Maybe this is a coincidence, but I've been playing a lot of IRL games with kingdoms biased towards Dark Ages (since I recently got the expansion). So many times I see an engine on the board that would be terribly fun to play except for the fact that there's no way to increase hand size on the board. At all. I'd say this happened in 50% of the games I've played (maybe 20 or so).
I know my sample size is small, but is there anything to this?
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DISCLAIMER: Your definition of a draw card is probably different from mine. Scout (and others like it) didn't make this list because even though it increases hand size, I don't like to build engines with Scout being a draw component. If you don't like it, do your own math.
Number of draw cards, by expansion:
Base 6/25 24.0%
Intrigue 7/25 28.0%
Seaside 5/26 19.2%
Alchemy 4/12 33.3%
Prosperity 4/25 16.0%
Cornucopia 2/13 15.4%
Hinterlands 5/26 19.2%
Dark Ages 4/34 11.8%
Promo 2/05 40.0%
All 38/191 20.4%
All but DA 34/157 22.3%
DA has the lowest percentage of draw cards out of any expansion, about 8.5% below average.
Choosing a completely random kingdom from all expansions (ignoring YW bane pile and BM shenanigans), the probability of no draw cards showing up is 10.2%. Without DA cards in the kingdom at all, that percentage goes down to 8.0%.
Choosing a kingdom which requires at least x DA cards will multiply this percentage by (88.2%/79.6%)^x or about 1.1^x -- or an exact formula of
%age = (88.2%)^x*(79.6%)^(10-x)
(this is not exact, I know, since I don't remove the selected card each time I pick one out of DA for the requirements. It should be close though)
Choosing a kingdom which has exactly y DA cards gives a percentage of
%age = (88.2%)^y*(78.7%)^(10-y)
(again, not exact, same reason)
So, in table form, the percentage chance of having no draw card available in the kingdom given a number of DA cards in the kingdom either as an exact requirement or a minimum requirement
| Exact | Minimum
0 | 08.0% | 10.2%
1 | 09.1% | 11.3%
2 | 10.4% | 12.5%
3 | 11.8% | 13.9%
4 | 13.3% | 15.4%
5 | 15.2% | 17.1%
6 | 17.2% | 18.9%
7 | 19.5% | 21.0%
8 | 22.2% | 23.3%
9 | 25.2% | 25.8%
10 | 28.6% | 28.6%
So I was playing with a minimum requirement of 4 DA cards, where before I had the expansion it was exactly 0. That means almost twice the kingdoms have no draw cards as before.
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Conclusions:
DA has less draw cards than any other expansion, by a significant amount. This significant amount results in one of every 50 kingdoms being deprived of a draw card if you play full random. In my case, there was an increase of 7.4%, or one in every 13.5 kingdoms.
Big Deal.
I noticed this because of a small sample size of games. There should be at least *some* draw in most kingdoms you play regardless -- you should expect about than 9 or every 10 kingdoms to have a draw card -- so I just got an unlucky streak and got a few in a row with no draw. Does anybody have the WAHmbulance on speed dial?
Perhaps the heavy DA emphasis caused more engine-y boards that would have otherwise been viable, which caused me to notice this. I will remain intellectually honest here and just play more DA games.
Another conclusion: I'm a huge nerd.