Innovating - Management of Science in the World of Deck Drafting (Patreon)

A while ago I wrote about how the mantra 'Always Be Innovating' was not a good one to follow (the phrase 'sometimes be innovating, but avoid it early on because there are more important things to spend your limited resources on' is NOT catchy); and I've explored a few specific innovations/innovation trees (I really rate the new music tree and cooking). So I wanted to follow this up with a more general and basic look at the Innovation mini-game.

Everything starts with Language (we are going to work with the standard deck here, not Stars/Sun) and this instructs us to build our six card starting deck.

At this point in the game we have a slim, six card deck, so when we innovate:

We will draw two different cards. If we are looking for a specific card then at this stage we have two chances to draw the card.  The first draw is one out of six options (1/6) and the second draw is one out of five options (1/5) - this is because we do not replace the first card when drawing the second one.  So we end up with a 1/6 and a 1/5 combined for about a 1/3 chance of getting the card you want on this draw.

The formula for calculating odds when drawing cards from a deck is rather fun. It's:  

P = 1 - ((((S-T)!)-((S-T-D))!))/((S!)-((S-D)!)-1))  

Where: 

• P = Probability of getting what you're after
• S = Size of Deck (in cards)
• T = Amount of the Target Card You are after (usually 1 in innovations)
• D = Number of Cards Drawn (usually 2 or 4 depending on Symposium)

(I'm writing that formula from memory, so I hope the brackets are correct! I suppose I should check, if I had the time!)

However, in this day and age you really do not need to know that kind of thing, especially for a board game - the broad strokes are sufficient, so we'll keep our "No maths nerds allowed" sign on the door, they can wait outside. :D  (Plus there are calculators for this kind of thing).

The main things here is to know are that the more cards you can draw from the innovation deck and the smaller the innovation deck is, the higher the chance you will get what you want.  Which I am sure you are saying 'That's obvious!' 'Learn to math Fen!' and other such things!  But these basics are essential in order to help increase your chances of getting the innovation(s) you are after and try to mitigate the situation you see at times of 'We're at lantern year 12+ and we still don't have Dash' as much as possible.

Symposium

Symposium is known to be the best Innovation to get early on, the reason for this is best explained as follows; we'll look at two settlements on their second innovation.  

Settlement A has innovated Drums first Settlement B Innovated Symposium (core game only so this is the tech tree we are dealing with here).

Both Drums and Symposium Add 2 cards to the deck so the deck size is now a total of 7. (One card removed, 2 cards added in).  Let's say that next year both settlements want to innovate and gain Surge so they can kill monsters faster and prepare for The Butcher.

Settlement A will get to see 2 cards out of 7

Settlement B will get to see 4 cards out of 7

So Settlement A has a ~28.6% chance of getting what they want while Settlement B has a ~57.1% chance.  That's two times as likely (which is what we expect when you are drawing twice as many cards with a single target card)!

If the settlements are less picky and say they want either Surge or Dash then the odds look like this:

• Settlement A: 52.4%
• Settlement B: 85.7%

So I think you can see that picking Symposium whenever you can get it early(ish) is a huge benefit to your settlement, it's going to improve every single draw you have for the future.

Before we finish here are the deck sizes you end up with after your first innovation depending on what you pick:

• Ammonia: 7 
• Symposium: 7
• Drums: 7
• Inner Lantern: 7
• Paint: 8
• Hovel: 8

However there are other things we can be doing to help our situation apart from just jamming out Symposium as early as possible.  Avoiding Deck Bloating and Prioritising Deck Thinning.

Deck Bloat

A lot of innovations have this neat little bar at the bottom of their card, this means that they will add more cards to your deck.

When you have all the expansions added in Hovel is a huge offender of Deck Bloat and it's one of the reasons why I consider it to be the weakest innovation tree when you take the whole game into account.  Even in the core game only it directly adds 3 cards to the deck (Bed, Family, Partnership) while many others add just 2 - Paint is the other offender for deck bloat early on btw - and Bed + Partnership are woefully underpowered to boot!

To fully understand this I recommend you take a look at Hobo's core game innovation tree (link here again) or lay out the innovation trees yourself.

Here's a rough representation of how I do it (these are 1.31 cards in the screenshot, it's just for the numbers/layout).

You can see that the core game trees tend to hold a total of between 4 and 6 cards before everything from them is exhausted.  We can also see that there are 4 tiers of technology. Language is T0 and something like Clan of Death is T3 - that helps with evaluating how good a card is, because having to innovate at least 3 times to get something means that it should be very powerful.  (By the way, I count tiers by the minimum number of innovations it takes to reach them from Language).

Also here's how I present it to my friends so they can make decisions without knowing what's coming up and having too much spoiled. They get to see the numbers of cards that are added in, but not exactly what will be added.

So as you can see Hovel and Paint are going to put a lot of cards into your deck, so if you are not after the cards in their tree, you should hold off on putting them down.  For me it's just Family and Clan of Death in Hovel that I typically want (new Till Death Partnership should change that somewhat thank goodness) so that's 2 dead cards added (even more with expansions... ugh Shadow Dancing).  Paint adds 5 cards to the deck overall, but so many of them are very powerful and/or essential for success like Paint, Pottery, Face Painting and Sculpture so we have to live with that!

In contrast you can see how lean the Symposium tree is; it has a total of 4 cards. However, these cards tend to be more useful later on in your campaign, so that's the price you pay, you have to carry those deadweight cards for a while before they become useful.  

To demonstrate here are our two settlements.  Settlement C and Settlement D.  Both are looking to draw Symposium for their second innovation, but their first tech was different.

• Settlement C - Hovel - 25%
• Settlement D - Drums -  28.6% 

Now at this stage that is just a ~3.6% difference between the odds, and that might not seem that bad, but if you miss symposium and you are going to have to innovate another technology and that one might even make the deck larger!

So one of our long term aims when innovating is to avoid bloating, because it's going to ruin the chances of reaching the cards we want. So sometimes we might pick something suboptimal in order to help our deck get thinner, I refer to these cards as...

Terminus Cards

A terminus is a card that does not add any more cards to the deck. It represents the end of that particular branch.  There are a lot of these, and here's an example of a good one.

Apart from all of the great uses that this card has (and the passive protection it gives against Plague) this card is fantastic because it is a T2 Terminus Card (most are T3). So you can go Ammonia -> Bloodletting and then that branch is done, it doesn't add anything more to the deck.

Again, we'll do a simple demonstration.  Settlements E and F both have innovated Ammonia and Hovel (9 card deck) and they are now after Surge.  Their basic chance of hitting Surge this year is: ~22.2% which isn't that great.  These settlements both draw the same 2 innovations however; Bloodletting and Paint.  Settlement E choses Bloodletting (-1 card), Settlement F goes with Paint (+2 cards). 

The following year both these settlements innovate, still seeking Surge.

• Settlement E is now at 25% chance
• Settlement F is now at ~18.19% chance

That's quite a large swing and I think it demonstrates the difference between deck bloating cards and terminus cards quite nicely! So if a card doesn't have that 'consequences add X cards' text at the bottom of it you should value the card a little more than ones which add additional cards in.  Especially if those cards which get added are not interesting to you in the near future.

Summary:

In truth all the maths behind this do not really matter in the end.  There are a few simple guiding principles that can be used in most of the situations and everything else is just posturing for the sake of looking smart. :P  Here they are:

• Pick Symposium
• When offered choices that are the same level of desirability, pick the one that adds the least number of cards to your deck.
• When you are aiming for a specific high level tech card like say Pottery (to get the Barber Surgeon); pick cards that get towards that card over terminus cards over anything else.
• A thin, Innovation Deck means a healthy settlement with a bright future!
• Don't innovate every year if there are better things you could do with those resources, especially early on.
• Hold off on getting Hovel and Paint for as long as you can (but you will need them at some point because Family/Clan of Death and Dash/Sculpture/Face Painting/Pottery are too good to ignore).

Before I close out, I'd like to quickly note that there are certain innovations that can be gifted to you by events/monsters - Ammonia can be gained from both The Gorm (Showdown AI card) and the White Lion (Hunt Event), while things such as the Lion Knight and Gorm can give you free innovations of other cards.   There are also some monsters that manipulate the Innovation deck a little by adding or reordering things (Flower Knight and Manhunter for example), plus there are also some monsters that give benefits for having certain innovations when you beat them, you'll figure out what these are and if you want them as time passes!

Sometime in the future I'll run through the assessment of various innovation cards maybe, I can either do a detailed breakdown or I can do it by trees/expansions, it depends what people want!

Final Note: If you want a game that helps you with understanding the principles of drawing, drafting, deck thinning and deck bloat while being fun and not boring the way maths can be - I recommend Ascension (Card game), Dominion (The original deck drafter) or Slay the Spire (PC rogue-lite deck drafter/rpg).