.

I certainly think I want enough Menageries to get my Orchard points no matter what I'm doing here.

You talk about a "good stuff deck" and if you're using the same definition of that that I would, I'm thinking you want to draw a good chunk of cards each turn, but not necessarily the whole deck. I would agree this is eventually the type of deck I want to build, and this is a point in favor of Menagerie because I'm going to worry less about having dud hands with two Provinces or Ghost Towns in them when I don't intend to draw enough to see all of them on most turns.

I'm not sure exactly how many Menageries I want in the deck, but it wouldn't surprise me if that number was 5 or 6 or maybe even more.

Good episode! I think the key thing about Menagerie is that the effect you get when it goes off is so overpowered for a card costing $3 that (a) you can afford to jump through a fair few hoops in order to build a deck around massive Menagerie draw; and (b) if you're doing something else with your life you can often throw in a few Menageries even if you don't expect them to go off a lot of the time. If your Menagerie activates one time in three then you're still getting two-thirds of a Lab on average, which isn't bad for $3. And as long as you aren't worried about drawing it dead then it doesn't get in the way even when it misses (compare with, say, Stables, which is disastrous when you draw it without a Treasure).

Really interesting kingdom at the end. Pilgrimage can't gain you Overlords, correct? It's not an Overlord once it's in play, so that must be right. On the other hand, Pilgrimage is a good way to gain your second Ghost Town because (as you said in the podcast) you can't gain it to your hand with Develop and it totally sucks to gain it with Ironworks.

I'm inclined to go for full-on Menagerie draw with exactly two Ghost Towns, using Develop as my first terminal most turns to help me get rid of duplicate Coppers or whatever and hence keep the Menagerie draw running while I'm still thinning. This could be tough though. If I fail to draw my Ghost Town one turn I not only miss out on the precious extra action next turn but also run the risk of the Ghost Towns turning up together and killing my Menageries for the whole turn. Overlord really helps though, and I can see myself using a single Courtier (it should usually be able to find a two-type card to activate it) for +1 Action and coins, perhaps gaining a Gold the first time as a single Gold is a good extra unique card. Maybe Swindler is going to kill me, although if my opponent is using Swindler for one of his terminals every turn then that's a big opportunity cost for him too.

Anyway, I'll look forward to hearing what works next week!

I think you're too far down on Menagerie in a money density paradigm. Even with no trashing, it starts getting better than silver around the point you have e.g. 2 silver, 2 terminal silver, 2 gold, and your starting cards. (I mathed it out). And then it mostly gets better after that. So ok, not amazing, but very often worth getting.

(along with this, I'm much more on Adam's side rather than Jake's about when menagerie starts to be good - if you activate only half the time, it's a 3-cost lab on average, which is improving as the game goes on; you should be getting some before that).

 

You also mentioned a couple times the Menagerie split usually, often, or almost always being important. I think it's very rarely important. Usually I find menagerie more of a supplemental draw source or just some nice extra good stuff in my Stew, and not doing all the work. Even when it is doing the heavy lifting, though, it's a LOT of heavy lifting to get to actually be activating it *that* many times - if I have 4 and you have 6, I'll skip some of the hoops you jumped through to both get the extra ones and activate them, and I don't think I'm very far behind usually. Basically, it becomes increasingly difficult to activate each successive menagerie, especially in a meaningfully beneficial way. (i.e. look I added a Curse and some ruins to diversify doesn't count).

 

But in general, really nice episode and I am with you!

Quote from WanderingWinder on October 27, 2018, 9:25 PM

I think you're too far down on Menagerie in a money density paradigm. Even with no trashing, it starts getting better than silver around the point you have e.g. 2 silver, 2 terminal silver, 2 gold, and your starting cards. (I mathed it out). And then it mostly gets better after that. So ok, not amazing, but very often worth getting.

This is a really good point, and this data point you mention is a lot closer to Menagerie being good than I thought it was. I'll trust you did the math right and I kind of want to address this in the next episode. May I assume that as you add more Silver/Gold/Terminal Silver that Menagerie just gets better?

Quote from Adam Horton on October 28, 2018, 3:05 PM
Quote from WanderingWinder on October 27, 2018, 9:25 PM

I think you're too far down on Menagerie in a money density paradigm. Even with no trashing, it starts getting better than silver around the point you have e.g. 2 silver, 2 terminal silver, 2 gold, and your starting cards. (I mathed it out). And then it mostly gets better after that. So ok, not amazing, but very often worth getting.

This is a really good point, and this data point you mention is a lot closer to Menagerie being good than I thought it was. I'll trust you did the math right and I kind of want to address this in the next episode. May I assume that as you add more Silver/Gold/Terminal Silver that Menagerie just gets better?

Yes. A big part is that money density increases make cards more valuable, but obviously it also helps to actually have your menag-o-no-dupe-os. I had the math worked out before, but you're less than 30% to activate here, it's just that 25% of a double lab, 75% cantrip is still pretty good. That's also a rough break-even point - silver might slightly have the edge instantaneously (it's close), but menag is going to be better in the long game, because your diversity naturally increases. Obviously silver is better with terminal draw cards, menag is going to be better with even like 1 heirloom, any sifting or copper trashing, etc.

This is now the third time I've tried to math, so getting frustrated, though admittedly these are more my fault than the forum eating, which has happened before.

 

Money density of a menagerie = D(1-P) + 3DP, where D is average money density of other cards, P is chance of menagerie activating. If we set this to 2, we get D + 2PD = 2, and can compare to silver.

D = 1 -> P = .5

D = 1.2 -> P = 1/3

D = 4/3, P = 25%

D = 1.5, P = 1/6

etc. (I've actually taken these from memory by now... annoyed-face)

Obviously higher money density or better chances to activate is going to help menagerie here.

 

Chance to activate is harder to calculate, since you have to get into some conditional probabilities. If we focus on copper collisions for a moment, we can use our favorite hypergeometric calculator to help work out your activation rate.

 

With some more math, it seems the activation rate isn't actually that variable, though, and my earlier estimations were slightly optimistic. The case I discussed in a post above ends up with 18.2% activation rate, and the density of course is 1.31, which gives us a value for our menagerie of only $1.79. You don't actually do better until you're at 3 silver and 3 gold. Of course, adding in extra kinds of cards will help - if your terminals are different, once you add province, adding cantrips, etc.

 

So ok, against silver, with zero help, it still can come into play, but it's very very marginal. However, with any help at all, it can be a reasonable to good card - that help can be sifting, discard, any copper trashing, or even a single heirloom.

Quote from WanderingWinder on October 29, 2018, 4:26 PM

This is now the third time I've tried to math, so getting frustrated, though admittedly these are more my fault than the forum eating, which has happened before.

 

Money density of a menagerie = D(1-P) + 3DP, where D is average money density of other cards, P is chance of menagerie activating. If we set this to 2, we get D + 2PD = 2, and can compare to silver.

D = 1 -> P = .5

D = 1.2 -> P = 1/3

D = 4/3, P = 25%

D = 1.5, P = 1/6

etc. (I've actually taken these from memory by now... annoyed-face)

Obviously higher money density or better chances to activate is going to help menagerie here.

 

Chance to activate is harder to calculate, since you have to get into some conditional probabilities. If we focus on copper collisions for a moment, we can use our favorite hypergeometric calculator to help work out your activation rate.

 

With some more math, it seems the activation rate isn't actually that variable, though, and my earlier estimations were slightly optimistic. The case I discussed in a post above ends up with 18.2% activation rate, and the density of course is 1.31, which gives us a value for our menagerie of only $1.79. You don't actually do better until you're at 3 silver and 3 gold. Of course, adding in extra kinds of cards will help - if your terminals are different, once you add province, adding cantrips, etc.

 

So ok, against silver, with zero help, it still can come into play, but it's very very marginal. However, with any help at all, it can be a reasonable to good card - that help can be sifting, discard, any copper trashing, or even a single heirloom.

To expand a little more: If we switch to having the two terminal silvers be different from each other, menagerie value increases from 1.79 to 1.89; if instead we just add a province to the deck, menagerie value goes to 1.84. (Another province has it go back down, though, as the devaluing of average card starts to kick in more). So it's also reasonable to good in money decks where you can afford to get different stuff with pretty minimal losses to deck quality.

 

I should also note, of course, that it gives the money deck game against discard attacks, which are usually brutal against such decks. (You activate very close to 100% after very long in money decks from a 3 card hand, of course).

That's super-interesting and not what I would have expected. I've been playing round with the numbers myself, and it turns out that in the money-type decks the activation chance is greatly increased by the presence of more unique cards, but substantially less so by the trashing of Coppers or the addition of a second copy of (say) Silver.

Take the starting point WW describes: starting cards and Menagerie plus two Silvers, two Royal Seals (to avoid collision complication of terminal Silver) and two Golds. As he says, the activation chance is 18.2%. Trash a Copper and it goes to 21.1%, but add another unique instead and it goes to 24.6%, well over twice the improvement. Switching to Shelters instead makes it 27.9%, while one Heirloom is roughly the same at 28.1%. Adding a single Menagerie with a 25% chance of activating to a money deck is surely going to be right most of the time in preference to Silver, since your money density will need to be at least 1.6 at some stage if you're going for Provinces.

As WW says, with any help at all (Shelters, Copper trashing or cards that non-terminally reduce hand size) there's surely going to be a point at which Menagerie will be a better buy than Silver.