Bonus card overlaps

[ArrestedBird]

I've found charts and rankings of bonus cards telling you how valuable each bonus is in isolation. Those rankings are great for helping you during turn zero (the setup phase when you discard birds, food, and a bonus card.)

This chart is for the early- to mid-game when you already have your first bonus card and you draw two additional bonus cards and have to choose one.

How to use it: find the row with the bonus card you already have in your hand, then find the column where it intersects each of the two cards you just drew. A higher number means you have better odds of getting birds that advance BOTH bonus goals.

For example, if you already have Anatomist as your first bonus card, and you draw Historian (.02) and Photographer (.46), you would be better off keeping Photographer since nearly 50% of the cards that match either Anatomist or Photographer match both of them, whereas only 2% of the cards that match either Anatomist or Historian match both of them.

In other words, given that you already have bonus card A, will a second bonus card help you by drawing from the same bird pool?

Note: this chart helps you pick bonus cards when you still have time to draft birds that qualify for them. By mid-Round 3 or later, forget the chart. Just look at the number BGA shows you on each card for how many birds already on your board qualify. At that point you're not flexible on your goals anymore, you're just counting what you've got.



You can view or download the image at https://csnizik.github.io/Wingspan-Stat ... erlaps.png

[admitted]

Posts like this really make me happy. I think a conditional probability chart might be a better choice?

[ArrestedBird]

Posts like this really make me happy. I think a conditional probability chart might be a better choice?

Thanks!

Can you explain a little more about what you mean by conditional probability? If you're saying what I think you're saying, i.e. "what percentage of Anatomist birds also count for Photographer", that's useful, but it has a catch: the answer changes depending on which direction you ask. The percentage of Anatomist birds that alos count for Photographer is different from the percentage of Photographer birds that also count for Anatomist. So you would need to have two different numbers depending on which card you already have.

This chart is basically serving as a Venn diagram drawn for every possible pair of bonus cards, showing how big the overlap is relative to the total area of both circles combined.

But I'm curious what you had in mind?

[Cos-]

Thanks for making this!

What's the pool of bird cards you based this on? Is it the base game plus swift start cards, without any cards removed?

[admitted]

The purpose of this analysis is to help determine which goal works best given the goal already selected, so it may be more appropriate to frame the calculation as a conditional probability. Specifically, we would want to compute the probability that a bird advances Goal B given that it advances Goal A, using the formula P(B|A) = P(A and B) / P(A). Here, you are creating a table using P(A and B)/P(A or B).

One implication of using conditional probabilities is that the results would generally be asymmetrical across the diagonal. Specifically, P(B|A) would not necessarily equal to P(A|B), since both expressions share the same numerator but typically have different denominators