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Subject: The Real Value of Adventurer rss

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medward s20x6
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http://www.boardgamegeek.com/thread/478064/adventurer-strate...

I was reading this thread the other day, and it seemed to me that all the discussion is focused around thinking of the adventurer as a replacement for gold that costs an action, and so should produce more coins each time you draw it than gold does. I think this perspective misses a very important aspect of the adventurer card, and no I'm not talking about deck cycling.

First I must say I have relatively little experience actually playing with the adventurer, and all my theory-craft may fall flat in practice, but I think a careful analysis of what the adventurer card does to the expected value of drawing one of your treasure cards produces quite surprising results.

I'll take an example case to start with to illustrate the idea. This case may be unlikely, but it's intentionally simplified for demonstration purposes and I'll generalize later. Let's say we have a deck with 2 coppers, 2 silvers, and 1 gold. If you draw a _treasure_ card from this deck, the expected value of that treasure is (2*1 + 2*2 + 3) / 5 = 9 / 5 = 1.8. That's not the expected value of a card, but given you're drawn a treasure, the expected value of the treasure. Now let's assume on your next turn you have 6 coins to spend and have a choice between buying a gold or an adventurer. If you buy a gold, the new expected value is (2*1 + 2*2 + 2*3) / 6 = 12 / 6 = 2. So as expected, the expected value of a treasure card is improved by adding a gold to your deck.

If you buy an adventurer, it's slightly more complicated. First, I'm going to speak of the adventurer as a "treasure" card in quotes, since it's purpose is really just to get you coins. We'll ignore it's other effects for now. If you add a gold to your deck, then you'll spend 6 draws picking up treasure into your hand during a given shuffle. However, if you add an adventurer, instead you'll draw your adventurer and play it to draw 2 other treasure, then there are only 3 treasure cards left in the deck to draw, so you spend 4 of your draws pulling treasure into your hand total. You'll also discard a number of random cards. This assumes the adventurer occurs before at least 2 of the other treasure cards on a given shuffle, which we'll stick with for now.

So, now we need to think of the denominator in our expected value calculation, rather than being the number of treasure cards we have, as the number of "treasure" _draws_ per shuffle. Adventurer actually reduces this number by one, without modifying the total treasure in the deck, so we get (2*1 + 2*2 + 3) / (5 - 1) = 9 / 4 = 2.25. So now that we know the impact of the adventurer on the expected value of a "treasure" draw, we can calculate it's effective treasure value with respect to it's effect on the expected vaue. We had 5 cards before, now we have 6. 2.25 * 6 = 13.5. Our treasure was worth 9 before, so the adventurer increases our expected value equivalent to a treasure card worth 4.5 coins.

Now, here's the key point. This expected value calculation is not affected by what the adventurer actually draws. Even if it pulls two copper, it still increases the expected value for this shuffle. This is because, loosely speaking, it "thins" the copper for you for this shuffle only and gives you a "silver". It's sort of like a one shuffle trading post.

Okay, so the adventurer is sort of worth 4.5 coins in this situation. Well, how special is this particular setup? Let's do some algebra. We'll let T = the total treasure value in your deck. in this case it was 9. D = the number of draws it takes to draw all your "treasure". If you have just real treasure, it's equal to the number of treasure cards, but the adventurer reduces it by 1, instead of increasing it. X = the expected value of a "treasure" draw.

So we start with X = T / D, if we buy gold we get:
X = (T + 3) / (D + 1)

Adventurer gives:
X = (T) / (D - 1)

If we solve for when the adventurer will increase the expected value by 50% more than the gold would, we get:
1.5 * (((T + 3) / (D + 1)) - (T / D)) = (T / (D - 1)) - (T / D)

Simplifying gives:
18*D^2 - 18*D = 10*T*D - 2*T

(Edit: This isn't actually correct. The delta on the expected value is not linear in the coin value of the card. Should be:
(T + 4.5) / (D + 1) = T / (D - 1)

Simplifies to:
4.5*(D - 1) = 2*T

End Edit)

I'm not sure what to do with this for analysis, but if you plug in some values for D you can get a feel for it:
D = 10, X = 1.65 (Edit: 2.03)
D = 12, X = 1.67 (Edit: 2.06)
D = 20, X = 1.72 (Edit: 2.13)

Basically, the value of X is the expected value that your existing treasure must exceed for the adventurer to be worth at least 4.5 coins toward your expected "treasure" draw value. Even for large D it doesn't get much over 1.65 (Edit: 2.0), which is pretty easy to achieve. Of course, there are X thousand other considerations, terminal action collision, dead draws, etc etc. The adventurer discards cards from your deck, which generally maintains roughly the relative fraction of treasure draws per shuffle, and sort of shrinks your effective deck size(cycling). The point is, this simple analysis hints that there might be some power there, even if it is a bit situational.

(Edit: In light of my original mathematical errors my conclusion that Adventurer should be worth 4.5 coins most of the time is overly optimistic. You don't hit this point until X = 2.0 or so, which comes back to thinning(some) copper like everyone else has said in the past. Still, you don't need to thin all of it, nor do you need mostly gold(as opposed to silver) for Adventurer to be significantly better than gold, and you should still be happy with the Adventurer if it pulls up two copper, because it's still increasing your X. It's also worth at least 3 coins toward expected value very early in the game, at 5 copper and 3 silver, as I mention below, and it amplifies the impact of your future treasure purchases, similar to a duke amplifying a duchy)
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Franklin Millar
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This is interesting but I kind of think you're talking about deck cycling.
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medward s20x6
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There certainly is a similarity to deck cycling. But deck cycling is about getting to your next shuffle quickly, _specifically_ so that you can get your new buys shuffled into the deck to pull your average up.

This has more to do with some kind of pseudo-thinning effect. Obviously if your adventurer hits for 5, everybody's happy. Sure, it's going to pull up your average coins per turn if you draw that many coins.

But when the adventurer hits for 2, everyone says boo-hoo, i wish I bought a gold instead. My point is, even when it hits for 2, it still, surprisingly, pulls up your average. Explaining _why_ this happens is the hard part, and I'm not 100% sure I know why, but it has something to do with this weird thinning like thing.

Specifically, your average still goes up, BEFORE your next shuffle. The remainder of your deck has to play catch up to the expected value after you hit low, so you expect to hit high afterward, even before the shuffle, even before the cycling kicks in.
 
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Andrew Hardin
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I think the Adventurer is a little underused and I have seen it played very effectively.

But, I always hesitate to recommend expected value calculations since they ignore the problem of skewness. You never draw 3.25 Coin, you always draw whole numbers. But having a higher expected value is still 'good' since it will usually result in better draws (ignoring the impact of variability).

But, the Adventurer has to overcome 3 problems:

1. Your deck starts with 7 Copper. Your example was fine but you removed some of the Copper. It takes 7 Silver buys to get a deck containing 7 Copper to average 1.5 expected value.

2. The Adventurer puts the cart before the horse. You really want the Adventurer early so you can cycle your deck while regularly drawing your Gold. Unfortunately, until you get Gold the Adventurer isn't strong enough but if you get Gold you can't get the Adventurer. By the time you get the Adventurer there is not enough time to use the card the way it wants to be used.

3. It requires a terminal Action and provides no +Buy. The first problem means you have to have the ability to use the Adventurer. Fortunately it doesn't draw dead. The second problem means that if you draw big you have no way to use the extra Coin. So the card has to be paired.

The Adventurer is a fine card in the right circumstances. The trouble is the right circumstances don't happen enough. Since the Adventurer really needs to be bought as your 2nd (or 3rd) Gold purchase you have to wait until the middle game to even buy the card. Then you have to get it back in your deck to use it. Then you have to be able to use it, all for the privilege of typically buying the exact same thing you would have bought with the Gold draw.

If the card was cheaper (even 5) it would probably be too strong since the early cycling and not losing your Gold buy would vastly strengthen this card.

I still think players don't buy this card enough, but it just doesn't make enough of a difference in practice to be as useful as intended.

- Lex
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Ted Vessenes
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This still doesn't account for the opportunity cost of buying something else, however. You're just saying that if you have enough cash in your deck, Adventurer is better than Gold. Fine. But by that time, Laboratory is almost certainly better than Adventurer. Even Market is probably better.

Adventurer is worse than most 5 cost alternatives at nearly every stage of the game. Its worse than Merchant Ship, and when was the last time you bought that card? I would play the Adventurer if he cost 4 for sure, and there are a few boards where I'd buy him when he cost 5. At six I almost never buy him.
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Andrew Hardin
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tedv wrote:
This still doesn't account for the opportunity cost of buying something else, however. You're just saying that if you have enough cash in your deck, Adventurer is better than Gold. Fine. But by that time, Laboratory is almost certainly better than Adventurer.


This is the danger of using probability calculations.

Then again, the Laboratory is just that good.

- Lex
 
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medward s20x6
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As I said, I have little practical experience playing with him, and this may all be in vain. I must admit this whole thing is partly just me cheering for the underdog.

After reading so many articles about the plight of the chancellor(by LexH), and feeling like I've come to see it's real value, I picked another dark horse to cheer for. And just calling Adventurer a crappy gold, which seems like most people do, misses a lot of the subtleties involved.

My example was chosen specifically because it involved only 5 cards, easy to calculate. You could replace it with, for example, a Big Money deck at turn 7, with 7 copper, 4 silver, and 2 gold. This gives:
X = 1.61
add a gold
X = 1.71
add adventurer instead
X = 1.75
(Edit: using the new math from above, this actually means the adventurer is worth 3.57 coins toward expected value, not 4.5)

Yes, it takes some work to get it into the deck and working... but if it's actually worth 4.5 coins? That's big. Yes, need extra buys. Yes, extra actions are fantastic.

And Merchant Ship is an awesome card, btw.
 
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Andrew Hardin
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medwards20x6 wrote:

Specifically, your average still goes up, BEFORE your next shuffle. The remainder of your deck has to play catch up to the expected value after you hit low, so you expect to hit high afterward, even before the shuffle, even before the cycling kicks in.


This a very real effect and does help the case for the Adventurer slightly. Though drawing 5 and overdrawing produces the opposite effect and the Adventurer lacks a Buy.

When dealing with finite populations (such as your draw deck) there is a negative correlation between any two samples from the same population. So drawing high does tend to cause you to draw low. This is why using the Chancellor power right the same turn you draw a Province is not a bad play.

The Adventurer needs a +1 Buy to justify the cost of 6, just like the Council Room at 5.

- Lex
 
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medward s20x6
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Actually, come to think of it, the Chancellor and Adventurer should be good friends. When the Adventurer hits for 5 or 6 and you say "rah rah Adventurer" you should really say "Damn, i need that chancellor now."

When the Adventurer hits low, those are exactly the times you wouldn't want to flip your deck, and allow regression to the mean to occur.(i think that's the right term.)
 
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Andrew Hardin
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medwards20x6 wrote:

After reading so many articles about the plight of the chancellor(by LexH), and feeling like I've come to see it's real value, I picked another dark horse to cheer for.


Much like you I want to cheer for this card, and there are some situations in which the card is great.

For example, I will buy it to prevent stalling in a Chapel deck after I have 2 Gold. I will buy it instead of a 3rd Gold.

Sadly, I have backed a few wrong paths myself with the Chancellor. For example, Chapel/Silver looks much better in simulations than Chapel/Chancellor and I open Smithy/Silver over Chancellor/Silver now. I still love Chancellor/Silver as a solid opening in games dominated by Treasure and 5 cost cards (which account for many situations in Dominion).

But it is still good to know when the card is useful. The issue is that it is useful very late in the game in situations where you are already Treasure heavy. In that case, use the Adventurer and skip another Gold buy.

- Lex
 
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Andrew Hardin
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medwards20x6 wrote:

When the Adventurer hits low, those are exactly the times you wouldn't want to flip your deck, and allow regression to the mean to occur.(i think that's the right term.)


Not quite, but close enough for government work.

- Lex

(Edit: I should have clarified. What you are talking about is actually the opposite of regression to the mean. Regression to the mean is related to the probability of a result far from the mean having a greater probability of being closer to average the next result. This is one reason mutual funds have to provide the completely false statement that 'past performance is not indicative of future performance'. In this case the opposite happens. Draw low produces draw high. The most common version of this is the 5/2 split, which averages 3.5 but which has two extremes relative to 4/3).
 
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medward s20x6
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LexH wrote:

But it is still good to know when the card is useful. The issue is that it is useful very late in the game in situations where you are already Treasure heavy. In that case, use the Adventurer and skip another Gold buy.


Maybe. Remember, the 1.65 threshold is to make the adventurer worth 4.5 coins. If you start MoneyLender+Silver, by the time you thin 2 copper and buy 3 silver, an Adventurer is already better than a gold in terms of it's effect on your expected value. The 4.5 coins was to justify the action cost for most people, but you could buy it early and let it scale(and help you scale, just like labs).

(1*5 + 3*2) / 8 = 11 / 8 = 1.375
(1*5 + 3*2 + 1*3) / 9 = 14 / 9 = 1.555 GOLD
11 / 7 = 1.571 ADVENTURER

So you can get adventurer before gold, then it just scales up with you as your deck grows.
 
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Andrew Hardin
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I can see pairing the Adventurer with the Moneylender or the Chapel. It is a strong card when mixed with Copper trashing cards.

- Lex
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Brandon Richards
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That article about Adventurer strategy wasn't really to support the Adventurer, but rather to show statistically how the Adventurer performs. And the table I set up does have a few shortcomings. For instance, the table shows only the total number of treasure cards in the deck, but fails to account for treasure cards that are in hand. If I have seven Coppers and one Silver, and the Silver is in my hand, that is a gaurantee that I will only draw Coppers. Hence, my statisical analysis is thrown out the window.

As for the OPs claim that it is good to even hit two Coppers, to me that just sounds like deck cycling because you can hit other treasure cards just as easily.

I do agree with Lex, and I think I stated it in my original article that a +1 buy would probably help Adventurer a lot.

Quote:
I can see pairing the Adventurer with the Moneylender or the Chapel. It is a strong card when mixed with Copper trashing cards.


Mine is another good card to pair with this if you plan on upgrading Coppers only.

As for Chancellor: I have had a lot of success with this card and I am kind of happy that more people don't realize how good it actually is.
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tedv wrote:
Its worse than Merchant Ship, and when was the last time you bought that card?


Are you implying that Merchant Ship is a bad card? I nearly always buy MS with my first 5 buy when it is available. And with throne room, it's downright awesome. It's a nice addition to a "modified Big Money" strategy, as is adventurer.

There tends to be a point in the game, especially when deck thinning is not available due to the tableau, where you hit 6-7 coin repeatedly and keep buying gold over and over again. Decks are especially vulnerable to this when there are no good 3-4 cost cards available so too much silver ends up being purchased. Rather than buy a 3rd gold in that case, buy the adventurer to push over the top and get some deck cycling. It's also less vulnerable to a duchy clog in the endgame.

If someone is waiting to Saboteur, Pirate Ship, or Thief your gold the adventurer is a nice alternative (in the case of the sab, it is not actually touching your total coin and you can morph it to a silver if you need).
 
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Andrew Hardin
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filovirus wrote:

As for Chancellor: I have had a lot of success with this card and I am kind of happy that more people don't realize how good it actually is.


Another true believer!

I am actually thinking of pairing it with the Fishing Village then first game I get both together in the same set. I think some of the new cards in Seaside make the card easier to use safely.

- Lex
 
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Ted Vessenes
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theright555J wrote:
tedv wrote:
Its worse than Merchant Ship, and when was the last time you bought that card?


Are you implying that Merchant Ship is a bad card? I nearly always buy MS with my first 5 buy when it is available. And with throne room, it's downright awesome. It's a nice addition to a "modified Big Money" strategy, as is adventurer.


No, I think Merchant Ship is a slightly underpowered card. It is properly costed at 5 instead of 4 though. The real problem is that it's a terminal action that just provides cash, and for a 5 cost card, I'd rather have one of:

* Non-terminal action that's good in multiples (eg. Minion, Lab, Market, Upgrade)
* Terminal action that cycles the deck or improves deck quality (eg. Library, Wharf, Council Room, Trading Post, Mine)

This might be due to my personal bias towards deck thinning, however. The more you thin your deck, the stronger each card is, which makes card drawing better relative to the option of cash generation. If you don't do any thinning at all, Merchant Ship is about as good as Council Room. Remove 3 estates from your deck and Council Room is an awful lot better.
 
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John Anderson
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tedv wrote:
The real problem is that it's a terminal action that just provides cash
But it provides it on two turns! And on the second turn, it's not a terminal action - it's just free cash on that turn. Very useful in certain setups.
 
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puck71 wrote:
tedv wrote:
The real problem is that it's a terminal action that just provides cash
But it provides it on two turns! And on the second turn, it's not a terminal action - it's just free cash on that turn. Very useful in certain setups.


The Merchant Ship fits right into high treasury, low Action strategies. That makes it perfect for a number situations. Like the Bazaar the Merchant Ship is a card that if it had been part of the Base 25 would be appreciated more. But Seaside has cards that make Action heavy strategies playable and includes a few really game changing cards that catch the eye. Cards like the Merchant Ship end up getting ignored in all the glory. The same thing happened to several cards in the Base 25.

Starting a turn with +2 Coin and 5 Cards is a recipe for a Province buy. Any situation that would normally buy a Gold now buys a Province. Any situation that might otherwise buy a Silver is buying a 5-cost card. And the +2 coin is immune to the Torturer, Militia, Cutpurse, etc, etc.

Deck thinning is wonderful. But it isn't always available, it isn't always fast enough, and it isn't always as good as it looks.

The Merchant Ship is effectively 2 Silver spread over 2 turns. That bad part is that it is 2 turns and the duration means it goes back into your deck a bit slowly (though that isn't always bad for a terminal action). But there aren't that many cards in the game that give that kind of Coin power.

So many strategies in Dominion look pretty and powerful until you get down to the fact that all they are really trying to do is increase your Coin per turn. The Merchant Ship does this efficiently since one of the two turns gets +2 Coin without burning an Action or drawing a Card. And you don't have to buy another Treasure or Action Card to get the effect.

- Lex
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Matt N

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Adventurer is good with mine/moneylender/trading post type situations, or general trashing.

Merchant ship is a powerful counter to pirate ship, particularly when throne room is out. I had a nice win once when I throne roomed merchant ship most turns and just kept buying provinces; the deck thinning effect of pirate ship was essential to pull this off. It's also a terminal action that you can mix in with others, since it isn't +cards, so you can transition to merchant ship once your attacks start getting weaker.

Merchant ship would probably be my favorite non-attack action to end a laboratory chain with, unless your deck is bloated enough that you could double province or something like that and need an extra buy. Even then, one market can do wonders.
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Charles Connaughton
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Gold looks to be the best card to compare Adventurer to, since they both cost 6. But I've found the best card to compare it to is Smithy, since the two do very similar things. Smithy, of course, gives 3 cards; Adventurer can be viewed as giving you a variable number of cards until you get 2 treasure, with the action and VP draws being dead draws.

In this sense, Smithy will return coins equal to 3 times the average value of your deck, while Adventurer will return coins equal to 2 times the average *coin* value of your deck.

You should find that outside of action heavy decks, these two values are very similar throughout most of the game. In an action heavy deck, the Smithy would be clearly superior (since it gives you actions to use with +actions); in an action light, but VP heavy deck (Gardens) Adventurer would outperform Smithy, card for card. The two effects are very similar in power level.

Of course, Smithy costs 4, and Adventurer costs 6, which makes Adventurer grossly overcosted and only very marginally playable.


Merchant Ship is definitely priced appropriately for its effect, it would be quite a bit stronger than most of the other 4s. But it's a weak 5, no question. It puzzles me why, between Wharf and Merchant Ship, the Wharf got the +buy; the Wharf would have been a strong 5 without the +buy, and is an exceptional 5 with it; the Merchant Ship would have been a reasonably strong 5 with the +buy, but is weak without it. With the cards doing very similar things at the same cost in the same set, it's surprising that obvious imbalances like that are part of the game. I have to wonder if that's intentional.
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I wonder if maybe the game designer/testers played the card more than most other people have yet, and know more about it than we do...

As someone mentioned before on another thread, +cards seems to scale much better than +coins. There are plenty of cards that provide draw 3, and even draw 4 cards. There isn't a single action card that provides even +3 coins. Probably because cards is mediocre early, and balanced late in the game. Coins is fantastic early, and solid late in the game.

+cards may be better in a deck that has been thinned and loaded with gold late in the game. But starting the game with a Merchant ship on a 5/2 split? That's a recipe to start stacking your 5 card of choice, or gold.

I think merchant ship is far better than wharf early in the game, buy or no buy. Wharf probably overtakes it late in the mid-game.
 
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medwards20x6 wrote:
I wonder if maybe the game designer/testers played the card more than most other people have yet, and know more about it than we do...


Having developed software for some time the one thing I will say about software is that it isn't until it gets in the hands of your users that you discover many of the trickier problems.

I have every reason to think the same applies to game design. Playtesters are human and playtesting won't reveal many of the issues that will come out once people have really played the game.

As much as I think a couple of cards are badly priced I think the game as released holds up rather well. But that doesn't mean the Adventurer is priced correctly. If I was changing the Base 25 I would put the Chapel at 3 and the Adventurer at 5, remove the Woodcutter entirely and do something to fix the Thief. You might have other preferences.

- Lex
 
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I'm in software too, and you have a point. No amount of QA can accomplish what one day in the hands of users can.

LexH wrote:
But that doesn't mean the Adventurer is priced correctly. If I was changing the Base 25 I would put the Chapel at 3 and the Adventurer at 5, remove the Woodcutter entirely and do something to fix the Thief. You might have other preferences.


Based on several of the posts I've read by Donald V, I'm guessing at one point during play testing, the adventurer DID cost 5. I could be over stretching his statement, but based on what he said I'm guessing that every card in the entire game cost at least one less at some point during play testing than they do now. They only increased in price if they were found to be over-powered.

As for fixing the cards, I guess I probably haven't logged enough games to comment. What exactly do you mean by fixing the Thief, other than perhaps it's near irrelevance in 2 player vs it's power in 3-4 player?
 
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Andrew Hardin
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medwards20x6 wrote:

As for fixing the cards, I guess I probably haven't logged enough games to comment. What exactly do you mean by fixing the Thief, other than perhaps it's near irrelevance in 2 player vs it's power in 3-4 player?


I think it is interesting that the Pirate Ship is considered so powerful and the Thief is so problematic. I really don't like the Thief and feel that something about the power is just plain off.

It is stronger with 3-4 players. It really needs 4 players to become 'strong'. Even then it is merely 'okay'.

Given a choice I would change the power. Right now it is too close to the Pirate Ship but lacks the ability of the Pirate Ship to accumulate steady +Coin even if it robs a Copper. I don't have an immediate suggestion since I think the best change I can think of off the top of my head is exactly what the Pirate Ship does.

- Lex
 
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