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markus

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Card Draw Statistics
« on: March 03, 2019, 03:36:46 pm »
+12

I’ve used my database of logs since the release of Renaissance to calculate statistics on draw and discard. (21,000 games with either the worse player having mu>1.3 or the better player having mu>1.8)
I’m tracking each time a card enters and leaves the hand of a player. (Or is played from somewhere else as if it entered your hand and was played immediately – Vassal, Throne Rooms, Band of Misfits,... see my notes below.) The results can be found in my stats sheet.



First, I’ll have a general look at the boards. I can check how many cards are drawn during the course of a game: 125 cards per player. The winner draws 136 cards compared to the loser’s 115 cards. (For example, playing a Village draws 1 card.)
This number is generally higher on boards with cards that increase your hand-size and also on boards with cantrips (playing each draws 1 card). Minion and Shepherd games top the list with 143 cards per player. On the other hand, if there’s trashing available, you don’t need to draw as many cards to get the game to an end. Donate is at the bottom of the list with only 92 cards. Other cards that can make a game short like Rebuild, Butcher and Salt the Earth are also listed there.

Most of this draw comes from drawing your 5 new cards during clean-up (75 cards). That’s more or less 15 turns drawing 5 cards each. (The exception would be Outpost turns and situations in which the deck contains fewer than 5 cards.) This number is 3 cards higher for the winner (the winner is more likely to have more turns).
Therefore, anything that makes the game longer like attacks will show up with a higher number there. Mountebank with 88 cards and Knights with 86 cards top the list. Donate with 60 cards and Governor with 62 cards are at the other end.

Hence, we’re left with 50 cards that are drawn by playing cards (or buying stuff). Some of that will be cantrips and when you play a Laboratory, your handsize only increases by 1. Therefore, I’m calculating “net draw”. It takes out the cost of playing the card to your handsize as well as discarding (Cellar) or trashing (Chapel) other cards from hand. Playing a Laboratory provides 1 card net draw, playing a Smithy 2 cards, playing a Warehouse -1 card. Summing up over all those cards with a positive net draw, I end up with 14 cards per player (winner 18, loser 12).
Margrave and Wharf are topping the list now, while Donate is still at the bottom, but you’ll also find Grand Market down there.

The second part of the table are the stats for the specific cards. I’ll present the stats from the winner’s perspective, noting that the loser drawing less is naturally also a sign of getting less lucky and not just being less skilled.
First in columns M and N, there is the total draw provided by the cards. Cards will be at the top if they draw a lot and are used a lot. (Counting House draws a lot per play, but unfortunately you often just ignore it.) Shepherd, Stables and Sauna/Avanto are the top with a draw of around 30 cards for the winner, Laboratory is at 21 cards and the Smithy family around 10 cards.
This can be split up into drawing on play, duration (Den of Sin and Wharf at the top), and on gain or trash effects (Villa, Fortress, Den of Sin and Ghost Town at the top.)
Next, I can look into how all this draw is used in practice. Columns O and P have the “discard” of cards from hand caused by this card. That could be discarding, putting on top of your deck, and trashing other cards from your hand. It could happen because you play the card, gain the card, call the card from the reserve mat, bought some event, etc.
Sifters are at the top of the list with Dungeon discarding 22 cards. Strong trashers end up with 8-10 cards. This discard number is decomposed into discarding and trashing further right in the table as well for whatever card that might be interesting (Count trashes 3.9 cards and discards 3.1 cards).
Another discard component that can be found there, is how often the card is “dead” in your hand (discarded during the clean-up phase). Because you either can’t, don’t need or don’t want to play it during your turn – not a good use of your draw. At the top of this list is the junk that you begin the game with (9.4 cards for Estates and 8.3 for Shelters). Cards that you typically can and want to play are below 1 in general.
Note that the measure is a bit too nice to terminal draw cards because cards that you draw dead with Smithy other than Smithies will count as a dead card in their respective row. But then it’s also partly Village’s fault that you can’t play it with 0 Actions left.

This allows me to calculate the net draw provided by each card. It is the draw minus the discard minus the number of plays and minus the number of being “dead” in hand. So the cards at the top of the list are the ones that provide you with a larger handsize. And the cards at the bottom better be useful in some other dimension to be worth the handsize reduction. Wharf wins with +19 cards, followed by City Quarter and Scrying Pool with around +15 cards for the winner. City Quarter and Scrying Pool are interesting because the loser only draws 6 cards with it. Partly, that’s because they gain fewer copies, but part of it will also be good or bad luck in aligning them in the right way. At the bottom there is Copper with -34 cards of course, followed by Ambassador (-20) and Forager, Remake around -15 cards. Artificer is the lowest card that doesn’t trash with -12 cards.

Some cards also affect the opponent’s handsize in a positive or negative way. I’m having those numbers in the decomposition of draw and discard. Minion tops both of those lists with the winner discarding 11.7 cards and drawing 9.3 cards due to their opponent’s Minion play.
I can add that effect on the opponent’s handsize to arrive at my preferred measure of card draw: subtract the cards that the opponent draws from net draw and add the cards that the opponent discards. Then, a usual Council Room play provides you with +2 cards relative to your opponent and a Militia play that makes them discard from 5 to 3 cards counts as +1 card. (Discarding your bad cards to Militia is not as bad of course as drawing fewer cards of course. But this exercise is just about drawing and discarding cards. Drawing a Curse to hand due to your opponent’s Torturer is usually not good, either…)
With this measure in columns S and T, Wharf keeps its top spot, but Margrave gets close to it with +19 cards as well. Ghost Ship also jumps up from +4 cards to +11 cards here, while Lost City loses from +9 cards to +6 cards.
For further statistics, you can download the sheet and calculate them from the available numbers (e.g. cards drawn per play or per gain).

Notes:
The accounting exercise is that cards “drawn” equals cards “discarded” over the course of the game. There are some errors and omissions in the official log, woodcutter, and my code that I try to correct for. But some edge cases that I’m aware of and probably more that I’m not aware of are missed (e.g. gaining Ghost Town not to hand but top of deck with Armory).
I can check for each game and player how big the absolute difference between draw and discard is and I’m satisfied with it being only 0.07 cards on average per player and game. The worst boards in that sense include Plan or Innovation, because those uses are not logged, but the error is still below 0.3 cards per game. If you still see something that looks odd (yes, Horn of Plenty shouldn’t have 1/700 cards drawn on trash/gain) and significant, let me know.

The general rule is that I want to attribute the draw or discard to what ultimately caused it. For example, if you play a Workshop and gain a Ghost Town, the gain to hand is Ghost Town’s effect and not Workshop’s. If you trash a Rats, the card that you draw gets attributed to Rats and not the trasher. The exception are boons and hexes which do get added to the card that caused their receives.

Only stuff that happens to a player’s hand before and during their last turn counts. For example, if you Militia your opponent and end the game, their discard doesn’t count.

For most cards it should be obvious from the numbers what is what (for example, setting aside with Island counts as trashing as does returning with Ambassador).

Vassal, Summon, etc count as +1 card draw for whatever caused the other card to be played. For example Vassal finding a Village counts as 1 Vassal and 1 Village play, and 1 draw for Vassal and Village each. As a result, net draw is 0 (your hand size is the still the same). Similarly, Summon counts as 1 card duration draw if it plays the card on the next turn.
Throne Room family: if a Throne Room plays another card, Throne Room draws 1 card. (Think of it as Throne Room putting the played card into your hand and immediately playing it again.) Playing Throne Room – Village means: 1 Throne Room and 2 Villages played, 1 card drawn by Throne Room, 2 cards drawn by Villages. It all nets to 0 and indeed your handsize is the same afterwards.
With the same logic, King’s Court gets +2 cards, when it plays a card (King’s Court on Village nets 1 card).

Band of Misfits, Overlord, Necromancer: playing them also draws 1 card. Overlord as Village means 1 Overlord and 1 Village play, 1 card drawn by Overlord and 1 card drawn by Village for a net 0.
Inheritance gets the Necromancer treatment: playing an Estate inheriting Village counts as 1 Inheritance play and 1 Village play, Inheritance and Village each draw 1 card. So “Estate” in the list of cards is never played.

+card token: Pathfinding and Teacher get the cards drawn from the token that they placed as duration draw.

-card token: counts as -1 card draw (if eventually removed), making Raid, Relic and Borrow the only cards with negative contributions in the draw decomposition.

Outpost, Mission, Fleet: the extra turns are not attributed to the cards but would show up as more draw during clean-up for that player.

Clean-up, Expedition, Flag, River’s Gift: clean-up draw is the 5 (or 3 with Outpost) cards drawn during clean-up. The cards due to Expedition, Flag and River’s Gift show up as duration draw for Expedition, Flag Bearer and whatever led to River’s Gift.

Donate: checks whether the 5 cards that you draw afterwards are more or fewer than what you drew in the previous clean-up. Often that will result in a small discard when trashing down to fewer than 5 cards. If you only draw 4 cards after your next turn, it will show up as only 4 cards drawn in clean-up.
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hvb

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Re: Card Draw Statistics
« Reply #1 on: March 03, 2019, 09:55:07 pm »
+1

These are nice statistics, but its hard for me to draw any conclusions that would have an impact on my game.

Did you draw any, maybe surprising ones?
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markus

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Re: Card Draw Statistics
« Reply #2 on: March 04, 2019, 02:14:07 am »
+5

One thing is to check how the cards with varying draw do. I'm taking averages between players now to not have the "got lucky and won effect":

Scrying Pools have a net draw of 10.7 cards, which is 3.7 cards per gain. City Quarter has (10.6 | 4.6).

Seer has a net draw of 8.2 cards (3.8 per gain), putting it ahead of Laboratory (8.0 | 3.1) and Stables (7.5 | 3.1).
Menagerie is just behind those with 7.2 cards net draw (3.0 per gain). So a gained Menagerie draws basically the same as a Laboratory. Admittedly, you can't make it work on every board, but it seems to work quite often.
Wishing Well on the other hand is at (2.3 | 1.2), Patrician at (1.3 | 0.7).

2.8 Caravans basically draw the same as the 0.85 Sinister Plots over the course of the game (6.3 cards). Per gained Caravan that is only 2.3 cards.
Magpie is just behind it with 6.1 cards drawn. Most of the gains will be free, so let's look at the buys: 3.9 cards per buy. (Ok, some of them will be gained by Workshops making that number a bit too high.)

Experiment is lower with 4.9 cards drawn and let's say 1.4 cards per 2 gains. Yes, it's nice that you can hold on to them, but you had 1 dead card on that turn.
Expedition is further down with 4.3 cards and 1.9 cards per buy. It's even bought less often than Experiment (yes, discard attacks hurt it).

Library vs Scholar: they basically get gained the same amount. Library draws (3.5 | 6.3) compared to Scholar's (3.2 | 5.7). Scholar has the advantage of sifting (3.1 cards per game), Library of skipping Actions that you don't want.
For comparison, Cursed Village is at (8.5 | 4.3).
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