Tom Mackel
United States Redmond Washington

This expansion review assumes that you already have a working knowledge of the base game.
The differences are minor, yet have a major impact on gameplay. I think this is largely because the game is pretty simple to start with, so minor ripples have the ability to create major waves. I fairly enjoy the original, but I really don't like this expansion for these reasons.
As I see it, there are basically two changes worth noting to the game (in addition to the extra tiles and playing pieces). The first change is that players are allowed to build after any other player's turn. I think this change reduces the amount of pressure (and fun) on each player to use resources or trade resources during their turn, as the threat of the robber is almost completely gone. Just buy something when you get a hand of cards.
The second change is the addition of more players. During trade phases, every player tries to trade with the currently active player, and this results in a lot of conversations. With more players, there are more trade phases along with more players to barter with. Conclusion: The play time for a game of Settlers is exponentially related to the number of players. Adding more than 4 players makes the game run from a respectable 30 or so minutes into a nightmarish multiplehour game, in which you spend much time just waiting for your turn to roll the dice and trade with anyone.
Between these two changes, I don't enjoy the expansion at all. It feels stagnant. If you have 5 people who want to play, I think this is one of the instances where it's substantially more fun for one player to sit out and watch, or play as a "team" with someone else, than to play with 5 players. If you have 6 people who want to play, I'd suggest getting another copy of the base game and just running two 3person games of the original. The games will go faster, and you'll be able to swap up players between games to keep it interesting.


Travis Hall
Australia Brisbane Queensland

I don't find that there is really a lot of pressure to build to avoid the robber in fourplayer. In fourplayer, if I am holding enough cards in my hand at the end of my turn to put me in serious robberdanger, it is because I don't have the right combinations to use them. In fiveplayer, this still occurs, and it doesn't matter whether it happens in my turn or somebody else's. If I can't build, I can't build. And in either form, I would generally much rather have my new build on the board and ready to start producing as soon as I can. The exceptions are development cards and roads. Sometimes I want to hold a wood and a brick for a road until I am ready to build a second road or a settlement at the same time, so that I can ensure I won't waste my road when somebody beats me to the settlement. That's not terribly common anyway, though. And in fiveplayer, I may be inclined to hold off on buying a development card until the turn of the player before me. Again, I don't think that's a big deal.
As for the extra time required to play with more players, it certainly isn't an exponential increase. As a mathematician, I can tell you that trading time is theoretically a quadratic function, but that is unlikely to mean much to most. In practice, though, a lot depends on the attitude of the players. A group that recognises that the only meaningful negotiations involve the active player and allows that player to control the flow of negotiations shouldn't see trading take much longer than in the fourplayer game. Let the active player say what he has and what he needs. Players who can't work with that don't have meaningful input, and by trying futile negotations just add noise and time. Working this way doesn't really change the game but does reduce playing time. (That is so no matter how many players there are, but the more players, the more significant the improvement.)
Yes, Settlers does take longer with more players. However, if you are playing fourplayer games in 30 minutes, there is no reason 5player games should take more than 45 minutes. I have played torturous multihour 5/6player Settlers games, but the length has come from players who aren't really concentrating on playing the game at all.


Tom Mackel
United States Redmond Washington

I'd have to admit that I'm not unbiased, as there were two players in the one game of the expansion that I played with a tendency to take a long time on their turns.
In 4 player, there isn't a lot of pressure to build to avoid the robber, but the pressure is existent. By the expansion rules, there is virtually none.
I, like most players, would rather have my buildings on the board producing as soon as possible, it's good for me to be able to build between turns, but it's also good for everyone else. In fact it's just about equally good for everyone. It "smears out" the distinction between turns. "My turn" isn't really all that special in the expansion, might as well be anyone's turn.
I stand corrected on my analysis of the play time; given the information presented in my last post, the correct relationship between play time and number of players is quadratic, not exponential. The play time only becomes exponential if all players are permitted to discuss trades with all other players (which they aren't) on every turn. Hey, if you're a sharp mathematician, would you be able to provide me with your opinion on a somewhat difficult probability computation that I worked on a few months ago?
As I lost some geek status by using a mathematical term incorrectly, I'll attempt to redeem that geekness in triplicate here. I'd be okay with a math error, but I can't live with a terminology error haunting me for the rest of my days.
A more accurate assessment of play time is a cubic relationship. If there are N players, there are N turns per round. Each turn, 1 player may conduct N1 trading sessions. In addition, N players may build things every turn. This leads to a (N1)(N)(N), or approximately N^3, play time relationship to the number of players.
In the regular Settlers game, play time is quadratic (N^2N), as the rules do not permit building every turn. With this model, a 2 person game would take 2 time units to complete. Since we don't know what unit of time is being used, the time unit should be represented by a constant which scales this result. Let's add that into the model as K and call it (N^2N)K. Note that in this model, a 1 person game would take 0 time units. Even though a 1person game is absurd, the model should not have it taking 0 time units, so let's add in another constant C to the model and make it (N^2N)K+C. Okay, now we're set to go. A 1player game takes C time units, a 2player game 2K+C time units, a 3player game 6K+C time units, and a 4player game 12K+C time units. Now let's pick some reasonable values for K and C. I think a 3player game might take about 15 minutes, and a 2player game about 10. I have no empirical data to back up these time estimates, but I think they reflect the shortest of my shortest Settlers game experiences. If these time estimates sound reasonable, then we can let K=1 and C=8. By the models then, a 2player game takes 10 minutes, a 3player games takes 14 minutes, and a 4player game 20 minutes. I think K would be a bit larger if we used actual game playtime data to find it, using this model.
Building a similar model for the expansion results in (N^3N^2)K+C playtime, using similar reasoning. Using the same values for K and C, this model would state that a 5player game would take 108 minutes, and a 6player game would take 188 minutes. These results ARE accurate reflections of my only time playing the expansion.
So if you believe: Settlers of Catan playtime is quadratically related to the number of players, and Settlers of Catan, 56 Player Expansion playtime is cubically related to the number of players, and A 1player game doesn't take 0 time units, and Initial playtime estimates for 2 and 3 player games are within the ballpark, (10 minutes for 2 player, 15 for 3) then these math models are accurate models for predicting the game's playtimes. Results Summary, using the expansion when the number of players is 5 or 6... Number of PlayersPredicted Playtime (Minutes) 1 8 2 10 3 14 4 20 5 108 6 188
Geek me.
Even not considering the math, I just didn't have nearly as much fun with the expansion as I did with the regular game. That's really the bottom line.


Travis Hall
Australia Brisbane Queensland

I said that trade time will increase as a quadratic, not total play time. However, after looking at this as well, I believe total play time will still only increase as a quadratic, and certainly not as not an exponential.
Suppose T is the mean amount of time required to conduct all trades between two players in a single turn. As there are N1 trading partnerships which can form in a turn, mean trade time per turn should be T(N1).
Suppose B is the mean amount of time it takes for a player to conduct all of his builds in a turn. When each player can build in every turn, the mean build time per turn should be BN. There is no reason this should be multiplied for the number of trading partnerships. Being able to build in every turn doesn't allow you to trade any more often.
There will also be an amount of time per turn which is spent rolling dice, distributing rolled resources, trading with the board, and other such actions. This should not increase as the number of players increase. Call this A.
Mean time per turn should then be A+BN+T(N1).
If the same number of rounds of play are required to reach a conclusion, total play time should then be given by the expression ARN+BRN^2+TR(N1)N, where R is the mean number of rounds played  still only a quadratic.
However, even that may well be an overestimate. In a larger game, the average amount of resources being produced per turn is greater (more players with more settlements/cities on more hexes with an additional copy of most numbers). Each individual players' production will be about the same regardless of the number of other players in the game. The amount of resources needed to win (achieve 10 VPs) is relatively constant. So, the game should end in about the same number of total turns. R should be inversely proportional to the number of players.
So the actual increase in play time may well not be much more than a linear function.
I would predict some extra increase in playtime because there are still only 9 VPs available from development cards, longest road and largest army, and R varying with 1/N doesn't account for that, but I don't see that the model should be cubic.
You can plug some numbers into that, if you like, and see what happens.
(For regular 4player, we see the expression A+B+T(N1), and on from there.)
And I don't know about me being particularly sharp, as mathematicians go  I've got the piece of paper from uni, but I don't work in the field, so I am rusty in a lot of areas  but probability theory was my specialty, so you can question me about that if you like.


Travis Hall
Australia Brisbane Queensland

Oh, and a couple of other things... Even if all players trade (or at least discuss trades) with all other players in every turn, that still only makes trade time (and thus total play time) cubic, not exponential. A cubic function is a type of polynomial, not exponential.
And my point about building immediately being better is that this principle means I am already motivated to build as soon as I can in 4player, so robberfear doesn't do anything other than make me want to do what I want to do even more. In 5player, there will be a slight decrease in the number of times I get robbed, because there is a certain situation (can't build in my turn, gain resources I could use over 7 in another player's turn, get robbed before my build returns) that no longer occurs. However, "can't build in my turn, gain resources over 7 I still can't use, get robbed" still occurs, and "can build in my turn" produces the same response from me.


Tom Mackel
United States Redmond Washington

I'll buy the argument that the trade time shouldn't be multiplied by the build time. I'm also convinced that the game mechanics don't lead to an exponential play time increase with the number of players. It only feels that way. Another game mechanics model revision might go as follows:
In the original game, if there are N players, there are N turns in a round. In a single turn, there's some dice rolling, resource distribution, etc. Let's represent this time with the constant, A. There's also a trading portion of the turn, in which the active player conducts up to (N1) trading sessions between 2 people of mean time T per session. The player then builds, with mean time B. Turn time is then A+B+T(N1). Let us also assume that the game ends in a constant number of turns, K, an assumption not included in my previous model. The entire game would then take K(A+B+T(N1)).
The expansion would follow the relationship K(A'+BN+T(N1)). It can be argued that A'>A due to the fact that it takes longer to find which resources have been rolled on the larger board, and there are more resources to distribute.
Both models, let's call them game mechanics models, have a playtime which is linearly related to the number of players. The exponential comment in my previous post wasn't meant to apply to the same models. Let's challenge the trading time assumption. Trading sessions involve a number of events outside of the scope of the game mechanics. The result of a trading session is included in the models, but not the process of obtaining that result. The process would include each player considering all possible combinations of trades which (s)he can conduct (2way, 3way, 4way, 5way, and 6way). The mean trading time between 2 players, T, is no longer a valid representation of the mean time spent in the trading phase, since the active player must consider all of these combinations of multiway trades. T is not simply a constant, since it depends on the number of players. Let P(n,r) be the number of permutations of size r from a set of size n. T is the sum over i from 2 to N of P(N,i), a factorial function.
I'll send you a message with that probability problem that I faced in it; I think I found "a solution", but I would like someone more mathematically inclined to support it.


Travis Hall
Australia Brisbane Queensland

It might be valid to argue that it takes a little longer to distribute resources from a larger board, but this certainly won't be more than a linear increase with the number of players.
Once you start seriously considering multipart trades (remember, by the rules any trade involving more than two players has to really be broken down into a series of twoplayer trades), you have to remember that the circumstances in which a multipart trade is really viable is relatively rare. Thus, a smaller amount of time is spent considering such larger trades. In practice, I have never seen a true 4way trade, and I only see 3way trades maybe once every halfdozen games on the average. And don't forget, 3way trades occur in 4player games too. (Actually, 3way trades may well be more common with 4 players than with 5, because there will be a higher probability of being able to trade for what you need with only a single player  advantageous because it shuts another player out of the trading.) Also, there is a practical limit to the size of trades due to the limited resources. With only five different resources, there is only so much that potential trading partners can bring to the table, and those without a unique resource can often be discounted without real negotiation.
So while in theory you could regard play time as reaching a higherorder polynomial, in terms of practical modelling it isn't really going to be higher than a cubic  and even then I would expect the cubic term to have a low coefficient. Unfortunately, you now have enough coefficients in the formula that you can't extrapolate from playtime estimates for 2, 3 and 4 players up to 5 players, unless you do indeed assume the highest coefficient to be small in which case you are back to a quadratic model.
I can, though, understand your disappointment when the expanded game took close to two hours to play the single time you played it. The game just isn't worth two hours of your time or mine. However, I think the assumption that the long playtime is due to the expansion itself is unwarranted. I've played 6player games in under an hour, and the people I play with are, I think, significantly slower than what you describe for your group even in 4player. With a larger group, though, the social dynamic often changes, and players may be more likely to become distracted by conversation not relating to the game  especially since there is a natural human tendency to socialise in groups no larger than 5, so in a 6player game you wind up with two conversations going on over the board, and only the players involved in the active player's conversation stay fully aware of the situation in the game. In other words, the other half of the board sometimes don't notice that a new turn is starting!


Tom Mackel
United States Redmond Washington

I can agree with that. Most of the game delay isn't caused by the game mechanics itself, if you have serious players not chitchatting much, it's sure to go by faster. Theoretically, the game can get much longer with more players added. A model which included the higher order terms is pretty likely to have small coefficients on those terms.
However, there are the "human social factor" interactions which were not added in, and while I do sometimes like to talk to people, too much chit chat and not enough playing helps to make the game more irritating.


Tim Kilgore
United States Sturgeon Missouri

I just had an opportunity to use the 56 player expansion for the first time this weekend, play a pair of backtoback 5 player games.
I personally didn't think that the game played that much differently from the original. In the second game we elected to monkey with the rules; instead of being able to build at the end of each players turn, we placed a pair of "invisible players" at opposite ends of the table and allowed building to occur whenever the game arrived at the position of a virtual buddy.
We did this largely because it something of a drag on the game to stop and ask if anyone had any building that they wanted to do at the end of every turn. By adding set positions, building was almost always done by someone and the game felt like it was flowing a bit more naturally.
I should also mention that my group follows the game pretty closely; they tend to know if a given resource is available and very little time is spent trading for an unavailable or scarce resource. There is also very little megadeal brokering, so it is rare that a trade round takes more than 15 seconds or so to conclude.
Tim



