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Subject: toward an objective ranking of cards rss

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Frederic Bush
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Here’s my first take at an objective ranking of the Agricola base cards. I looked at data from games from play-agricola.com. The most popular format, where all the data comes from, is a 4-player game with an 8-card draft: players draw 8 cards, keep one card and pass the rest to the next player, ending up with a hand of 7 cards; the final card is discarded.

The method I took was to start with the percentage of times a card is played when it’s in someone’s hand ( http://play-agricola.com/forums/index.php?topic=1583.0 ), then multiply by the difference between the observed win rate when the card is played ( http://play-agricola.com/forums/index.php?topic=1582.0 ) and the average 4-player win rate of 27.2% (some games are ties with more than one winner.) So, a card that’s played 100% of the time when drafted and results in a 32.2% win rate would have the same value as a card that’s played 50% of the time when drafted and results in a 37.2% win rate when played. 1*(32.2-27.2) = .5*(37.2-27.2).

In addition, I used info on draft order ( http://play-agricola.com/forums/index.php?topic=1570.0 ) to determine which cards are over/undervalued: anything in bold is heavily undervalued and drafted on average 2 or more spots later than it should be, while anything in italics is heavily overvalued and drafted on average 2 or more spots earlier than it should be.

Certain cards are banned by common consensus for being too powerful, so there’s no way to gather data on their strength. In the base set, these cards include the occupations Taster, Wet Nurse, Lover, and Chamberlain, and the minor improvement Reed Hut.

I’ve separated the cards into tiers based on 2.5% changes in win rate. Cards that come earlier in each tier are more valuable than the ones that come later. The top cards result in just over 14% extra wins, or about a 52% boost to the 27.2% average win rate.

There’s also a Hall of Shame for cards which (a) are very rarely played and (b) result in a very low win rate when played.

My analysis comes later, but feel free to fire away. I'm not totally confident in the valuations of the less-often-played cards located around the middle of the distribution, but any frequently-played card, and any card beyond +/-2.5 should be pretty accurate.



Occupations:

+15

Churchwarden, grocer

+12.5

Educator, reeve, chief’s daughter, charcoal burner

+10

Plow driver, constable, scholar, house steward, mason, puppeteer, village elder

+7.5

Lord of the manor, wood distributor, head of the family, chief, social climber, clay hut builder, basket maker, braggart, net fisherman, fence overseer, organic farmer, patron, wood deliveryman

+5

Land agent, farm steward, adoptive parents, milking hand, storehouse keeper, foreman, hut builder, master builder, manservant, cattle breeder, clay worker, woodcutter, quarryman, clay deliveryman, field warden, perpetual student

+2.5

Berry picker, hide farmer, fence builder, cowherd, stone carver, thatcher, wood collector, master forester, guildmaster, tinsmith, wellbuilder, groom, maid, slaughterman, animal breeder, stablemaster, storehouse clerk, tenant farmer, swineherd, market woman, harvest helper, academic, outrider, traveling salesman, hobby farmer, rancher, reed collector, veterinarian, dock worker, renovator, fencer, shepherd, sheep farmer, wooden hut builder, pastor, tanner, water carrier, field watchman, master shepherd, butcher, estate manager, cabinet maker, pig breeder, conservator, clay firer, wood carver, mendicant, schnapps distiller, resource seller

0

Layabout, basin maker, storyteller, pieceworker, plow maker, gardener, hedge keeper, stonecutter, reed buyer, forester, fence deliveryman, farmer, turner, street musician, master baker, seasonal worker, stone buyer, clay seller, cattle whisperer, manufacturer, frame builder, cook, corn profiteer, master brewer, businessman, brush maker, stockman, stone carrier, stone breaker, animal keeper, animal tamer, dancer, potter, smallholder, bread seller, undergardener, animal handler, mushroom collector, sheep whisperer, clay plasterer, animal trainer

-2.5

Serf, tutor, magician, wood buyer, bricklayer, brushwood collector, fisherman, fieldsman, animal dealer, yeoman farmer, stablehand, clay mixer, baker, meat seller, clay digger, merchant, carpenter, plowman, market crier, acrobat, pig whisperer

-5

Sycophant, seed seller, weaver, juggler, countryman, conjurer

-7.5

Greengrocer


Hall of shame: Fieldworker, pig catcher, midwife



Minors:

+15

House goat

+12.5

Swan lake, fruit tree

+10

Turnip field, beehive, clogs, pelts, animal pen

+7.5

Goose pond, punner, wooden path, reed pond,clay path, fish trap, quarry, ox team, clay roof, wooden strongbox, clay hut extension, wooden hut extension, carp pond, chicken coop, clay pit, village well, duck pond

+5

Simple fireplace, rake, building materials, writing desk, loom, planter box, sawhorse, strawberry patch, cooking corner, paved road, riding plow, yoke, granary, lumber, broom, herb garden, mansion, canoe

+2.5

Forest pasture, lettuce patch, spinney, bookshelf, half-timbered house, liquid manure, stone house extension, madonna statue, milking stool, swing plow, clay supports, gypsy’s crock, flagon, manger, greenhouse, feed pellets, tavern, dovecote, stone cart, plane, landing net, wildlife reserve, alms, clay deposit, straw-thatched roof, corn sheaf, reed exchange, sack cart, mini pasture, shepherd’s crook, wood cart, guest

0

Windmill, fishing rod, sleeping corner, sawmill, horse, manure, hand mill, weekly market, animal yard, milking shed, turnwrest plow, private forest, corn storehouse, boar breeding, copse, field, brewery, axe, schnapps distillery, baker’s kitchen, beanfield, market stall, wooden crane, drinking trough, stone tongs, raft, wood-fired oven, brushwood roof, spices, lasso, slaughterhouse, baker’s oven, shepherd’s pipe, spindle, builder’s trowel, cooking hearth

-2.5

Butter churn, threshing board, clapper, stable, outhouse, basket, ceramics, flail, potato dibber, bread paddle, cattle market, bakehouse, spit roast, stone exchange, moldboard plow, helpful neighbors, acreage

-5

Ladder, millstone, grain cart, harrow, crooked plow, corn scoop

-7.5

Baking tray


Hall of shame: Animal Feed, watermill, holiday house
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Gareth Reynolds
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A similar listing for different game types would possibly be quite interesting, although less statistically valid considering the available sample size.

Some of that surprises me. Especially the Grain Cart and Corn Scoop at the end of the minors list. House Goat being good isn't surprising, being the "best" minor is a little.
Midwife being poor doesn't surprise me, even after I seemed to make good use of it a few nights back. I found that others were likely to be getting Family Growth before me and made the call to get it out. At least six food without really slowing down anything else I was intending.
Of course, I fail to beat 30 consistently, even against inexperienced players, so my expectations probably aren't the most valid.

Also, I notice that Architect doesn't seem to be in the occupation listing. I noticed because I was interested in how it compared to Mason.
 
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Frederic Bush
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The cards ranked are just from the base game, EIK decks. I don't have data on the G deck, which is where Architect is from.

Perhaps you're thinking of Master Builder, which is from the base game and has a similar effect to Mason? They are both valuable cards, but Mason (+8%) is nearly twice as good as Master Builder (+4.4%).
 
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James Klemm
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This is a useful list of cards that are better or worse than expected. I would be interested in an objective ranking of the cards, in general. Although, many times the proper card to choose is dependant on other factors.
 
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Gareth Reynolds
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fbush555 wrote:
The cards ranked are just from the base game, EIK decks. I don't have data on the G deck, which is where Architect is from.

Perhaps you're thinking of Master Builder, which is from the base game and has a similar effect to Mason? They are both valuable cards, but Mason (+8%) is nearly twice as good as Master Builder (+4.4%).


I was thinking more about 2, 3 or 5 player games and single letter decks. As well as how different draft types might influence things. (Deal 10 drop 3 for instance to see what people never seem to want but that actually helps when played.)

Master Builder is the card I was thinking of, the Agricola Solitaire game translates at least that card different. Not surprising Mason is better, you're typically playing better already if you get to four stone rooms than if you've got to five clay or wood rooms.
 
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Mike T
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This is very interesting, but I'd beware of drawing strong conclusions from it. If you think Organic Farmer's ranking in the top 25 occupations is reflective of its quality, prepare to be disappointed.
 
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Alex Chen
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Yeah, it's important to remember that this is a list of occs that winning people play (in DRAFT), not a list of occs that will make you win if you play them. It's an important distinction. Probably the reason cards like Chief's Daughter and Organic Farmer pop up is because they are low picks that good players tend to take advantage of, but that bad players don't.
 
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Mike T
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Some possible distortions that may move cards up or down this list:

Draft/No-Draft: These rankings don't take into account the fact that most of the games that created the underlying stats were Draft-8. This inflates the play rates of terrible cards. For example, the stats say that Academic was played in 24% of the games in which it was drafted... but it was only drafted in 180 games, compared with 300 or more for popular cards.

Skill cards: As Alex says, there's a divide between the cards that everyone plays and the cards that only get played by those who really know what they are doing. The poor Field Watchman probably suffers from the fact that he is almost always played, no matter how incompetent his holder is. On the other hand, Plow Driver is usually only played when by players who know what they are doing and have successfully set up a Plow Driver game, which should lead to a high win rate.

Piling on: Cards like Paved Road, Chief, or Chief's Daughter are only worth playing in games where the player is doing pretty well already. The fact that they usually win once they get played shouldn't surprise anyone.


Finally, I'm really not sure about the basic methodology used to combine these two flawed stats. For example, this list would tell us that Greengrocer (-7.5) is a truly awful card, way worse than Animal Trainer (0 to -2.5). If you look at the underlying numbers, though, Greengrocer wins at a higher rate than Animal Trainer: the difference is that it is played at a much higher rate. Greengrocer gets such a terrible ranking simply because it has been played many, many times in losing efforts. Perhaps this tells us something about how many people have overrated it, but I don't see how it has anything to do with its relative value compared to other crappy cards that people have kept in their hands more often.
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Frederic Bush
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smcmike wrote:
Some possible distortions that may move cards up or down this list:

Draft/No-Draft: These rankings don't take into account the fact that most of the games that created the underlying stats were Draft-8. This inflates the play rates of terrible cards. For example, the stats say that Academic was played in 24% of the games in which it was drafted... but it was only drafted in 180 games, compared with 300 or more for popular cards.

Skill cards: As Alex says, there's a divide between the cards that everyone plays and the cards that only get played by those who really know what they are doing. The poor Field Watchman probably suffers from the fact that he is almost always played, no matter how incompetent his holder is. On the other hand, Plow Driver is usually only played when by players who know what they are doing and have successfully set up a Plow Driver game, which should lead to a high win rate.

Piling on: Cards like Paved Road, Chief, or Chief's Daughter are only worth playing in games where the player is doing pretty well already. The fact that they usually win once they get played shouldn't surprise anyone.


Finally, I'm really not sure about the basic methodology used to combine these two flawed stats. For example, this list would tell us that Greengrocer (-7.5) is a truly awful card, way worse than Animal Trainer (0 to -2.5). If you look at the underlying numbers, though, Greengrocer wins at a higher rate than Animal Trainer: the difference is that it is played at a much higher rate. Greengrocer gets such a terrible ranking simply because it has been played many, many times in losing efforts. Perhaps this tells us something about how many people have overrated it, but I don't see how it has anything to do with its relative value compared to other crappy cards that people have kept in their hands more often.


Maybe I should've set my cutoff for not ranking occs higher; animal trainer is right on the threshold I arbitrarily set of 30 plays. Academic doesn't have a lot of plays either. As I said, I'm not super confident about relative values of rarely-played occupations whose value ends up around 0.

That said, I'm confident that both animal trainer and greengrocer are very bad cards, but a bad card that lures you into playing it and wasting tempo is IMO much worse than a bad card that sits in your hand all game and doesn't waste an action.

Similarly, we need to know how often a card gets played to know the value of good cards, because otherwise we might rank Chief (45.3% winrate, played 39% of the time) above Grocer (43.9% winrate, played 83% of the time). Obviously the Grocer is good in a lot more spots than the Chief is, so it's a better card to have in your hand even though the winrate once having played it is lower.

Finally, I disagree with your interpretation of Chief and Chief's Daughter. A card that gives you 3+ VP in some spots, and 0 VP in others, *and can be played once you know whether or not you'll get the bonus*, is always going to be a positive card, because you can just play it in endgame when you have the pre-reqs, and ignore it when you don't. It doesn't cost you anything if you don't fulfill the pre-reqs, and it's better than other plays when you do.
 
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Frederic Bush
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vivafringe wrote:
Yeah, it's important to remember that this is a list of occs that winning people play (in DRAFT), not a list of occs that will make you win if you play them. It's an important distinction. Probably the reason cards like Chief's Daughter and Organic Farmer pop up is because they are low picks that good players tend to take advantage of, but that bad players don't.


Chief's Daughter and Organic Farmer are cards that you can play on the final couple turns for 1-2 points of marginal gain, or leave unplayed if the circumstances are poor. Even if they turn out to be an unplayable misery burden, all that costs you is the opportunity cost of their drafting. That's quite good!

 
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Frederic Bush
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In order to buy the paved road, you've either got a quarry or inflicted some severe stone denial on your opponents. The latter might be more valuable than you think.
 
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magic gecko
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I think the first post is awesome.

It actually lists lots of definate things in a definate order.
It can be attacked forever, it is still way interesting.
 
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Mike T
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magic gecko wrote:
I think the first post is awesome.

It actually lists lots of definate things in a definate order.
It can be attacked forever, it is still way interesting.


My criticisms should not be taken as attacks. I do think that using these stats is interesting and valuable. In fact, I'm the one that asked Chris to compile them in the first place on play-agricola.com.

I also think Frederic has proposed an interesting way to combine them. By doing so, I think he points the way towards making the basic stats far more useful. I'm just trying to point out some of the limits of this analysis, and hopefully begin to brainstorm ways to improve it.
 
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Mike T
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fbush555 wrote:

That said, I'm confident that both animal trainer and greengrocer are very bad cards, but a bad card that lures you into playing it and wasting tempo is IMO much worse than a bad card that sits in your hand all game and doesn't waste an action.


But if you are looking for the objective value of a card, this should not be a factor.

You don't really define "objective value," but in my mind, objective value should not be determined by players' mistaken valuations. I think your equation is very problematic when the win rate dips into the negative.
 
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Frederic Bush
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smcmike wrote:
fbush555 wrote:

That said, I'm confident that both animal trainer and greengrocer are very bad cards, but a bad card that lures you into playing it and wasting tempo is IMO much worse than a bad card that sits in your hand all game and doesn't waste an action.


But if you are looking for the objective value of a card, this should not be a factor.

You don't really define "objective value," but in my mind, objective value should not be determined by players' mistaken valuations. I think your equation is very problematic when the win rate dips into the negative.


Welllll... it depends what you mean by "objective". I meant using clearly defined, measurable terms to come up with a ranking; anyone can go through the data and replicate my rankings. Your suggested meaning would be more like an attempt to quantify the value of the card in the hands of a player who uses perfect strategy. I'd call your approach "intrinsic" value I think. Hard to calculate!

The way I thought about it is, "over the course of these 3000 games covered by the data, which were the best cards to take? Which were the worst?" By those standards taking the greengrocer was a much bigger mistake than taking the animal trainer since players were so much more likely to slap down the greengrocer and thus hamper themselves.

If you are a perfect player you may well prefer the greengrocer, since just looking at the two cards it seems far more likely that you'll be able to squeeze some use out of it than out of the animal trainer, but historically it's been a colossal blunder.



 
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Mike T
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Fair enough. I guess my point is that what most people are really interested in is that intrinsic value.

How does your statistic compare with "Probability of Winning Given Drafting a Card": http://play-agricola.com/forums/index.php?topic=1585.0.

It seems like it's an attempt to measure essentially the same thing. The main difference between the two that I can think of is that Win rate if Drafted measures the actual outcomes of the games where the card stays in your hand, as opposed to applying the flat 27.2. This may or may not be useful: it adds in some random noise, and it also could add in some player skill bias, since some cards are more likely to be in the hands of strong players, whether they play them or not.
 
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Frederic Bush
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smcmike wrote:
Fair enough. I guess my point is that what most people are really interested in is that intrinsic value.

How does your statistic compare with "Probability of Winning Given Drafting a Card": http://play-agricola.com/forums/index.php?topic=1585.0.

It seems like it's an attempt to measure essentially the same thing. The main difference between the two that I can think of is that Win rate if Drafted measures the actual outcomes of the games where the card stays in your hand, as opposed to applying the flat 27.2. This may or may not be useful: it adds in some random noise, and it also could add in some player skill bias, since some cards are more likely to be in the hands of strong players, whether they play them or not.


Yeah, I thought about using that stat. The tables are similar. But I think the value of the card is best measured when it's actually played, and set to 0 when not played. I really wouldn't want to try to figure out why someone didn't play grocer or house goat, for instance. Not everyone drafts, so that would also bring it closer to a valuation for a non-draft game.

There are some cards where that's not a wise choice -- the games where you play the cook, for instance, you have more peeps earlier than in the games when you don't, so you do a lot worse when you have the cook and don't play it than you'd expect. I might look and see which cards have the biggest delta between my calculated value and the observed draft value and use observed value instead of calculated value.
 
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Matt Shields
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Thanks for throwing this together. The kind of stats are always very interesting to look at.

I think this is a really good attempt at valuations, but as others have said, there are a lot of complications that are worth thinking about.

I think the most basic is you may have a bit of a correlation/causation problem. There are some cards that tend to get played a lot when a player is already doing well, but which arguably didn't contribute a whole lot to the fact that the player has played well. A lot of the bonus points cards fall into this category - I'm only going to play them if I'm reasonably sure I'm going to get the bonus, which correlates strongly (though obviously not perfectly) with me already doing well. To take an admittedly extreme example, if I drop the Church Warden with my last action, and it means I won by 10 instead of 7, did it really help me win, or is it merely correlated with me winning?


The other tricky bit is that while obviously whether or not I play a card is very important - and must be calculated - the fact that I declined to play a card doesn't mean that it didn't help me win. A lot of cards give you flexibility and insurance simply by having them in your hand. If I have the Mendicant in my hand, for example, I can gamble on taking a big pile of resources instead of taking the food in need to feed, because I have a backup plan. If it turns out I'm able to take food the next action anyway, and never play my Mendicant, he was still very very useful, even though I never played him. There are actually quite a few cards that have a similar but more subtle effect.


I'm not sure how to correct for that though.
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Matt Shields
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TwitchBot wrote:

Thanks for throwing this together. The kind of stats are always very interesting to look at.

I think this is a really good attempt at valuations, but as others have said, there are a lot of complications that are worth thinking about.

I think the most basic is you may have a bit of a correlation/causation problem. There are some cards that tend to get played a lot when a player is already doing well, but which arguably didn't contribute a whole lot to the fact that the player has played well. A lot of the bonus points cards fall into this category - I'm only going to play them if I'm reasonably sure I'm going to get the bonus, which correlates strongly (though obviously not perfectly) with me already doing well. To take an admittedly extreme example, if I drop the Church Warden with my last action, and it means I won by 10 instead of 7, did it really help me win, or is it merely correlated with me winning?


The other tricky bit is that while obviously whether or not I play a card is very important - and must be calculated - the fact that I declined to play a card doesn't mean that it didn't help me win. A lot of cards give you flexibility and insurance simply by having them in your hand. If I have the Mendicant in my hand, for example, I can gamble on taking a big pile of resources instead of taking the food in need to feed, because I have a backup plan. If it turns out I'm able to take food the next action anyway, and never play my Mendicant, he was still very very useful, even though I never played him. There are actually quite a few cards that have a similar but more subtle effect.


I'm not sure how to correct for that though.


The other consequence of only counting played cards is that it sounds from your description like there are a lot of bad cards in the "middle" of your distribution (say the -2.5 range) that don't get played enough to fall to the bottom. That may be a flaw in the methodology. A card has to have a certain baseline of utility in order to get played enough to get a bad score, whereas a card that's just totally useless will hover around zero, because nobody will ever play it.

It's kind of like being the pitcher in a baseball league who leads the league in losses. If he was the worst pitcher in the league, he never would have played enough to rack up the most losses. He actually has to be a competent pitcher to get enough playing time to lose that much.

I suspect the cards at the very bottom of your distribution are the same. They are cards that ok, but seem better than they really are. Thus they get drafted and played by inexperienced players more often than they should. Because those players are bad, they lose the game more often. But it's less that the Greengrocer is a terrible card, and more because there was a better card that the player didn't recognize to play or draft instead.
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Frederic Bush
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TwitchBot wrote:

Thanks for throwing this together. The kind of stats are always very interesting to look at.

I think this is a really good attempt at valuations, but as others have said, there are a lot of complications that are worth thinking about.

I think the most basic is you may have a bit of a correlation/causation problem. There are some cards that tend to get played a lot when a player is already doing well, but which arguably didn't contribute a whole lot to the fact that the player has played well. A lot of the bonus points cards fall into this category - I'm only going to play them if I'm reasonably sure I'm going to get the bonus, which correlates strongly (though obviously not perfectly) with me already doing well. To take an admittedly extreme example, if I drop the Church Warden with my last action, and it means I won by 10 instead of 7, did it really help me win, or is it merely correlated with me winning?



I think that most of the value of the 4/3/2/1 cards is in the free wood, not in the bonus points. The Constable might be an exception. The other bonus cards, scoring points for them doesn't necessarily mean you're doing well (consider Organic Farmer or Wooden Strongbox)
 
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Mike T
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fbush555 wrote:

I think that most of the value of the 4/3/2/1 cards is in the free wood, not in the bonus points. The Constable might be an exception. The other bonus cards, scoring points for them doesn't necessarily mean you're doing well (consider Organic Farmer or Wooden Strongbox)


I'd argue that both Organic Farmer and Wooden Strongbox are usually played in relatively successful games. If you can score 3+ points from Organic Farmer, you've got at least 3 pastures that can hold 4 animals each, and at least 3 animals. That's not enough to win a game, but it at least represents competent play. Wooden Strongbox isn't quite as good of an example, since it might get played early in the hopes of a successful big-house, but the ability to build a 5 or 6 room house is still likely to positively correlate to scoring well.
 
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James Huang
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A quick glance at the rankings seem to suggest that Baking in general is an inferior feeding strategy. I would have to disagree with this, although I think that in general it's more difficult to pull off than some sort of fast food/ranching or alternative food source strategy.
 
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Frederic Bush
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erajah wrote:
A quick glance at the rankings seem to suggest that Baking in general is an inferior feeding strategy. I would have to disagree with this, although I think that in general it's more difficult to pull off than some sort of fast food/ranching or alternative food source strategy.


I don't think baking is an inefficient feeding strategy -- you'll feed just fine. I think it's an inefficient scoring strategy.
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smcmike wrote:
This is very interesting, but I'd beware of drawing strong conclusions from it. If you think Organic Farmer's ranking in the top 25 occupations is reflective of its quality, prepare to be disappointed.


Totally. This listing shows cards that are better than most people think. It doesn't show which cards are the best in order.

I'm still waiting for an objective ranking of cards. I can easily make a winning hand out of the negative value cards in the above list.

Church warden is a nice card, but if someone picks it first every time, I want to be behind them.
 
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Frederic Bush
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MisterBond wrote:
smcmike wrote:
This is very interesting, but I'd beware of drawing strong conclusions from it. If you think Organic Farmer's ranking in the top 25 occupations is reflective of its quality, prepare to be disappointed.


Totally. This listing shows cards that are better than most people think. It doesn't show which cards are the best in order.

I'm still waiting for an objective ranking of cards. I can easily make a winning hand out of the negative value cards in the above list.

Church warden is a nice card, but if someone picks it first every time, I want to be behind them.


My guess about Church Warden: the 4w gives you a better than average chance of getting the bonus, and there are very few cards opponents can have that will give them the edge in getting to 5 peeps by the start of the final round. With most of the other 4/3/2/1 cards, opponents with the proper cards can easily beat you to the bonus.

Church warden gets played 80% of the time and wins 45% of its games. Compare to consensus top draft pick Head of Family -- 86% play rate, 35.5% win rate.

 
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