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[AdamH]

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?

--------------[does math]----------------

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:

Code: [Select]

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

Code: [Select]

%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

Code: [Select]

%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

Code: [Select]

   | 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.

-----------------------

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.

[SirPeebles]

True, but Catacombs, Hunting Grounds, and Madman are the strongest drawing cards yet, aside from perhaps Wharf and Apprentice.

Edit:  Cultist chains can be pretty crazy, too.

[HiveMindEmulator]

DISCLAIMER: Your definition of a draw card is probably different from mine.

You should probably give a definition then. I'm not exactly sure what you mean by "draw card". Anything with +1 card? +2 cards, net handsize increase?

The results are interesting, I guess, but you could do the same thing with cards with on-buy effects, and see that Hinterlands is significantly higher than everything else. It's not clear that "draw cards" however they are defined are vitally important or even highly correlated with more interesting games.

[theory]

All         38/153      19.9%
All but DA  34/157      21.7%

This is a typo, right?

[AdamH]

All         38/153      19.9%
All but DA  34/157      21.7%

This is a typo, right?

Yeah, and there was one in the Seaside line as well. They are fixed in the OP. Thank you for catching that.

DISCLAIMER: Your definition of a draw card is probably different from mine.

You should probably give a definition then. I'm not exactly sure what you mean by "draw card". Anything with +1 card? +2 cards, net handsize increase?

The definition is "What I thought was a draw card when I looked down the list." If you want something more specific, the best I can give you is: "net handsize increase, with exceptions" and mostly those exceptions are related to how useful those drawn cards are. Vagrant didn't make the list because that second card is hardly every useful. Adventurer didn't either, because usually what you want out of handsize increase is the potential to have more "payload" cards, and the only "payload" card I know of that Adventurer can get you is Horn of Plenty. I don't even remember if Wishing Well made the list. EDIT: Ironmonger didn't make the list, even though it's possible for that to increase handsize with a good card, but Crossroads did make the list. Library and Watchtower made the list but Jack did not.

I make no claim that this list is precise, rigorous, or exact. I'm an engineer, I approximate things.

Is this definition enough, or should I attempt to go through the list again and list all the things I think are draw cards? I'd rather not, since I don't think it will help the discussion very much.

The results are interesting, I guess, but you could do the same thing with cards with on-buy effects, and see that Hinterlands is significantly higher than everything else. It's not clear that "draw cards" however they are defined are vitally important or even highly correlated with more interesting games.

The only correlation I'm claiming is the few games I played in my small sample size -- they would have been more interesting for me if there was some draw on the board. There are very few times I would go engine without draw on the board in some form, so without thinking about it too much, I'll put myself out there and say that draw makes games more interesting, though I might regret saying that.

[pinkymadigan]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

[Tables]

Your numbers make me curious. What are Base's 5? Smithy, Council Room, Library, Laboratory presumably are four, what's the 5th? It can't be either Moat or Witch because if one, then surely it'd include the other (and both are terrible for handsize increasing anyway). No other card draws more than one card, except Cellar, and that can't really draw you cards.

[GendoIkari]

I played a Dark Ages IRL yesterday with 10 random cards, and there was no card-drawing available.

And yet I had 6-8 cards in hand on most of my turns.

Procession-Fortress = Card draw.

[soulnet]

I guess DA probably has more trashing opportunities and thinner decks can be built into engines without so much card draw, or even with pure cantrips+sifters?

Warehouse+Conspirator+Cantrips can be a pretty good engine without any real card draw, especially if you have good trashing to go along with it (I could even say that you could do with just trashing or just sifting, although a combination is probably superior).

[AdamH]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

Well I'm not going to share the company I work for on the internet, but I'll say that I develop software. I had a professor explain that there's a time to be precise and a time to approximate things (or make a prototype that was quick and dirty, like writing a shell script or an Excel sheet or something). This was definitely the latter, and that phrase is one I stole from that professor that resonated with me.

Your numbers make me curious. What are Base's 5? Smithy, Council Room, Library, Laboratory presumably are four, what's the 5th? It can't be either Moat or Witch because if one, then surely it'd include the other (and both are terrible for handsize increasing anyway). No other card draws more than one card, except Cellar, and that can't really draw you cards.

You can see an example of my "quick and dirty" ness here, where I leave out one of the draw cards in the base set. I don't know which one I left out, but all 6 of those should definitely be in there. Unfortunately, I'm now away for the weekend and I don't have access to my spreadsheet so I can quickly change the numbers. You'll have to use your imagination. I was hoping not to get bogged down in the details though, since they probably aren't exactly right...

[serakfalcon]

Yeah, not sure about this one, Hunting grounds, and Catacombs are powerful drawers, you can procession a catacombs and, bam, instant engine, rats gives +cards on trash, cultist has wacky ways of getting cards, there's madman...
I haven't really found getting an engine hard with DA, what I have found strange is the sheer size of the trash pile by the end of the game

[AdamH]

Yeah, not sure about this one, Hunting grounds, and Catacombs are powerful drawers, you can procession a catacombs and, bam, instant engine, rats gives +cards on trash, cultist has wacky ways of getting cards, there's madman...
I haven't really found getting an engine hard with DA, what I have found strange is the sheer size of the trash pile by the end of the game

Yeah there's no denying that the draw cards in DA are super-strong; I just haven't been seeing them. That's the point of my post. You mentioned pretty much all the draw cards in the set.

I thought about including KC, TR, and procession, but I decided against it because I couldn't put BoM on there since it depended on other cards in the kingdom. It's definitely a grey area, but the whole approximation thing was there so we don't get bogged down in edge cases, which I know we all like to do here.

[serakfalcon]

Yeah there's no denying that the draw cards in DA are super-strong; I just haven't been seeing them.

Well, just some math I guess, if there are ~10% draw cards in DA and you only pull DA the odds of getting no draw cards at all is 34%, (0.9^10 right), so thats only 1 in 3 games, and I guess you didn't include rebuild, if you're doing half and half its only ~20% of the time that you'll get no draw cards. So I guess thats fair, not every game can be an engine game, seems like you just got unlucky?

[serakfalcon]

I guess I just came out of a procession/catacombs/altar/forge/squire game where the engine would literally trash half of itself, gain a ton more cards, draw them all, resulting in a 3 province 2 duchy megaturn. Probably could have done better but all the trashing and gaining was making my head hurt

[heron]

More precisely, if there are 35 DA cards and 4 are considered draw cards, thats (31!/21!)/(35!/25!)=~24% chance of there being no strong draw in a pure dark ages set.

Hopefully I did my math right this time.

[qmech]

More precisely, if there are 35 DA cards and 4 are considered draw cards, thats (31!/21!)/(35!/25!)=~24% chance of there being no strong draw in a pure dark ages set.

Hopefully I did my math right this time.

Yes, take a Gold Star.

[AdamH]

I've updated the numbers in the OP with six draw cards in the base set. Perhaps I'll upload the spreadsheet I threw together to calculate all this stuff if I get ambitious.

[Kirian]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

The old joke is that if an engineer can make an approximation to make the math easier, s/he will.  It comes under the heading of "If X... you might be a Y" jokes:

If you can say 'let's approximate this horse as a sphere to make the math easier' with a straight face... you might be an engineer.

[eHalcyon]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

The old joke is that if an engineer can make an approximation to make the math easier, s/he will.  It comes under the heading of "If X... you might be a Y" jokes:

If you can say 'let's approximate this horse as a sphere to make the math easier' with a straight face... you might be an engineer.

pi is exactly 3.

[LastFootnote]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

The old joke is that if an engineer can make an approximation to make the math easier, s/he will.  It comes under the heading of "If X... you might be a Y" jokes:

If you can say 'let's approximate this horse as a sphere to make the math easier' with a straight face... you might be an engineer.

pi is exactly 3.

This is true for very large values of 3.

[Kirian]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

The old joke is that if an engineer can make an approximation to make the math easier, s/he will.  It comes under the heading of "If X... you might be a Y" jokes:

If you can say 'let's approximate this horse as a sphere to make the math easier' with a straight face... you might be an engineer.

pi is exactly 3.

This is true for very large values of 3.

In all seriousness, though, when you're doing the initial math for things in engineering, using pi = 3 is kinda common.  Remember that up until the 1970s, engineers only worried about three significant digits... on their slide rules...

[SirPeebles]

In physics it's common to start by estimating orders of magnitude, in which case pi may be rounded to 1 or 10.

[LastFootnote]

So, I'm not a physicist, but why are orders of magnitude powers of 10? Why not powers of 8 or 16?

EDIT: Hmm, actually, maybe I don't want to derail this thread any more than it already has been.

[pinkymadigan]

I'm an engineer, I approximate things.

Not trying to start something, but an engineer for who? That statement is one of the oddest things I've read today, and it was a big reading day for me.

The old joke is that if an engineer can make an approximation to make the math easier, s/he will.  It comes under the heading of "If X... you might be a Y" jokes:

If you can say 'let's approximate this horse as a sphere to make the math easier' with a straight face... you might be an engineer.

pi is exactly 3.

This is true for very large values of 3.

In all seriousness, though, when you're doing the initial math for things in engineering, using pi = 3 is kinda common.  Remember that up until the 1970s, engineers only worried about three significant digits... on their slide rules...

Maybe that's why in the 70s you could buy cars with two inch gaps around the door where it was supposed to meet the frame and it was considered fairly acceptable.

[michaeljb]

So, I'm not a physicist, but why are orders of magnitude powers of 10? Why not powers of 8 or 16?

EDIT: Hmm, actually, maybe I don't want to derail this thread any more than it already has been.

I'm not quite a physicist, but I have completed a physics minor. I'm guessing the reason is just that you can move the decimal point around or add/remove zeros on the end of a number to adjust it by orders of magnitude.

In other words, probably just because we use base 10.