text:
House rule to fix vindictive behavior in Princes of Florence
In Princes of Florence, the bugbear is this rule:

A player may move his figure backwards
  on the fame track at any time during
  the game.  For each space moved
  backward, the player takes 100 Florin
  from the bank. (p.10)

What I've seen (and experienced...) a few times is a player sacrificing their chances of victory by spending ludicrous numbers of prestige points to deny other players auctions in the late game.
Basically, I'm trying to find a house rule that will prevent this "taking you with me" behavior.

An alternative to a house rule is often a good defensive strategy. In this case: try to create a situation where multiple of the auction options would be acceptable; if all the other players bankrupt themselves to outbid you, you win! I believe this is really the essence of the game: to manoeuvre yourself into a position where there is nothing that you absolutely need in order to do OK.

I don't know that this would solve all of the problem cases I've encountered... but its good enough general advice to accept.  :)

And even if you need 1 thing, put on your best poker face and start a bid for something else

Something you might consider is a rule that "detects" this behavior--if they move back far enough, late in the game or whatever, you call it an automatic resignation.  I apologize for not having a precise definition--you might need to playtest it with a group and have someone play the vindictive, atmosphere-ruining jerk [oh, sorry, was that phrasing judgmental? :) ].  Basically, the idea would be that you could calculate that they are actively hurting their final standing, and take that as a trigger for automatic resignation.
Either that alone. or that with two votes by other players that someone is using that anti-strategy could be enough to declare a house-rules resignation (either kicking them out, or preventing any more money collection via that method for the remainder of the game).  Even without an exact numerical standard, you could have a two-vote rule.
Finally, something you could do is change your viewpoint and consider the original behavior you're objecting to here to be a valid meta strategy.  I have a son that plays like this--if he perceives that you have slighted him in a game, he will make the rest of the game be about hurting you back.  It's like the way poison dart frogs have evolved bright colors to let predators know that they are dangerous to eat.  People know this is a strong possibility and avoid singling him out in any obvious way.
This is a serious suggestion--if you can view it with amusement or appreciation as a meta strategy, it might be something you can laugh about rather than be irritated by.

This is just opinion, but the meta effect that such behavior would have on me is to make me not want to play games with that person anymore. (Not meaning to insult your son; depending on the age, I've found that most children play games this way).

Yeah, I totally understand and basically agree.  I wouldn't recommend this way of playing for exactly that reason.  But as far as how you, personally, deal with it when a person does this kind of thing, you might be able to make it a little less painful if you can either laugh it off or give it a sort of grudging respect.  Like either seeing the humor in getting sprayed by a skunk, or at least just noting that it's interesting how powerful a deterrent nature has evolved, even if it is, at the moment, making you suffer.  Doesn't mean you like it--the point is to have a "psychological hack".


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Carcassonne -- problem telling the difference between the Big Meeple and regular Meeples
In our gaming group, we have a very hard time picking out the Big Meeple from the other Meeples on the board.  While the Big Meeple certainly is bigger than the others, it's not by a significant factor, and most of our group (epsecially me) just can't tell it apart from other Meeples on the board.
It has gotten to the point where we have implemented a house rule that when you play the Big Meeple, you must state you are playing it, and if someone asks where your Big Meeple is, you need to point it out.  Still, it's easy to loose track of, in my opinion.
Has anyone else experienced this?  Have you implemented a similar house rule?  Have you altered your Big Meeple (painting on it, drawing a smiley face on it, etc.) to help identify it?  Or are we all just seriously visually impaired?

Interesting. Can't say I've ever had this problem.

Just wait until you play with Abbey & Mayor and you have to tell the difference between the big meeple and the meeple with flare pants.

Yep, same problem, same approach: We also announce our big meeple when playing it, but that hasn't been an issue ever.

I've mentally lost track of big meeples before, so I don't see a problem with visually altering it to make it stand out.  Perhaps you could borrow a hat from a set of Legos?  Honestly, I'm more surprised that your gaming group is cutthroat enough to need a rule to force people to announce when using big meeples.  Carcassonne is a game of perfect information (other than tile draws).  You should always be able to ask where something is.

I wouldn't say our group is cutthroat... it stemmed more from an "Aw crap, that was your Big Meeple?  I didn't realize that" when people went to contest cities, etc.  You're right, though, we should be able to ask where something is.

@LittleBobbyTables, I see what you meant now.  It's really a rule to promote honorable and friendly play then.  My wife and I usually talk a little trash when someone plays the big meeple, so we wouldn't need such a rule.

Unrelated but fun: In our latest game we had a 33 tile city with cathedral (99 points), when it was finished, only 3 tiles were left on the pile. But at least 2 big meeple were stuck in that city for almost the entire game.

You are not visually impaired. Telling at a glance whether one thing is bigger than another, when they are not immediately next to each other, can be fairly difficult. I have never played Carcassonne with the big meeple, but I've noticed this problem in other games, such as distinguishing medium and large Icehouse pieces in certain circumstances.
My solution would be to alter the big meeple in some way. Paint its head, glue a helmet or coronet onto it, or something of the sort. That will make it stand out a lot more than size alone, and be a lot more convenient than a house rule requiring it to be announced.

SpeilMaterial has a lot of options if painting the head in silver or something isn't enough
Cowboys (might have to paint yourself) & dwarfs for example.

That's pretty awesome, I didn't know about that site, thanks!

I never thought of this as a problem, but always as a deliberate feature - sometimes it's possible to slip a Big Meeple into a city without drawing attention to it.
"Okay, so I finish the city and I get the points, because I have two workers to your one."
"Actually... you might want to look at my guy again..."
I'm aware that some groups' sense of fairness will result in a lynching if anyone tries to pull off something as "underhand" as this, but still, I'm pretty sure the Big Meeple is close in size to his smaller brethren as by a deliberate design choice.

I would suggest that if you wanted to do something simple to make the big meeple stand out, that doesn't cost a thing, juts make a house rule to play it on it's head or some other similarly different position.

Or glue a penny to the meeple's head so it's clearly intended to do a headstand.

I have this problem too.  Placing the meeple on its back (rather than standing up) doesn't work for us because we use that for farmers (to resolve ambiguity with adjacent placements like roads).
If you don't mind permanent alterations, several suggestions have already been made.  If you want your changes to be more temporary, consider a bit of tape of a contrasting color on the front and back.  Duct tape comes in small rolls in all sorts of colors these days, and even though duct tape is sticky, it can be scrubbed off of a polished wooden surface like the meeples.
Alternatively, you could replace the big meeples with similarly-colored pieces from a different game, like the pawns from Pandemic.

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Do Race for the Galaxy expansions allow more players without changing the base game's rules?
I just acquired the game Race for the Galaxy, and I plan to play it at work.  It would be nice to play with up to 5 or 6 players, though, and the base game supports only 4.
I see that two expansions to the game ("The Gathering Storm" and "Rebel versus Imperium") each add one player.
Since none of us has played the game before, I'd prefer not to add extra complexity to the game right away.  However, it would be nice if we could make use of the extra players provided by these expansions.
If I were to purchase these expansions, would I be able to play the "base" game with more players (as is the case with Pandemic's "On the Brink" expansion), or do the extra players promised come at the price of more complexity?

Bear in mind that extra players adds extra complexity anyway, since they all get to choose actions, so there's a lot more to look at when trying to guess what actions might come up each round.

Yes. It's possible to just use the new player cards and take out the cards which use new mechanics.
I've also just left all the cards in and just simply ignored the Prestige rules, Goals and Takeovers; although that makes some cards weaker as they are costed with these additional mechanics in mind.

Leaving out goals doesn't usually imbalance things too much; the goals mostly just reward you for making particular decisions, say prioritizing consume powers, or aliens worlds. The game was also designed to be played without takeovers half the time, so removing them isn't a huge deal. Prestige has a much more direct VP impact, though. I'd argue that at a minimum, you should make cards that come with prestige worth 1VP more. This doesn't fix everything, but it helps. (e.g. Interstellar Casus Belli is still completely worthless)

@Jefromi Yes, I was specifically thinking about Prestige. Good idea to add 1VP per prestige card.

The expansions for Race for the Galaxy give identical phase selection cards.  They can be used alone with no other components of the expansion to add more players.
The only limiting factor becomes the size of the deck.  Without adding the expansion more people are drawing from the same amount of cards.  This will trigger more reshuffles.
This can be mitigated by not using cards form the top of the deck to track goods.
Also the first two expansions do not add many more rules.  After a couple of plays I strongly recommend adding them.  While the takeover rules are difficult, players often choose to not use them.
Overall base-game + two expansions and no takeovers, seems like the most fun the game has to offer.

The deck size can get really strained with 5 players and only the base game deck.  Towards the end of the game when players hands and tableaus are full of cards, you end up with a very, very small draw deck.

But you reshuffle the discard pile if the supply runs out; doesn't seem like a huge deal.

The cards get super stale.  If the players are any good, no good late game cards get shuffled into the discard, the game feels very different than usual.  You can either trust me (or the designer, Tom Lehmann), or just try it.

Ah, I missed that you said only the base deck - the question was asking about playing with expansions. In any case, when I've seen two or three players go through the base deck, or more players go through the deck with expansions, there's still usually plenty of good stuff left, because you simply can't hold onto most of the good stuff you draw.

If I parsed the original correctly (and I think I did), the question is about buying the expansions just for the additional action cards for the 5th (and possibly 6th) player.  OTOH, The first expansion cards, without adding goals, aren't much additional complexity, so introducing a new player to the base game + gathering storm without goals is barely any more difficult than just the base game (Improved logistics and the parrallelness of the settles is the only actual confusing thing it introduces, IIRC).

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text:
Advanced two player rules clarification for 7 Wonders
Perhaps I overlooked the following when reading the rules, but I don't recall these questions being addressed in the two-player advanced rules for 7 Wonders:
Can the free city build its wonder, or must it only build cards?
What does the free city do if it can't afford to build anything, since it isn't allowed to discard for coins?

here is an idea: set up 4 cities and you play two each and use the team rules, i.e. victories points for military victor and defeats are doubled. Doves only half the military points gained.

According to the rules, the free city can take any action a 'normal' player can take with a restriction on discarding cards for money. The free city CAN build a wonder. In fact, a good strategy for the third city is to use it to bury cards your opponent might want, e.g. by building the wonder.
The free city CAN also discard a card for money, but only if no other playable card is available. Therefore, if the city has no playable cards, you can choose a card to discard and the free city gains the coins.
(Rules are here: http://www.rprod.com/en/7W-rules.html)

I must have missed the clarification in the rules:
Clariﬁcation : The Free City cannot discard a card to get 3 coins unless it cannot play a card. The player must then choose, when possible, a card which can be played by the Free City (structure construction or wonder building
stage).

No problem. Glad I could help!

Another useful strategy is to have the free city buy resources from you so you can get money. Having the free city buy a resource from you to build a wonder and get a discard is a double advantage.


text:
How To Mitigate The Random Factor In Agricola?
Agricola is my favourite boardgame and I'd love to reach a level where I could call myself a master of it.  However, having found a place to play it online and gotten a lot more games in, I've been finding myself a little frustrated by the random elements of the game, which are few in number but can have an enormous impact.
In particular, I'm talking about the Family Growth spaces that become available in Stages II and V.  It seems to me that if you're the only player planning ahead for room building and Family Growth becomes available in Round 5, you can get a substantial advantage in terms of extra actions by having a third person to use early.  However, if Family Growth doesn't show up until Round 7, the other players have more time to play catch-up (and reap the benefits of having sown fields or obtained a breeding pair of sheep before the first Harvest).
And then this happens again with the Family Growth Without Space action.  It feels like someone getting this at the start of Round 12 can really influence the way the endgame plays out, such that there's often a big race to grab Starting Player in Round 11.  But if by chance Plow & Sow is revealed instead, dreams can easily be crushed - especially as the starting player typically then changes before Round 13!
What's the best strategy for playing Agricola in order to maximise your chances of doing well whatever order the action spaces become available?  Is there a "middle-ground" approach that allows you to do well whether or not the ostensibly more powerful actions show up early?  Or in the end is it better just to roll the metaphorical dice and take your chances?

It sounds like it's not the randomness of the action spaces that bothers you, but the unknown factor. If you're playing in person and others share your opinion, I'd suggest revealing the cards after they're shuffled and just use something else to track what round you're on. You'd have to keep an eye on upkeep to make sure you're not letting things accumulate too early, but that seems like it would address all the concerns you brought up.
If you want to play with the rules as written, you really can't assume that something will come up in any particular spot. For the first Family Growth, what you're describing is exactly the dilemma; if you invest early actions in the hopes of growing your family in Round 5, you have no way of knowing if that will pay off or not, and that's not something that will change with experience. You just need to factor your decision to build early (or not) with the possibility that it will not work out for you. I don't think there's anything you can do about that. For the second family growth, if it's that important to your strategy to get that first, I would say plan on being the start player in both Round 12 and Round 13, probably holding back some Minor Improvements so that it's not a total "waste" of the first move in Round 12 if the Family Growth action isn't the one that comes up.
In general, I think your question is looking at Family Growth in a vacuum, which seems to run contrary to the idea of Agricola. The best path to victory (generally) is diversity, and I realize that Family Growth is instrumental to that since it gives you precious additional actions, but regardless of what you're trying to do, relying on a specific space to be there exactly when you need it is risky. Competent opponents will often block you if possible (since there are few actions that would be detrimental, only slightly less attractive in a vacuum that would be pushed over if it both benefits them and hurts you), and if you spend too much time trying to manipulate turn order, you won't do well. Agricola is also not Chess; the random bits mean that there's not really an "if X, do Y" truism that will be a silver bullet winning strategy.
The way the question is worded makes it sound almost like you consider Agricola to be a zero-sum game, but it's not - it's more along the lines of a Nash equilibrium, even when played two player. I guess my answer to your question would be to "always have a plan B", or maybe plans 1-n where n=the number of players. If you have multiple viable options at all times, you can't be blocked easily (I've never seen the entire table collectively decide to leader-bash in Agricola, and I play with a cutthroat group of people). Ways to do this will vary considerably with the cards you get, the cards your opponents get, and what their biases are (e.g., I've played games where the 3 Wood space was taken literally every Round because most of the table thought they needed to have a 5 room house and use all of their wooden bits - as you may imagine, that took a big strategy adjustment). If you're looking to master Agricola, I think the best thing to do would be to understand how ROI works with scoring in the different categories and watch what everyone else is likely to go for. This extremely long analysis might be a good place to start in terms of Agricola's in-game economy.

I like lots about this answer, but I do feel like you can't look at Family Growth as "just another action" like any other.  Not only does an extra family member pay for itself REALLY quickly (it's almost impossible for a family member not to be able to derive at least 2 food from its actions per Stage - and usually you'l get lots more too), every one is also worth 3VPs at the end. If it wasn't by far the best action in the game I'd be less worried about it!

@thesunneversets: Yes, 1 more turn can easily net 2 more food.  But, that is NOT the entire cost.  There is also the opportunity cost - IE what else could you do if you weren't doing that.  (which that agriconomics essay mentions).   At poster: +1 for that agriconomics link!  That's a fantastic article.

Also, it's noteworthy that if you're in a balanced N-person game, you're doing well to win over 1/N of the time. So if there's a play that gives you a guaranteed win with 30% probability, it's a probably the right move, even if it costs you the game 70% of the time.

@thesunneversets I agree with about the opportunity cost. Maybe in theory family growth is always the optimal action, but what if there are 12 wood sitting there? Or you have a card that would make taking one vegetable net you 4? Or if you really need both clay and reed this turn? One of the things I like about Agricola is that everything is a trade-off - family growth is investing in the future at the expense of the present, and while it's certainly a worthwhile investment (especially due to the 3 points as you mention), I don't think it's always the best tactical move.

You definitely always take 12 wood, or 9 wood, over a family growth I think.  6 wood could easily be worth it too.  I'm talking about things that happen in real games though, where ridiculously good opportunities don't tend to build up over time.  @DavidOneill: the "opportunity cost" is pretty much always compensated by the 3VPs a person is worth.  Getting 3VPs for a single action is well above average profit for any Agricola move.

@thesunneversets Absolutely: the 3VPs are huge.  But you get the same victory points whether you do it now or later.  Since your question was regarding the value of making sure to do it earlier (vs later), the VPs aren't part of the now vs later choice.

Seriously, I'll play you at Agricola any time if you think it's ever possible to go through most of the game with 2 family members and do at all well.  The earlier you get any given family member, the more return you get on that family member; before the last turn they always pay for themselves and considerably more.  Yes, you don't pass up massively good actions just to grow your family (if you're playing with people who leave massively good actions lying around), and yes, you need to develop your food engine in parallel too.  But that's as far as I'll concede.

@thesunneversets If getting family growth actions immediately is indeed the optimal strategy in all situations at high levels of play (I don't have enough experience to assess whether or not that's true), then I don't think there's an answer to your original question; you would need to keep yourself in a position that you can take it immediately regardless of when it comes up (which I think is what warbaker was referring to). For what it's worth, I'm not talking about most of the game here; I'm saying if it comes out at Turn 5, it may make sense to wait for Turn 6, depending on the game state.

Okay, sorry, I actually agree with that.  And in fact with most of the above talk about "opportunity cost" - it's just that (IMO), Family Growth generally has such a high payoff that you need to have above averagely good reasons not to take that opportunity.  My best opponents tend to make it very hard for anyone to build rooms and grow their family cheaply - they maximise my opportunity costs until, yes, I do have to think twice!

@thesunneversets: I'm not at all saying that I could do well with only 2 people.  And you probably would beat me - I've only played 4 times.  I edited more details into my answer, clarifying absolute vs marginal value...

When it comes to the stage 2 Family Growth I'd agree with you somewhat. If you prepare for family growth to come in Round 5 and no one else does, you won't have to waste moves to get Starting Player. If it doesn't show in Round 5, grab the wood or the reed to delay room building for your opponents. You still get compensation for being prepared but of course you would have been better off if that FG had come in Round 5. (Also do not focus too much on getting FG. I always laugh inside when my opponents grab Starting Player in Round 4 hoping for FG in Round 5, and then they take SP again hoping for it in Round 6. All this without the ability to play a minor improvement when taking SP and certainly no minors left when FG comes.)
What I think is worse about Stage 2 is that you never know when Renovation comes. Even though I can find awesome card combinations for early renovation I never want to take the risk as it would be horrible if it comes in Round 7. I rather discard the cards and grab new ones instead (I usually play with Mulligan).
I've previously proposed to my opponents that we fix the Stone action in Stage 2 to Round 5 and then FG and Renovation come in Round 6-7 (random). This way Renovation strategies are more viable and the players not getting the first Family Growth likely gets good compensation in the form of 2-3 stone.
For the Stage 5 Family Growth even without room I don't agree that it is too random. You should always have a grain or vegetable ready if the Plow and Sow comes up instead. And don't be too disappointed, that too is at least a 3 point action that probably gives you food, compared to FG that gives 3p and costs you food (the extra action which you may have to spend getting that extra food). There's also often 2 Cattle available at this point which is also worth at least 3 points (4 if you afford to breed it twice). Nowadays if I in Round 13 or 14 get to choose between FG without room and Plow and Sow I often choose Plow and Sow.
Conclusion: Don't overvalue Family Growth. If you make efficient actions like taking 6 wood, 3 Stone, 2 Cattle it doesn't really matter if you delay your FG.

Mm, I guess the issue I have is that growing your family does not generally preclude you from taking sweet actions like 6 wood/3 stone. In practice I find that the player who grows their family first often gets a whole round of such actions cheaply - the round in which the other player has to play catchup by building a room/ family growth.  Even if there's nothing great on the board that round, the 3-action player can grab some food, take starting player, do something else too - and be in a position to take 6 wood next turn.

I will agree with you that taking starting player (multiple times?!) just to be first to Family Growth is horrible play though. I can't see how that would help anyone win the game. The action you gain from having a bigger family has already been lost by taking starting player, plus you now need more food when the harvest comes around!

The spaces on Agricola are designed to give the game variation and chance.  You don't know when you're going to get a Family Growth or not, same as not knowing if you'll get Fences first turn or fourth turn, which can sometimes hamper strategies, though the early game isn't as critical as people are just starting to get resources.  I feel this is what makes the game fun and helps to make it a dynamic play each time I play it.
As for some suggestions, what I usually end up doing in game, when I have a win condition in mind and I'm working for it, is expecting the action I want to flip up first in the phase I want it to.  Say you're trying to maximize everything and plan for your house expansion and then family growth to start getting that extra action.  If that's what you're going for, house expansion should be done well before you get that far and you should have a food source ready to feed your third person before you get to the year that has Family Growth.  Then, you adjust your tactics accordingly.  Don't expect to have the third person right away, but plan for it to happen the first round.  Watch what other's are doing.  If they have expansion already, then all of you are getting ready for that spot and it's a matter of who's going to hold First Player.

I'm not saying the random factor isn't good for Agricola, just that quite often I've found it makes a HUGE difference to player fortunes.  Playing for Family Growth to show up on Round 5 may well be an excellent strategy, but if you have no backup plan for the times it doesn't appear till Round 7, your chances of doing well are seriously reduced, I'd have thought.

Two responses come to mind:
If you are playing on a physical board, and with people who are willing, simply pre-determine the order.  (Yeah, I don't like this idea either, but it is a way to mitigate the random factor).
Otherwise, it's a value calculation.  The value of a decision based on chance is equal to the value of the desired outcome times the chance of the desired outcome minus the value of what you had to give up to get it.
The value of the desired outcome is 1 more action in the next turn.  (This assumes if you don't bet that it will come up a particular round you'll get it the next turn - could have greater value if not getting it now means you're unable to get it exactly when you want it later)
The chance of a particular action appearing on the first round of a stage is very straight forward - 1/4 for the 1st stage, 1/3 for the 2nd stage, 1/2 for the rest.
The cost (that is, the value of what you give up to get it) is hardest to figure.  There are two types costs:
1) The costs of being able to support an additional person (food, room if needed).  However, at least for person #3, it's a safe bet you'll do it sooner or later, so the only real cost is action order IE if you're expanding you're house you can't use those turns to plow and sow.
2) The costs of making sure you're able to cash in (IE taking starting player).  Given that it takes a turn to take starting player, and there's only a 1/3 chance that it will come up, it's a losing proposition.  But if there's a big pile of food there, it might be worth it. (if food gained > 2/3 of a turn, go for it)
~~ edit
To know if you should be prepared in case FG flips on turn 5, ask if the following is positive or negative:  (Note, I'm slightly misusing the term marginal here.  Sorry to any econ majors)
VF+P(1-F)-C
where
V = Value: marginal Value of doing FG on turn 5 (That is, how much more valuable is it to have FG on turn 5 vs. turn 6)
F = Flip: likelihood of FG being Flipped on turn 5.  (This is equal to 1/3)
C = Cost: marginal Cost (including opportunity cost) of being prepared if it is flipped on turn 5 (That is, what is the value of the choices you can't make because of your preparations)
P = value: independent value of Preparation (that is, what is the value of these preparations if FG is NOT flipped on turn 5)
What you said (in your comment) about getting a better return on a family member the sooner you get them is right on.  But, it's important to differentiate between marginal and absolute value.
Absolute value vs marginal value:
The absolute value of using FG on turn 5 is: 3VP + 9 additional turns (which is a 32% increase*).
The marginal value of using FG on turn 5 is: 1 addition turn (~3% increase*).
*(these are compared to the base 28 turns.  Obviously, you'll use FG more than once, and thus have more than that, but it is still useful for comparison)
You use the absolute value in determining if you want to do FG at all, but you use the marginal value to determine if I should do it right now.
Note about P in the equation:  this represents the value of already having the room (and food) for an additional person.  If you are prepared for FG on turn 5, and it doesn't flip, the opportunity cost of preparing for it to be flipped on turn 6 is 0!  In a sense, P is the opposite of the opportunity cost of preparing for FG on turn 6 or 7 times the relative likelihoods of it flipped on those turns.
This is not an answer per say, but more of a framework for finding the answer.  I've only played Agricola 4 times, so I don't have a feel for the relative values of V, C and P.  By making sure you're ready for FG on turn 5 or by preventing your opponent from being ready, you're saying that VF+P(1-F) is greater than C, that is you gain more by doing that than you could gain by doing something else.

I do like the random element as a tool for keeping Agricola interesting, I just feel like it can prove very "swingy" in determining people's fortunes.  One thing to keep in mind is that you don't always get a free choice of what strategy to adopt in time for Round 5: if you're not starting player, and the person who is is aggressive about taking wood, I'm pretty sure he can stop you from building a room by round 5 if he wants to.  (The question then becomes if you are willing to take all the reed to keep him honest too!)

If your opponent is taking all the wood, the 'cost' (so to speak) becomes infinite, since you can't afford to do the preparations (without cheating).  I would think that the situation where your opponent is taking all the wood and you're taking all the reed would be better for them, since there is more you can do with a big stack of wood than a big stack of reed, but as you said, that's the question:  Is the value of preventing your opponent from getting FG worth the turns spent not doing something more useful than a bunch of reed.

for sure - in fact I posted a question a while back about how to deal with a game in which your opponent goes first and aggressively takes as much wood as possible.  Didn't get many suggestions, but the conclusion I came to was basically that wood is too good just to let your opponent have it all, you have to compete for it eventually. http://boardgames.stackexchange.com/questions/5178/is-it-possible-to-win-2-player-agricola-without-taking-wood

I love random elements in games. Randomness doesn't mean you can't play optimal, it's just a lot harder to find optimal strategy because you have to correctly determine EV (expected value) and the odds.
Let's say you build up to prepare for FG on turn 5. If it appears your chance of winning is 75%. If it doesn't your chance of winning is 40% (just random numbers here). The odds of the first happening are 1 in 3 (so 2 in 3 for the second). This gives:
Win% = 1/3 * 75% + 2/3 * 40% = 52%
If the swinginess is higher (random numbers again):
Win% = 1/3 * 84% + 2/3 * 24% = 44%
So if the "prepare for FG on turn 5" strat is very swingy it's probably best not to try it (I've only played Agricola a few times, so I have no idea what the actual win% for a strategy are, so maybe an expert player can fill these numbers in)

My problem is really that players pursuing a relentless "I will take all the wood" or "I will completely ignore wood" strategy can really do an awful lot better or worse based on what order the cards proceed to turn it. I guess that makes for an interesting game, as once you've worked out what they're up to you then have to plan for various outcomes.  I think Agricola, like many great games, is one that does favour people who have the power to adapt their strategy to circumstances - I'm trying to work out the best way of doing that I guess!


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What happens when a gate moves onto a vortex?
If a moving gate (from the Lurker at the Threshold expansion) would move into a vortex in Dunwich, what happens? My best guess is that, since the rules say it moves as a normal monster, it moves into the vortex, and, like a monster, adds a horror token to the track.

Moving gates cannot move onto Vortexes.
From a post on Fantasy Flight's forum:

Gates can't enter Vortexes. In this situation, the vortex is treated like an open gate, and gates can't move onto gates.
If a gate has to move into a vortex, it just stays in place instead.

I do not believe that the answerer, Tibs, is an official representative of Fantasy Flight.  However, he has nearly 4000 posts in their Arkham Horror forums and seems to have a very good grasp upon the rules.


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Is there a limit on how good you can get at Hearts?
If you had the best players in the world, and they knew everything about Hearts and had decades of experience playing it, then if they were to each play the same identical game, would they all play the game exactly the same? That in my eyes would prove that in Hearts, given a situation and taking into account everything, there is always an optimal way of proceeding, and that would prove that there is a finite limit on how good you can get at Hearts.  Is this in fact the case?

I appreciate the question, but I think the question is too subjective and open-ended.

@Little Really?  Whether there is an algorithm that will always get the best possible result is subjective?  I'd be very interested to see anyone argue yes.

Short answer: Yes, it can.  At time of closure I was about to suggest that the question almost belongs on Mathematics, where it will draw a short lecture on the fundamentals of game theory.  (I'm too tired to type it myself, but the short form: Yes, there's always a 'best move' algorithm... for a suitable choice of the meaning of 'best'.)  To ask more meaningfully here, I think you need better definition - what do you mean by 'skill' if you don't mean 'algorithm to select the best possible move', for example?  I can't agree that the question is subjective though, just hard to answer well.

Since I'm new to the whole moderating thing, I'm going to re-open this for now and see how it plays out.  Sorry about the confusion, and carry on!

@LittleBobbyTables, it's definitely way too subjective, I've cast my vote to close.

I don't see how it can be "way too subjective" when it has a yes/no answer.  Admittedly I don't know, so any answer I gave would be a matter of speculation, but I'd be interested to hear what someone with a better grasp of maths and game theory would say.  I have a friend who said that there was no possible way he could get better at Hearts, he'd mastered the game - I'd like to find out if he was talking out of his hat or not!

Okay I've added some additional info to try to make the question less subjective

@Lance: I'm stunned by people saying this is too subjective. There is nothing subjective about this question. At all. If you think there is, you misread.

@Lo'oris, See my answer, and the link to SE defined subjectivity.  Mostly this question is just silly from a game theory and mathematical point of view.

@Robo You seem to have actually made the question more subjective, because you're making the answer all about the result of a hypothetical situation.  We're trying to tell you that it isn't possible for there to be one absolute best way to play in a game like Hearts.  If you insist on making it about what would happen if the best Hearts players ever all played each other, then I'm going to have to agree with LittleBobbyTables that it is subjective and should be closed.

@bwarner : To me, the winner is determined by two factors. Strategy and luck. A strategy in any given situation has a certain probability of winning and generally, the best players will know which strategy is the best (or not? it's part of the question). Sometimes a player may use an alternative strategy with a lower probability of winning in order to surprise an opponent but only if he thinks that this surprise move will overcome the decreased odds against him. My Q is is it ever beneficial to use the surprise move or is it always use the optimal strategy of winning?

@Robo I still believe that in a game like this where interacting with your opponents can have a direct impact on the game, the idea of there being an always optimal strategy is impossible for any practical purposes.

I just want to say, as a mathematician who has studied Game Theory for several years, that you DO NOT need perfect information to have an optimal strategy.  In fact, Game Theory has a very rich body of results about games of imperfect information.
It is a common misconception.  Here's another one: an optimal strategy means you win every time.  This is also not true.  An optimal strategy is one that maximizes your expected payoff.
Now that that's out of the way, I want to commend the questioner on a great question.  I was actually just googling this question myself, trying to see if any journal articles have been written about it (I was thinking about doing a game-theoretic analysis of Hearts for a thesis paper).  I haven't found anything yet.
Like most nontrivial games, Hearts has a HUMONGOUS game tree.  There are 52!/(13!^4) hands that could be dealt (each of the 4 players gets 13 cards).  That's just how many nodes there are at the second level of the game tree.  Each of those nodes has a huge number of branches (the number of branches at each of those nodes is the number of ways four players can choose three cards from 13).  Then each of those have yet more branhces, and so on.  Even a rough calculation shows that there are far more nodes in the game tree than there are atoms in the known universe.
So using Zermelo's algorithm to "solve" hearts (though theoretically possible) is - in practice - not possible.  So much more sophisticated techniques must be used.
If you want to write a computer program to play near-optimal Hearts, I would suggest using random samples and Markov-type simulations to estimate optimal moves.
In short, yes, optimal play does exist.  But it could be very hard to find without some pretty slick game-theoretical analysis and/or a lot of computational power.
I hope this helps.  :)

Good answer, but i think you are wrong about the number of possible hands (not that it is all that important). Since order in a player's hand doesn't matter, I think the number of possible hands should be (52 choose 13)*(39 choose 13)*(26 choose 13)*4! (I haven't done this kind of math in a while and I could be wrong, but I'm fairly certain it isn't as simple as 52!)

@Matt: You're absolutely correct.  Of course, as you say, that doesn't change that this is an excellent answer.  +1 each.

There are 635,013,559,600 different combinations of 13 cards that can be dealt from a 52 card deck. Theoretically, some of these combinations are equivalent as far as the game tree goes. (ie. it doesn't really matter if a suit is diamonds or clubs.)

Its another result from game theory that there is NO OPTIMAL STRATEGY for MULTIPLAYER (3 or more sides) games.  There's not even a good definition of what "optimal" might mean for such games, as players may collude.  As hearts is such a game (the 4 players have independent winning conditions), there is no optimal strategy.

Once you're looking at your 13-card hand, I believe it's (39 choose 13) * (26 choose 13) = 8.4 * 10^16. Just imagine each opponent in turn taking the top 13 cards of the shuffled deck.

An important part of Hearts (like most card games) is how the other players react (how likely they are to try for the lot, how quick they are to notice when you do, etc). So computer simulations don't assist with the real-life problem, though they can with the Microsoft version.

How is 52 factorial 64x63x...? That should start with 52 and go down from there.

Also, @Matt, I think the number of possible starting hands should be (52 choose 13) * (39 choose 13) * (26 choose 13) * 4 without the 4 being factorial, since it doesn't matter how the other hands are distributed, just that you get one of those four hands.

@SQB I think the order of hands does matter because of the card passing that occurs at the beginning, as well as the turn order. If cards were played simultaneously then I would agree that hand order doesnt matter. But swapping two of the players' hands would very likely result in different optimal plays.

No, because in hearts there is private knowledge
The answer to this question is a categorical no. Having a perfect memory of cards that have been played and in what order is insufficient to guarantee optimal play, and we can say this without even having to define optimal play.
On the first turn of the game, you have limited knowledge of how the cards have been distributed. You know about the cards in your hand and those you've passed (if applicable), and you can potentially infer something from the cards you've received. But that's only 16 cards out of 52 and you don't know how the remaining cards are distributed. This private knowledge means there is no deterministically optimal play; you don't have enough information to know what move is always best. Even given a stochastic play model (where you're looking for the play most likely to give you the best results) it is possible for two different distributions of the hidden cards to suggest different plays, which means the hypothesized algorithm must make a random selection.
I'll prove the point with an obvious example: the first play of the first round. Since the scores are tied at zero, a good definition of optimal play is to get the lowest score in the round.
If you had only three clubs in your hand, the Ace, a fairly high card and a low rank card, a typical play in the first round is to play the Ace and take the trick and then to lead the higher card to burn it before playing the low ranking card or switching suits. Given a fairly nominal distribution of clubs, the odds of someone being out of clubs on the second round (so they can sluff a heart or the Queen) AND someone else not playing a higher club are not insignificant but low and usually worth the risk. If you had perfect knowledge however the right play would be obvious, but without perfect knowledge the right play depends on knowledge you don't have.
So no, the fact that there is private knowledge in hearts means that even with a perfect memory you cannot always guarantee optimal play.

Helpful anecdote: I had a group of friends, the four of us played hearts, a lot, over a long period of time.  It got to the point where after being dealt, we all knew who had the queen, who was trying to shoot the moon, etc, just from the body language of each other.  So even though the 'private knowledge' was gone, there was still strategy in the meta-game, e.g. how do play to make sure friend X has to be the one to take the sacrificial hearts trick so that friend Y doesn't successfully shoot?

This private knowledge means there is no deterministically optimal play Not true, games of imperfect information can have optimal strategies. The hidden nature of the cards just makes the game tree much harder to analyze.

@NealTibrewala: Then the crowd you were playing with is particularly incompetent. The best way to Shoot the Moon is to not even decide whether you're going for it or not until about round 5 or 6 of the play. One should always build a 2-way hand if attempting to Shoot the Moon, which is not usually difficult.

To the question whether Hearts is such a simple game, that it is possible after a while to completely master it (meaning that several players can reach this level where it is not possible to improve, and between them only luck will decide who wins), the answer is definitely no.
Some of the answers here are a bit inaccurate though. People argue that because you don't know the cards of the other players, it's impossible to always pick the best strategy for yourself and therefore it is impossible to master the game. This is missing the question as I read it. Obviously no one will ever master the game at a level where every play they make is the same as someone knowing all the cards would make, it doesn't even make any sense to  discuss.
The question must be whether there is an optimal strategy for every situation, meaning that with the information a player has a in a certain situation, there is one option that gives him the best chances of achieving his goal in the game. The key here being "the information a player has". Playing human opponents, it's possible to pick up on little tells and signs about their cards or from their actions that forms part of the information you would use to determine the best option. If I've played for hours and hours against a certain player, I would know his style and tells better than someone who's never played him, and I would then have more information and better chances of making the right decision. Your friend who has "mastered the game" wouldn't play as well against the player I know as I would (unless he is better at something else in the game than me or he is lucky), and would therefore find it hard to beat my score. People who play poker will know this very well. If you only look at the maths and don't try to figure out what your opponents are doing, you are going to lose a lot, and reading your opponents is something that can never really be mastered, meaning it will always be possible to improve. And that's not even considering the game-improving potential of trying to manipulate your opponents into doing what you want them to, which is also something that I don't think anyone will ever master, as in having nowhere to go to improve. Curiously in theory it's possible to both read your opponents and manipulate them successfully in every single situation, but then again in theory it's also possible to randomly choose your actions and by luck having them turn in to be right every single time.
If you remove the part about reading your opponents and only look at your own game, it's possible in my opinion to always find a "best choice", and thus possible to master the game. Your friend has probably played the computer, and playing the computer there definitely is a "best way" to go if you've memorized all the cards etc. The thing being overlooked, though, is that you're actually reading the signs the computer players give, without noticing it. You develop a kind of intuition sensing danger develop etc. It gives you a great edge being able to read the computer players, especially since they're not able to read you or manipulate you. It's therefore easy to get the feeling that you've mastered the game and found the optimal strategy in every situation. The truth is you're probably just close to consistently finding the best options against one specific opponent (computer*3), and that opponent is severely handicapped by being completely predictable itself, and unable to read your play or adjust its own. Not really a big feat.

I think a better way of thinking about this question is "Is it possible to create a Hearts playing program that would get the best possible result 100% of the time"?
I think Hearts is similar to a simplified version of Bridge.  There are LOTS of studies of Bridge hands, and in most situations there is a clear optimal play.  But there are also times for intuition, reading your opponents, etc.  So I don't think you could ever just generate an algorithm that would make the "optimal" play in every situation and have it do as well or better than a human would 100% of the time.
It is also worth pointing out that Hearts is a game in which the individual play that earns you the best result might not be the best for your overall results, and part of optimal play is convincing your opponents to play in ways that are optimal to you.   Examples would be encouraging people to "save" hearts to throw at the leader, or to take the Queen of Spades themselves to prevent a potential Shoot the Moon by another player.  The inventor of Diplomacy has even said that playing lots of Hearts influenced his design of a game that is all about stopping the leader. This also makes me confident that there is no such thing as an algorithm for optimal play.

bwarner: Your phrasing of the question is excellent.  Your answer is unconvincing, however; 'intuition' in this context means 'guessing at the optimal play'.  But I'll add my own answer rather than argue in comments.

By intuition I don't mean "guessing at the optimal play".  I mean understanding the playing tendencies of your opponents, and determining how that affects your optimal play.  Hearts is a game of incomplete information, but good players can get more information from their opponents than might be immediately obvious.

Part of the thing about Hearts is that you pass cards between the players before the round starts.  This means that you can try to improve your hand and hope your opponents don't mess that up.
However, at least in 4-player games, 1 of every 4 hands has no pass first.
Having said all that, the best hand involves taking every heart and the Queen of Spades, which usually depends a bit on luck based on what the other players play... but often you do need to keep track of which hearts were played when.

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If I attack with 2 creatures that both have "All creatures able to block this creature do so", how are blockers determined?
Say I have 2 creatures enchanted with Lure or 2 Taunting Elves attacking: Does my opponent get to choose which of their creatures blocks each one or do I? What if one of those attacking creatures also has flying but the other does not? If one of my opponent's creatures can block multiple creatures, must they block both?

Comprehensive Rule:

509.1c The defending player checks each creature he or she controls to see whether it's affected by any requirements (effects that say a creature must block, or that it must block if some condition is met). If the number of requirements that are being obeyed is fewer than the maximum possible number of requirements that could be obeyed without disobeying any restrictions, the declaration of blockers is illegal. If a creature can't block unless a player pays a cost, that player is not required to pay that cost, even if blocking with that creature would increase the number of requirements being obeyed.
Example: A player controls one creature that "blocks if able" and another creature with no abilities. An effect states "Creatures can't be blocked except by two or more creatures." Having only the first creature block violates the restriction. Having neither creature block fulfills the restriction but not the requirement. Having both creatures block the same attacking creature fulfills both the restriction and the requirement, so that's the only option.

Answers to your questions, as covered by this rule:

Does my opponent get to choose which of their creatures blocks each one or do I?

Nothing in the Lure ability says that you get to choose. The defender has to follow the maximum number of requirements without disobeying any restrictions.
One of the restrictions on the defenders, barring any additional abilities, is that they may only block one creature. Therefore, the defender must block one of your attackers and may choose which one to block, as that fulfills the maximum number of requirements without disobeying the restriction of only being able to block one creature.

What if one of those attacking creatures also has flying but the other does not?

Obviously, if a defender is unable to block creatures with flying (that is a restriction) that defender must block the one it is able to block.

If one of my opponent's creatures can block multiple creatures, must they block both?

If a creature is able to block multiple creatures it must meet the maximum number of requirements that could be obeyed, therefore it must block both creatures if able. (Unless that blocker is something like an Anurid Swarmsnapper… as rule 509.1c states, the defender is not required to pay a cost to increase the number of requirements obeyed.)


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Does Forbidden Island usually need any rule variants for playing with 5+ people?
I don't see any reason why Forbidden Island wouldn't be able to handle 5 or maybe even 6 players with some simple variants. Does anyone have any experience with different player numbers with some wisdom to pass on?
It would be slightly harder to gather the required 4 treasure cards at one person, but there would be more people total to trade with. The island would sink faster and it would take longer for a certain critical player to have their turn, even though the navigator and helicopter can move anyone. How can these disadvantages be offset to keep the game strong and sufficiently difficult?

After the first reshuffle of the Treasure deck, go down to drawing only 1 Treasure card per turn. Since you'll have all the cards drawn fairly quickly, the challenge becomes maneuvering them to the right player. Usually by the time you get through the entire deck this way you've gotten at least one treasure and discarded the 4 cards, which means you won't have every single card be a "Waters Rise!". This should let you play with 5 people just fine, and possibly 6 if you start at novice level.

If you are willing to do a little bit more work, you can beef up the game itself. This will give results closer to the feel of the original game. Keep using the rule I mentioned above! Here's what you'll need:

1 new treasure and 5 treasure cards for it.
6 extra tiles and their flood cards. 4 of them are just normal tiles. 2 of them correspond to the 5th treasure.

You can use index cards to make the tiles and regular playing cards for the flood and treasure cards. The four aces are the flood cards for the 4 new normal tiles, the King of Spades and King of Hearts are the flood cards for the 2 5th treasure tiles. 2-6 of Hearts are the treasure cards for the 5th treasure. Yes, it does look a little shoddy to have regular playing cards mixed in with the deck, but it works just fine and I've found it rarely hurts the gaming experience. If this still bothers you, just sleeve all the cards.This will let you handle 5 people just fine.
To play with 6 people, add one more card of each of the 5 colors, so there will be 6 cards of each color. I  just used a marker to color some normal playing cards to match the others. Since you now have added cards for the new 5th treasure and the old treasures, the issue of knowing exactly what's coming up by what the card back looks like is reduced. I also recommend that you allow players to either give or take a treasure card from another player on the same tile for an action, instead of allowing giving only. This lessens the time spent waiting to get to the right player's turn. I have played this 6 player variant several times with great success, to the point where I actually prefer to play with 6 people to playing with less.

If you want to play with 7 people, add another card of each color to the deck, so there are 7 of each color. I have not play-tested very often with 7, so I assume that the game starts to fall apart a little more, but it should still be playable. The nice thing about cooperatives is that you can have some players control 1 pawn as a team. Our groups tend to make decisions as a group often enough that we rarely notice that there are less pawns than players. If you need to support 7, you can choose if you want to try the 7 pawn rules or the 6 pawn with one team.
These tend to give good results as they keep the game fairly balanced. Having a bigger island suits extra players better as you have a better ratio of Waters Rise! to treasures and more island no-sink time. You'll have to plan a little more as you'll end up farther away from each other. The degradation of the island is more interesting as you can have bigger holes in the center. You can even start changing the shape of the island for extra fun. I will be posting a list of new roles shortly.

Feel free to post any question, comments, or reviews of these rules if you've played with them. :D


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How is Settlers of Catan different when playing with the 5-6 player expansion?
I've read a few reviews, and these are the things I've picked up:

game will be longer. This is totally fine and normal, but I'm curious, what's the average time increase?
Ports are a little less valuable and harder to get, and trade with other players increases.
Intermediate building between turns makes the robber a little weaker because its easier to get rid of resources.

Are these accurate? What other differences have you noticed when playing with 5 or 6 people?

The time increase depends a LOT on who is playing. But probably double a normal game. I think the fun payoff of the extra people is worth it, though. There are still only one each of longest road and largest army, with two more people, so those tend to get stolen a bit more.
I suppose the increase in shoreline is not quite in direct proportion to the increase in acreage, but I don't think ports are dramatically different. You add real estate to make up for the added players, so the overall ease of getting good position is about the same, I think.
Building in-between turns is probably the biggest contributor to the game going longer, since you have an extra phase to do it in. That said, if everybody knows what they want it can go pretty fast. And yeah, it can save you from the robber, although IMO the robber would be way overpowered if you couldn't do it.
I think that 5-6 is the most fun when you do it with Seafarers, perhaps the scenario with the fog-of-war, since now you can have everybody exploring in different directions. Pretty cool.

The ports are much less valuable as you can't use them during the building phases (between each players turns).  Consequently if you're saving up three-of-a-kinds to trade on your turn then you're much more likely to be hit by the robber.

Is there anything I can do to make it feel more like regular 3-4 player Catan

@tttppp You already couldn't use them during other players' trading sessions...this may make them slightly less valuable in the scheme of things, but certainly not "much less". Also, the majority of ports are not 3-to-1, so using that as your baseline is a little bit off.

@CJD It really doesn't feel that different to me. Maybe I'm just daft.

@Andrew However in a 5-6 player game then you can build when it's not your turn (in fact on every other player's turn).  In the 3-4 player game it is reasonable to pick central hexes that cover all the resources, OR focus on one type of good and get the port for it.  IMO, in the 5-6 player game the latter tactic is always trumped by the first.

Last time I played with six players (all experienced) I focused heavily on sheep, got a 2:1 port, and stayed ahead the entire game to land the win. I don't play often enough to be sure that game wasn't an outlier, though, and I definitely see your point.

I have played the 5-6 player version using the extra building phase and using the normal rules. Here is my assessment assuming that you are playing with people that know how to play the game:

With the Extra Building Phase
If you play with people that know the game, this actually makes the game go faster. After every turn, someone yells, "Anyone building?!".  There are still times during the game where there are shortages in resources.  At least 50% of the time, you will get a unanimous "NO!".  However, for those times that someone wants to build, it helps speed up the game because you are able to get your settlements and cities on the board quicker and ultimately win the game faster.
Without the Extra Building Phase
The game is slower due to the "robber effect".  If you're getting rolls left, right, and centre, you can easily end up with 10-15 cards in your hand by the time your turn comes around...especially later in the game when you've built up some cities.  However, it is more likely that someone in the 5 turns before you will roll a 7 and then "BAM", your plans of Catan domination go down the drain.  So much for building those 2 cities and collecting that development card on your next turn! That's the potential for 5 victory points in one turn. I've actually seen (on multiple occassion) someone get screwed out of building 3 cities in one turn because they happened to be getting their wheat and ore rolls one right after the other.  Long story short, it can take a lot longer to build what you need to build to get those VP's when you don't allow building between turns with 6 players. With that said, it can be a pretty fun way to play as well if you have the time!

Hope that helps!

Just like the 4-player is tighter than the 3-player, the 6-player is tighter than the 5-player.  The 'special build' really slows things down, but is pretty important to keep your hand culled to stay under 8 cards.

How does the 'special build' phase slow things down? It would seem like it would shorten the game by letting players do things more simultaneously. A 5-6 player game would be longer without it, right?

No, you have to stop and have everyone make a choice, and if it matters, it has to be done in order.  It really slows it down.

You don't have to stop. Players have to vocalize their intent and/or throw resource cards towards the banker before the dice are rolled or they miss-out. (*) - the way we play, that is

I find it's slightly easier to get boxed in - even with the additional real estate, there's still only a few sweet spots that everyone will cluster around and fight over.
Ports are slightly less valuable, but I find that's balanced by the fact that most players avoid the water so you have more room to work.


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How can I make Dominion play better with 5+ players?
I just got Intrigue, and it seems cool that it opens up the game to 5 or 6 players. However, the common consensus seems to be that its possible, but not recommended. Is there anything I can do to make Dominion play better with 5 or 6 people?

The biggest problem with extra players that I usually see is down-time. Dominion is partially a group solitaire game. There is some interaction between players with attack cards, but otherwise your opponents turns won't matter a lot besides keeping an idea on what piles are low and the game end. I find with 5 the main problem is "I know what I'm going to do, I just have to wait through 3 more people's turns to do it". You also might want to tweak the number of kingdom card piles to somewhere between 11 and 13.
The first and easiest thing you can do is lessen the cards that take longer to resolve. Spy, Throne room, Adventurer, Contraband, Counting House, Possession, and many others tend to make turns take a little longer. This doesn't mean that they are bad in any way, it just means if you are worried about long down-times with 5 or 6 people you might want to forgo them. Removing certain cards may annoy hardcore players who want a truly random layout, but my games usually aren't super serious and its worth it to fit in the extra person.
Another thing you can do if you are adventurous with 6 is play 3 teams of 2. Turns pass from one team to another. Both members of that team take their turns at the same time and have totally separate decks. Their attack cards only affect the players on the other teams. It helps to use attack cards that don't depend on order very much in case you both attack. What do you do if one of you plays a spy and the other a thief? What order do they go in? Instead of trying to make rules about this, just use attacks that don't clash with others too easily, like militia and witch. The team mechanism is mainly to allow some simultaneous turns; you can play as a team and do some minor collaboration, like who should buy what or who should focus on attacks vs. victory points, or still make it every man for themselves and have the player with the most victory points win.

Not forever, but for a while at least, don't play with the cards that require a player to make a choice for every other player.  I'm thinking of cards like the Spy, where you get to choose whether or not to trash the top card of each player's deck.
I suggest this because, if your group is inexperienced at Dominion, this kind of thing can easily slow the game down to a crawl.  Personally I find that a lot of my Dominion actions are really simple things like "buy a Treasure" or "buy a Province".  It drives me crazy if I'm waiting 5 minutes between each move when I'm just autopiloting my strategy.
Once everyone is experienced at Dominion, of course, they can get their moves done quickly and efficiently, even if multiple additional actions and draws are involved.  As long as the game is going pretty much as fast as it can go, there are no grounds can complaint.  But until then, it can be really frustrating to be sitting around non-interactively for minutes on end waiting to play a move that requires no thought on your part anyway.  So, yes, that's my suggestion: phase the more complex and fiddly cards in gradually!

Whenever my group has 5 or 6 for Dominion, I try to split it into two groups, either 3+2 or 3+3. With Intrigue, there are enough basic Treasure, Victory, and Curses to go around. Then when both groups are finished, you can switch and play with the other Kingdom with no additional setup time; then compare notes as to how the different groups handled the different boards.

One suggestion I have is that, once someone finishes playing all their actions, have the next person start playing.  There is only one Treasure card that involves any other player doing anything, and that is Contraband, where the person to your left can name a card you cannot buy.
Having said that, if a player has a card that affects other players, they need to stop and wait for the other players to catch up.  Two non-attack cards this applies to are Masquerade and Vault.
If you're going to play an action that requires you to count cards (Counting House, Philosopher's Stone), count the cards in advance.  The only time you can't do this is if you have other actions that will affect the card count.  In the case of Philosopher's Stone, this is any card that causes you to draw cards (cards in your hand and in play are not counted by Philosopher's Stone).  For Counting House, this big one that affects this is Chancellor, as long as you have two or more actions this turn.
This next part wasn't really what you were asking for, but for each player over 4, you should add 3 Estates, 7 Coppers, 10 Curses, and 3 Provinces to the game.  The Estates and Coppers make sure these piles stay at their respective starting numbers despite the number of players (12 and 32 respectively), as there are cards that may or may not manipulate these piles.  Increasing the number of Curses and Provinces is mentioned in the Intrigue rulebook.


text:
When to choose what colors I will play and vary my picks accordingly?
In the first round of a draft, I usually just pick the best card from every pack. After that I look at what I've picked, try to pick good on-color card in the second pack, and pick whatever my deck needs in the last round.
I've noticed in some of the commentated drafts I've watched online that the players often establish their colors by the fifth pick and then avoid picking anything off-color unless its a ridiculous bomb. For example, if you open something like a Sorin or Garruk on the third pack, you should probably pick it whether its on color of off-color unless there's some amazing uncommon that would work perfectly with the cards you've picked so far. Aside from monetary reasons, its often worth splashing just for that one card, and at the very least you deprive some one else of an ideal bomb. Otherwise they remain faithfully on color no matter what passes by.
When should I determine what colors I'm playing in an MTG draft? Should I try to start staying only on color as early as the middle of the first pack, or what until the beginning or even middle of the second pack? If I pick early I get a wider variety of card in my color, but I may end up not playing another color/deck that could be far better due to my narrow-mindedness. How can I establish a successful balance between these two?

If you're getting "ridiculous bombs" after the 5th pick you are a luckier Magic player than I!

@thesunneversets Whoops, I meant opening one at the beginning of a pack, not actually getting it on any pick after 2nd. The people I play with are too rude and inconsiderate to pass me anything good past pick 4...

I think the question you should be asking is not "when to choose what colours I will play", but rather "when to stop choosing what colours I will play"?
Magic, and especially Magic draft, is a game that favours the adaptable.  When you make a first pick of a bomb in one colour, that does not commit you to playing that colour, but it suggests that you should weight all your subsequent picks accordingly.  If after the first two picks, your colour has completely dried up, then you need to be adaptable enough to let go of that colour.
This is not to say that, on the 10th pick of pack 3, you should still be open to moving into a new colour!  Hopefully your colours and the basic nature of your deck (aggro/control/mill/whatever) will be more or less settled long before then.  So how do you determine when to start taking cards that fit into your deck (as you currently envision it), as opposed to more powerful picks?
Unfortunately there is no quick and easy formula.  But I would say it's when you can actually visualise the deck you're going to play.  Let's say your first two picks are white bombs: lucky for you, but you still can't visualise a deck on the back of two cards!  Let's say white dries up thereafter.  Now you have to visualise a new deck in the colour that you're actually being passed.  Can you visualise it with a white splash?  You should certainly be trying, but not so hard that you end up shoehorning in cards that don't actually fit due to your attachment issues.
At some point you will have double figures of cards that you can see working and playing well in the same deck together.  It's at about this point that I would suggest that you should be committing.  With half a deck already now you'll need to consider optimising your curve and filling any gaps in your deck (too few creatures for instance).
I'm always wary of people who stubbornly try to force a deck that they've visualised before they have a good number of the cards for it.  Sometimes it can really pay off, but passing early bombs in pursuit of a deck that may or may not come, well, that's the drafting equivalent of refusing to mulligan a no-land-hand in the hope that all of your draws will be perfect, isn't it?

The real way to force a deck is not in pre-game but in pack 1, pick 1. Dearly Departed is a decent bomb and all, but it's not as powerful as being able to pass your opponent a pack with zero black cards and zero red cards.

The key to Limited, like Constructed, is to build a deck with a gameplan. Your colors are a part of that, but not the totality of it: any given color can support multiple strategies, and focusing your deck around a particular strategy -- e.g. fast damage, 2-for-1 card advantage, evasive beatdown, just stalling long enough to drop your bomb, &c. -- is generally more successful than just drafting a two-color "good stuff" deck with some bombs.
When you're drafting, there's a bit of tension between going with the flow and controlling it. Every card you receive tells you more about what you're likely to see later, but every card you pass also directly influences what you'll receive later.
Ideally, you want to establish your plan quickly so that you can send coherent signals to the other players. The big reward for this is when they stay out of your space and you scoop up all the good cards for your archetype from around the table. However, you can't close yourself off to what the other players are doing, because other players' choice of colors and archetypes may conflict with yours.
Many draft strategy articles recommend choosing your first color immediately, within something like the first three cards, and then waiting until around your second pack to lock in your second. The subtext is that the best way to signal consistently is to start as early as possible, but leaving your second color choice for later makes it easy to adapt to what's open. This is a quick and easy rule of thumb, but it doesn't really capture all the nuances of drafting your deck. In particular, just because you have a steady stream of cards in a specific color doesn't mean they'll all work together nicely -- if you get stuck with a bunch of Skaab and midrange flyers in triple-Innistrad draft, for instance, you may be stuck unable to actually cast your big beefy Zombies until the late game because your graveyard is too empty.
My usual goal in draft is to work out a specific plan as quickly as possible so that I can pick up critical enablers for it, and just let the colors fall into place based on availability of cards that support my archetype. Sometimes this means shifting colors late in the game when I see that cards that match my deck are moving my way -- even if the color they're in is otherwise pretty picked-over.

I completely agree with the needing to be able to switch color/archetype late in the game. There was one 4-player draft I did where I was doing fairly well with black-blue control, but soon realized that NOBODY else was picking the red burn card. I think I picked nothing but red cards from the middle of pack 2 to the end despite my urge to avoid switching colors that late, threw in some black and a splash of blue, and did pretty well since I had such a consistent archtype. :)


text:
Why is Skullclamp banned?
The following card is banned in current tournament formats:

Equipped creature gets +1/-1.  When equipped creature is put into a graveyard, draw two cards.  Cast 1, equip 1 (artifact).

http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Skullclamp
Usually when a card is banned, I can figure out what the reason is, but for the life of me I can't figure out why this card is so dangerous. Its ability is good but not game-breaking, and I can't think of anything that it would pair with to become game-breaking.

Basically it's because it buffers you very, very well against creature loss. If you're playing a weenie deck it protects you from deck-clearing spells. Or if you're sacrificing creatures, this card gives you extremely cheap, essentially unlimited new draws. The equip ability means you can just reuse it over and over again.
It's also very wide-ranging - almost any competitive deck is going to be better off having a few of these around, so it distorts the format. The basis for that statement is discussed in this very detailed article from the development team:

Skullclamp was banned in Standard, frankly, because it was everywhere.
Every competitive deck either had four in the main deck, had four in
the sideboard, or was built to try and defend against it. And there
were a lot more successful decks in the first two categories than in
the third. Such representation is completely unhealthy for the format.
Your deck has to either have Skullclamps, or have Skullclamp in its
crosshairs—a definitive case of a card “warping the metagame.”
Look, for example, at the Top 8 decks from Ohio Valley Regionals. Or
at those from the more recent German Nationals. Combined, those 16
decks contained 58 out of a possible 64 Skullclamps. Never in my
memory have I ever seen a card show up in those numbers.

It's interesting to note that the development team themselves completely underestimated the power of this card. The story of how it made it to release, discussed in the linked article, is quite fascinating.

It works like "Mutually assured destruction." If you can make yourself immune to MY nuclear weapons, you have a greater incentive (or lesser disincentive) to use YOURS.

If I remember the information correctly either the -1 or the card draw was added very late in development of the card and the combination of those 2 for very cheap basically makes any deck with tokens have a card that says pay 1 and draw 2 cards which is much higher then the average cost of drawing a card at 1.5 mana per card.

I know this is an ancient post but I stumbled upon it in a Google search and figured I could add a bit more historical context.
As others have mentioned (and linked), Skullclamp was proven pernicious in the Standard and Extended formats of its day. There was actually a period where it seemed it was getting banned from a new format every B&R announcement (first Standard, then Extended, then Magic Online-only formats).
That said, nobody knows for certain what impact it would have on Legacy or Modern because it was never legal in either format. Both of those formats are relatively new, and unusual in that they're popular tournament formats that are younger than (most of) their card pools. Because both formats started with a large card base, both formats also started with banlists that are somewhat speculative. It's tricky business because if they started with nothing banned, both formats would have been ruled by known broken decks for quite some time (what Zvi Mowshowitz termed "Oh Lord, Not Again"), so Wizards extrapolated from past tournaments in other, similar formats.
The result is that both formats have a number of cards that were "preemptively" banned in this fashion. Sometimes those cards get unbanned; Mind over Matter, Replenish, and Land Tax are apparently not as bad as they were in their original contexts. I doubt the same thing can be said for Jace, The Mind Sculptor/Stoneforge Mystic in Modern, or Mind's Desire/Yawgmoth's Bargain in Legacy.
While Skullclamp was never proven broken in current formats as such, it ruined Standard, eventually proved broken in Extended and was almost Vintage playable. It's also arguably a more resilient Glimpse of Nature (and certainly has a similar effect in the same decks), and that card is also illegal in Modern. It's almost certainly staying banned forever in Modern, and deservedly so, since that format is intentionally kept at a power level at or below the old Extended formats where we already established Skullclamp was too good. Legacy is fast enough that I can see an argument for unbanning it coming up at some point in the far future, but there's a danger of it becoming an automatic 4-of in every aggro deck and becoming an autowin against control. There's also the risk that it fits too well in a creature-based combo deck like Elves!, or that it combos too well with some other cards printed in the many years since it was ever legal in a non-Vintage format (Stoneforge Mystic? Puresteel Paladin? Scars block in general?) So I don't like its chances there either.
[^1] Technically there was one Magic Online "Modern" tournament, which I believe was open only to employees, where Jace was legal. But then the standard bannings happened and by the time the Modern banlist was finalized for the general population Jace was on it.
EDIT: After some more googling I dug up the development articles from when the banlists were new: Aaron Forsythe on Legacy and Tom LaPille on Modern. It's telling that neither felt the need to go into much detail justifying the banning. Its effect on Standard and Extended really was that bad.

This is a pretty good discussion of the issues involved with Skullclamp in the context of competitive play as a whole. Welcome to the site!

Jace TMS has been unbanned in Modern https://magic.wizards.com/en/articles/archive/news/february-12-2018-banned-and-restricted-announcement-2018-02-12

"It's tricky business because if they started with nothing banned, both formats would have been ruled by known broken decks for quite some time" It's worth contrasting this with the approach they took with Pioneer.

Rather than try to summarize Wizards' reasons for banning the card, have it in their own words: http://www.wizards.com/Magic/Magazine/Article.aspx?x=mtgcom/daily/af17
On the surface of things this may not look obviously broken, but honestly, in the right deck it's an engine that says "pay 1 mana: draw 2 cards".  As the article points out, at the time all the top decks were playing 4 Clamps; much as Jace, The Mind Sculptor just got banned for being ubiquitous at recent Magic tournaments.  When a card becomes a non-optional 4-of constituent of any competitive deck that hopes to win games, it has to go.

Considering the number of decks that benefit either from creature deaths or creatures in the graveyard, it can actually be "pay 1 mana, draw 2 cards and make your engine go"

@KRyan Or with Ashod's Altar, "gain 1 mana: draw two cards".

The way in which in grants the creature it is equipped to -1 toughness is the real selling point for it's degeneracy. That means that any one toughness creature dies immediately to it and lets you draw two cards as a result.
Turning it into a one colourless mana, repeatable version of Altar's Reap.
Couple this with any semi efficient token producer that produces one toughness creatures and things get nutty pretty fast.

Usually when a card is banned, I can figure out what the reason is,
  but for the life of me I can't figure out why this card is so
  dangerous. Its ability is good but not game-breaking, and I can't
  think of anything that it would pair with to become game-breaking.

WOTC actually gives a pretty good explanation as to why they ban cards.

One key to the continued health of Magic is diversity. It is vitally
  important to ensure that there are multiple competitive decks for the
  tournament player to choose from. Why? If there were only a single
  viable deck to play, tournaments would quickly stagnate as players
  were forced to either play that deck or a deck built specifically to
  beat it. In addition, different players enjoy playing different types
  of decks. If there are plenty of viable options to play, there will be
  more players at more tournaments.
To help maintain the diversity and health of the Magic tournament
  environment, a system of banned and restricted lists has been
  developed. These lists are made up of cards that are either not
  allowed at all, or allowed only in a very limited manner.

When you take this standard you ask yourself how does this card fit into this? In regards to diversity this card would kill all of it. Every deck would run four of this card and every deck would have to have a way to deal with this card. You would basically have a slightly different version of the Jace wars we once had.
This would mean that the colours with good early creatures and artifact removal would be the most competitive. Control decks would be efficiently killed as you would never want to not run this.
So by WOTC own standards of why they ban cards this card most assuredly fits the bill.

I've always had an issue with the banlists in general, yes the cards on there are EXTREMELY good but most can be dealt with. There might not be a super efficient way of doing so but there aren't many cards that can't be countered or destroyed... Ok you're running 4 Skullclamps? Let me counter that with Quash and I just took all of them out of the game. I know Skullclamps a 1 drop and quash is a 4 but there's always the chance they don't play it before then and even if they do....ok I cast Splinter, Exile Skullclamp from battlefeild and any that might be in your hand, graveyard, or library.

Every card can be responded to by: I can just use XXX to stop it. But you should ask yourself these things then: 1: Would I play XXX to decks that don't run that card? or is this specific hate neccessary? 2: What did the opponent gain by playing that card? Skullclamp is at very low mana and hard to stop before they got 2 cards from it. Making removal a card disadvantage. 3: Why is the restriction on putting that card in my deck? Skullclamp as a colorless card that requires only creatures can go into almost any deck that has creatures as base = too easy.

All the other answers explain really well why this card is broken. I just want to focus a little on how the R&D made this card.
The first version of what ended being Skullclamp was

Suicide Sweater
  (3)
  Artifact — Equipment
  When equipped creature is put into the graveyard from play, draw two cards.
  Equip 2

Which was a very bad card even in Limited; it then evolved in

Sac Sweater
  (3)
  Artifact — Equipment
  Equipped creature gets +1/+2.
  Sacrifice equipped creature: Draw two cards.
  Equip 2

Which was better, but was quickly changed to

Sac Sweater
  (3)
  Artifact — Equipment
  Equipped creature gets +1/+2. When equipped creature is put into the graveyard from play, draw two cards.
  Equip 2

Then the card was considered being OK and nobody changed anything.. until one day they decided to improve some of the equipment, as it was one of the features of the block. It was then changed to what was actually published and, because this change has been made at the very last minute, it wasn't tested before the actual print; also it was not considered worth testing because the developers had in mind the old version of this card, which was pretty bad.
Then, although the R&D quickly understood that the card was broken, people didn't realize immediately how powerful it was, so Skullclamp wasn't banned at the first ban list possible; after that, the meta had evolved in pro-Clamp or anti-Clamp decks and the ban in Standard and Block-Constructed was needed. It took a little more time but then it was also banned in Legacy.

Well, it took a bit more time to be banned in Legacy because Legacy didn't exist yet, as explained in my answer. ;)

Let's look at each ability:

Equipped creature gets +1/-1.

Normally, you wouldn't want to equip this to a creature with toughness 1 because that would cause it to die (as a state-based action). However, the next ability makes it desirable to do so:

Whenever equipped creature dies, draw two cards.

Equipping Skullclamp to a creature with toughness 1 gives you two cards at the cost of that creature...

Equip {1}

...and one mana. (Note that equip is sorcery speed.)
Considering that it's generally trivial to create 1/1 creature tokens, this is a small price to pay. Furthermore, equip is a repeatable action, so if you have some mana and a handful of these tokens on the battlefield, you could easily draw four, six, or even more cards. The result is an artifact whose combined effects are tantamount to this activated ability:

{1}, Sacrifice a creature with toughness 1: Draw two cards. Activate only as a sorcery.

In essence, in decks that use small creature tokens, Skullclamp nearly duplicates the effect of Ancestral Recall at only a marginally higher cost. To make matters worse, Skullclamp itself only costs one mana to cast and doesn't require any colored mana, making it usable in any deck.
This is a classic example of a design oversight resulting in a card that looks innocuous at first glance turning out to be seriously broken upon further inspection.

You don't even need a token generator. Get something like Gravecrawler, and you have "1B: draw two cards".

There is one small difference which is mostly nitpicky - sacrifice as a cost can't be responded to, equip as an effect which causes the SBA creature to die can. An opponent can kill the creature you're targeting with skullclamp's equip but not the sac a creature to draw 2 version.


text:
Restoring worn-out deck of cards.
Many board games have a special deck of cards and over time get worn out.
When they start to get worn out, they get "sticky" and difficult to shuffle.
Is there a way or a product that can be applied to a deck of cards to make them "slippery" again?

You need deck sleeves.
They should be available at your local game store, or from any number of online suppliers.  They are available in various sizes, so be sure to bring a sample card along while shopping (or measure it precisely before hand).
Online you can find lower quality sleeves for around 1 cent apiece in bulk.  Higher quality sleeves may cost upwards of 10 cents/sleeve.  The higher quality will give you a sleeve that shuffles much easier and can optionally have an opaque back.  (An opaque back is desirable if some of your cards are marked or bent due to heavy use).
Ultra-Pro and Fantasy Flight are two high quality well known manufacturers to ask for if you want somewhere to start.

I only have experience with the cheapest sleeves I could find, and while they are great for protecting my cards, they actually make it harder to shuffle. So if you want ease of shuffling, then follow Pat's advice and go for the slightly more expensive ones.

Aside from laminating your cards, card sleeves are your best bet. If the sleeves are rigid enough they also make it a lot easier to shuffle the cards. You can simply split the deck and push the two stacks into each other.

The only problems with the more expensive (and thicker) card sleeves is that it may make your deck no longer fit in its packaging.  I'm thinking more of Dominion cards than anything else here, but it applies to other card types as well.  P.S. I'm still kicking myself for missing a sale on deck sleeves at Amazon a few weeks ago.

Yes. They are gonna get thicker but that's the price you pay. You can still work around that by not using the inlay and storing them directly in the box with elastic bands. Or if you have the time resleeve & unsleeve before & after games...

I finally got around to buying some sleeves.  I'm surprised I've never heard of them up until I posted this question.  I was skeptical, but they are actually much easier to shuffle with then I expected.

In my experience, matte sleeves are the easiest to shuffle -- it's harder to riffle the deck, but do a mash shuffle (which gives you similar  avoids card bending) more easily than with unsleeved cards. Glossy sleeves (like the kind with fancy card backs) tend to stick together a bit more.

The stickiness of cards is typically just due one of two things, the surface of the card becoming rough or warped due to actual wear, or the build up of oils from contact with the fingers.  In the case of oils, which you can tell thats what it is because the cards still have a reflective surface, you can just use a damp rag (not wet) with soap on it, and give it 2 fast light swipes on each side, making sure to hit the corners and dry it off with a paper towel afterward.  You can also just take a hair dryer to them, in a spray paint motion where you never stop moving the airflow, then wipe them with a dry paper towel immediately.
I don't know of any products to return them to slippery state, but most games you can buy replacement parts for through the manufacturer, right down to individual cards that may have been damaged or destroyed.

There's an easier solution available for those who don't want to invest in new cards or sleeves which might not even match in size:
- When cards get sticky, put them in a plastic bag.
- Add some baby powder to the plastic bag.
- Shake vigorously for 5-10 minutes.
- The baby powder (be sure to use the kind made from only the highest quality babies!) will absorb the moisture and oil that has built up on the cards.
- Remove cards from bag, wipe individually with a cloth.
And that should fix ya!


text:
How do Mine and Watchtower Interact?
When playing Mine while having a Watchtower in hand, can you put the upgraded treasure card on top of your deck instead of in your hand?

Yes, you can.  The card you get from Mine is definitely gained, therefore you can react to it with Watchtower and put it on your deck (or trash it!) if you like.
There's not usually much reason to do so, but the cards don't actually conflict - you can use them both in this manner if you really want to.

Yes
From the Prosperity rules pg. 5:

Watchtower -
...
If a gained card is going
somewhere other than to your discard pile, such as a card gained with
Mine (from Dominion), you can still use Watchtower to trash it or put
it on your deck.

I think it's great that Dominion always includes blurbs in their rules for each card.  They seem to have anticipated most rules questions.

Yes
Mine says you are gaining a card.  Watchtower says you can reveal the Watchtower from your hand and either trash or put the gained card on your deck.
Found a game log reference on councilroom.com showing this exact situation:
bandito plays a Mine.
... trashing a Copper.
... gaining a Silver in hand.
... ... revealing a Watchtower and putting the Silver on the deck.
(bandito draws: a Silver, 3 Coppers, and an Estate.)

http://councilroom.com/game?game_id=game-20101207-185856-0ab1f05b.html