The Tao of Gaming

I've metioned in various places that I'm fond of the Expedition force for it's "Draw +1 card" during explore phase. How good is this?

Mathematically, this is Hypergeometric distribution (I think). This tells you how likely you'll get X "good" cards if you draw Y cards (out of a deck of known size and with a specific number of good cards). You can look at the numbers in excel by saying "=HYPGEOMDIST(nGood, nDraw, deckGood, deckSize)"

Note that for us, the "Deck" is all unseen cards (including unseen discards, goods, etc). The real question is "What is a good card?" That's tough. Early on, most of the deck counts. As you specialize, I think this number shrinks. I'm making a number of assumptions ... I'm looking at trends, not exact numbers.

Let's start assuming that 60% of the deck is good. For simplicity, 100 card deck, 60 good cards. (That assumes we've seen a few cards built, and spent a few cards).

Let's assume someone else explores. If we don't the expedition force, we get crap 16% of the time. With it, that drops to 6%. Now, if the deck is really good (all great) or really bad, then drawing two or three cards won't matter. But if the deck is only 10% good (10 out of 100), then the extra card drops garbage from 81% shot to a 73% shot. (8 times out of 100, the +1 draw pays off). For a 'moderate' deck, the +1 pays around 15% of the time.

What if we play explore +1/+1. Now we're drawing 4 keep 2 (instead of 3 keep 2 without the expedition force). Now the odds of getting a terrible draw (nothing good) are pretty minor in a rich deck, but you draw two "good cards" an extra 15-20 times out of 100.

Unsurprisingly, where the +1 pays off least is when you are hunting for the last card in a sparse deck. Drawing 7 and 8 are fairly similar.

So, how good is it? Well, if you assume 5 explores after you get the +1 (whether done by you or others), you stand a expect a good card once more. (Which is to say that some games it won't help, some games will gift you twice or more, but once is about right). Five explores seems excessive (and you can't count any you Explore +5), so if you drop it to 3 explores, then the odds drop. (Given all the assumptions, I'm just going to pull a number out of the air and say it helps roughly every other game).

I'm still partial to Expedition Force, but I suspect Space Marines is a better early build (To be fair, it costs more, so it should be better).

[I've now split Race posts into their own category, rather than make a gigantic chain of posts].

Update: One point I missed ... by simply categorizing cards as "Good" or "Bad" I do miss incremental gains. For example, if there are 20 good cards, there may be 7 "Great" and 13 "Goods" and the +1 may let me improve my "Good" to a "Great." But we're getting above my mathematical paygrade. [The Dean of Engineering at my undergrad school always said ... "The next step is dating a mathematician, who solves this for us." Good advice.] This is the point where I could write a simulation, but I think I'll pass.