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Subject: Buildings too strong? rss

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Danny O'Donnell
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jgsugden wrote:
There is also the times when you use the building you own, meaning that there is no excess benefit going to any other player that round.

The thing I like about this whole discussion is what it pointed out to me about using your own buildings:

If I buy a 4 cost / 6 VP benefit / 2 VP owner benefit building on turn 1 and I never use it (but it is used 8 times), I get 9 VP of surplus benefit. 1 agent placement, 9 VPs. The other players spend 8 activations for 16 bonus VPs for an average of 2 VPs per agent placement.

If I buy is and use it 8 times, I get 17 VPs benefit and spend 9 agent placements - meaning I average 1.9 VPs per agent placement.

In other words, you are reducing you advantage per activation by using your buildings. Nifty. Of course, this does not mean that using your own building may not be the best move at certain times - it just - in some ways - undercuts the efficiency of you purchase.


I can kind of get behind some of your math in this topic, but this is completely bogus. The actual math isn't wrong, but what you're comparing is 'average effeciency of agents whose actions involve the building I built', which is a totally pointless statistic. Unless there's another building tile you can play on, there's absolutely no difference between placing on a basic building for 1 unit and then getting your owner benefit for .5 units or just placing on your own building for 1.5 units. In fact, you're probably better off placing on your own building to deny the other players the extra resources (assuming, of course, that all these resources are equally useful to you, which is the basic assumption of all of this math).

I hadn't realized the all the unit equivalencies in the game I played, though. Made me rethink the intrigue card that gives other players the chance to give you fighters for 3 VP each. If I don't think that player's my main competition, I should usually do it.
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Mikko Karvonen
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jgsugden wrote:
Let's say I put a 4 cost building into play on turn 1 that is NOT one of those progressive buildings. I immediately get 1 VP. I give up 1 agent placement and 4 gold. At that point, I'm down 7 VPs effectively, but I get back 2 VPs every time the building is used. If it is used 8 times, I go bac to +9 VPs.


How do you figure this? If you ignore the cumulative buildings, there are 5 4-cost buildings that give the owner 2 gold benefit, and one that gives fighter/rogue benefit, and those certainly don't convert to 2 VPs.

In fact, there are only two buildings that match your description: Heroes' Garden (instantly complete quests for 4 extra VPs), and The Palace of Waterdeep (Ambassador). I can't really see either of them being used 8 times - using Palace on the last round would even be sheer folly. In addition, with Heroes' Garden you'd actually be losing in comparison to the player who uses it, who by all probability gains 4 extra points to your two.
 
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John Sugden
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Gargoyle wrote:
jgsugden wrote:
Let's say I put a 4 cost building into play on turn 1 that is NOT one of those progressive buildings. I immediately get 1 VP. I give up 1 agent placement and 4 gold. At that point, I'm down 7 VPs effectively, but I get back 2 VPs every time the building is used. If it is used 8 times, I go bac to +9 VPs.


How do you figure this? If you ignore the cumulative buildings, there are 5 4-cost buildings that give the owner 2 gold benefit, and one that gives fighter/rogue benefit, and those certainly don't convert to 2 VPs...
In this game you gather resources and push them through quests into victory points. There is a fairly steady conversion rate of resources into quest points. 2 gold translates into 2 vp. 1 rogue = 2 vp. 1 fighter = 2 vp.

Look at the non-plot quests that provide more than 0 points. Then look earlier in the thread for the discussion of equivalent costs. Recheck the math and you'll see that DURING the game (not during final scoring, but while using quests to get points), the resources you mention certainly DO equal 2 VP.

As for another poster's quest - what if the building is not used 8 times? On the surface, it is obviously superior to use a building space for your own purposes because it provides more resources. Why pass up more resources to gain less resources, especially when I can save those resources (if I do not have a need for them now, I can use them later).

There is a Prisoner's Dilemma issue here that points towards someone using the building. Although the builder would get screwed a bit by a buiding not getting used one turn, the benefit to the opponents for using it rather than a board location give them all a strong incentive to do so... and if they do not, the builder can still use it.

Will all buildings get used every turn if out? No. Progressive buildings will not and there are 6 of them. The Stone House, Palace of Waterdeep and Heroes Garden will not be used each turn. However, here are ten 3 or 4 cost buildings and five 8 cost buildings that are so beneficial that they will get used pretty much every time UNLESS you have a ridiculous number of buildings out and there are too many 'high value' locations for the agents not devoted to a specific purpose (such as getting quest cards) to make use of them all OR players are devoting resources to a quest that muct be completed early to be highly useful (like the Lieutenant quest).

So - if there are 9 buildings in 24 that are not likely to be used every turn and 5 more that are too expensive to be purchased by the first player, why do I assume that you'll almost always have access to a building that does get used every turn when you go on turn one? There are three buildings drawn out of the build stack at the start of the game and the odds of not drawing a useful one are pretty slim.

In a 2, 3 or 4 player game the chance that none of the 3 or 4 cost good buildings will be drawn in those first 3 buildings is ~25%. If it doesn't come out turn one, many of the other buildings are still worth buying, even if they are less likely to get you the full value of being used 8 rounds in a row. If they do, the good 10 buildings are likely to appear at some point in the first few rounds and they will still be worth a net 5, 6 or 7 VPs in value if used when they come out.

In a 5 player game, the first four players might decide to pass on building if there are none of these 10 good buildings out there - but the 5th player will have the 8 coins needed to buy an 8 cost building on turn one. The chances that none of those 15 buildings comes up in that game is only ~5%.

It all comes down to this, at least as it relates to buildings:

Early (good) buildings, which are very likely to be available, provide a substantial advantage in terms of resources that - through reasonable quest acquisition strategies - can be translated into quest points efficiently in most games to create a 9 VP advantage if purchased on turn 1. Additionally, you're usually better off not using your own buildings when they are out if there is another move to be made that provides more than 1 unit of resources in exchange for your agent, including using other buildings or using the harbor.
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Mikko Karvonen
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jgsugden wrote:
In this game you gather resources and push them through quests into victory points. There is a fairly steady conversion rate of resources into quest points. 2 gold translates into 2 vp. 1 rogue = 2 vp. 1 fighter = 2 vp.


Ah, yeah, my bad there. For some reason I thought that the ratio was cleric/wizard being 2 points, and the others being 1 VP. Shouldn't write forum replies before having my morning cup of tea blush

jgsugden wrote:
There is a Prisoner's Dilemma issue here that points towards someone using the building.


This is bit of a tangent, but I really must take an exception to this. This is most definitely not a Prisoner's Dilemma situation. The players are not making their decisions simultaneously, not knowing the decision of the other, there are far more options available than simply to use the building or not to use, and the pay-outs are simply wrong. There is no big punishment or big reward, nor is the equilibrium result neither player using the building.

Other than that, I think I've got nothing more to add to this discussion. Your basic math is of course correct, but you keep ignoring so many things and points that affect how the game actually plays out that there is very little to learn here. The main lesson from all these calculations is probably that often you are better off not using your own buildings, but even that principle cannot and should not always be followed in practice, if you are actually trying to get quests completed - or trying to keep others from completing theirs.
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John Sugden
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RE: Prisoner's Dilemma.

It is not exactly a true PD situation, but the decision making situation is similar. Some people would say it is in the PD family. Although the decision making is not simultaneous (so few are), there are similar incentives and similar levels of unknown information when people make decisions.

Example: Player 1 builds a 4 cost building that provides 6 VP worth of resources when you use it and 2 VP of owner benefit. When it is player 2's turn, he doesn't know what players 1, 3, 4 or 5 will do over the rest of round 1. Even if they promise not to use the building, he doesn't know that to be true.

If all players pass on the building, player 1 loses out on the owner benefit and player's 2 through 5 gain a relative advantage to player 1.

However, every person looking at that board sees the same thing: If I use the building I get more resources than any other option on the table. As such, it is the best option for each player. The chances of all players passing on using it are slim. Thus, the owner and whoever uses it will come out ahead of the other players as they each get surplus value and the other players do not.

As such, player 2 might as well use it as there is little chance that it isn't going to be used by someone. Not true PD, but from the persepctive of a player decising what to do, the core argument of PD is there: If I can get collusion by all the players we can get a good situation (for all the players except the builder), but if someone breaks I'll suffer - unless I am the one that breaks. Either the owner loses out and everyone else gains an advantage relative to the owner, or the owner and whoever uses the building get an advantage.

The payouts are not quite the same as in PD, either, but the payout ratios have similarities to true PD:

If I use the building I know I am going to end up on the winning side fo the equation. If I do not, I could end up being one of the ones that is disadvantaged. Thus, even though the better relative advantage is found in nobody using the buildings (and we significantly undercut the value of the building if the owner uses it all the time), the individual incentives drive one of the other players to use it.
 
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Danny O'Donnell
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jgsugden wrote:
If I use the building I know I am going to end up on the winning side fo the equation. If I do not, I could end up being one of the ones that is disadvantaged. Thus, even though the better relative advantage is found in nobody using the buildings (and we significantly undercut the value of the building if the owner uses it all the time), the individual incentives drive one of the other players to use it.


Now you're really reaching. Unless the player is going to be able to use every single one of his agents on other players' buildings, avoiding his building doesn't hurt him at all. It lowers his 'benefits from that building/actions used on the building' ratio that you seem to be hung up on now, but that ratio means absolutely nothing in the context of the actual game. If everyone avoids the building, the owner is almost certainly going to have to choose between his building and a basic building. And he doesn't do any better taking the basic building and hoping someone else uses his building later. In fact, it denies someone else the extra resources, so it's generally the better move.

You're concerning yourself so much with the efficiency of that one agent that you're seeing lowering the efficiency of other agents as somehow better than lowering the efficiency of that one. I don't know how you can look at the choice between using a basic building and having your building used by someone else and using your own building and conclude that using the building yourself is worse somehow.
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John Middleton
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Your assumption that players will use your buildings is just false.

In many games I have seen players deliberately pass up certain players buildings because they did not want that player to receive the owner's benefit, to include them taking spaces that provided less resources.

This leaves the player with the choice of using their own building so that they at least gain some benefit from it, ASSUMING they need the resources that the building provides and are not just stock-piling for future, possible needs.


All your analysis relies on all players wanting what you have for sale, and not on the important resources for that that particular game. Anyone that has played this game multiple times knows that different resources are valued differently from game to game and that a space that is contested hotly in one play, can be practically valueless in the next.

Add to this the random nature of the buildings available, the random order they appear in, and the fact that you may not be the one to build them anyway, and your entire formula comes down to "Build buildings early and try to make players use them." And that is a pointless stance since nothing in your arguments supports that the are overpowered or even that if you build them early that you will win more often than never building a thing.

You do like to argue lost causes though...
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Cameron Chien
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YellowLab wrote:
Without buildings and their owner rewards this game would blow.
I have tried to follow the OP's math and as many people have stated, I think it is flawed. It has been said in other places, LoW is not a heavy game. If this type of analysis is important to you and you need it in a game, LoW is likely not the game for you. If you need some complex non-linear economy, LoW is likely not for you. This is a lite worker placement game that is loads of fun. If that is what you are looking for, just play the game. Or not.

I think he's having more fun analyzing Lords of Waterdeep than actually playing it.

John, while you apparently can't come to grips with this, I will repeat what others have already said many times: Your math is fine, it's when you start factoring in the other players' actions where your conclusions become IRRELEVANT. Here's a few examples:

1. Intrigue cards. Not only do most of the cards affect your opponents, you also usually get to reassign the agent. How do you factor for that?
2. Turn order. This is especially important if you think buildings are OP. how do you factor for if someone else takes the Start Player token and then you have to go get it back?
3. King bashing, or "players who don't think like you do". Players will frequently choose to avoid using a building just so they don't give the owner the reward (heck, sometimes you'll be forced to use your own building). They may decide to give someone a Mandatory Quest based on perceived values you don't agree with.
4. Number of players. There's a big difference when you are in a 5 player game and only start with two Agents and a two player game where you start with four.
5. It's not zero-sum. Even if your building was used eight times (or more) in one game, it changes things if it's one player frequenting it every round or if all of your opponents used it evenly.
6. Different actions change in value based upon your Lord. If your Lord rewards Warfare and Skullduggery quests, then orange and black cubes are more likely what you will need. If someone else wants Warfare quests, then I may be in competition with them, which also throws your conclusions out of the window.

[Edit] In case this is tl : dr, I leave you with this thought:

"Playing the most efficiently is not mutually inclusive of winning at Lords of Waterdeep."

Maybe you just want to be the most efficient and you don't care about winning, and maybe that's why most people are having such a disconnect with your fascination with assigning values to things in this game. [/edit]

Cameron
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Andrew Bird
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Zeede wrote:
I think he's having more fun analyzing Lords of Waterdeep than actually playing it.

Replace "Lords of Waterdeep" with "games" and you've described 50% of this site's membership.
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Marty Kane
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I give O.P big thumbsup for his enthusiasm in analyzing this game. And I've played a few games where an early building that was generally attractive provided a big advantage. Though it makes a big difference whether players are competing for the resource provided or not.

I think the buildings are balanced just right, with some inner variation in power.
 
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Ben Hodgson
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PsychoDan wrote:
Unless there's another building tile you can play on, there's absolutely no difference between placing on a basic building for 1 unit and then getting your owner benefit for .5 units or just placing on your own building for 1.5 units. In fact, you're probably better off placing on your own building to deny the other players the extra resources (assuming, of course, that all these resources are equally useful to you, which is the basic assumption of all of this math).


By adding your illustrious buildings to Waterdeep you bump the efficiency of your actions up. If you take your own building, the efficiency per action is greater (about 1.5 say) but if someone else takes it and gives you 0.5 you hopefully get 1 from your regular action anyway - more likely if nice buildings have been added! Great - average 0.25 gain per action per building. Taking them yourself gives you the best outcome (denying others the building) provided they are good resources for you, but as you have an agent limit this is not always possible.

If another player exclusively takes advantage of your building then they will also be getting an increase, but at this point you can take the building yourself to edge ahead. Also, as players are tend to fight over the efficient buildings, it may not be so much of an issue - so making sure that all your buildings are getting used keeps adding to your own efficiency whilst hopefully spreading out amongst other players. e.g. If you have three buildings that 3 different opponents use, they each gain 0.5 (1.5 minus the basic action efficiency of 1) compared with your 1.5 gain (from each 0.5 owner reward).

The next thing is about what buildings to construct, and this has a few points.
1. The basic actions of the game underpin the value equivalencies of the OP, and the buildings you add to Waterdeep distort these. i.e. Buildings that produce more mages will make mages easier to acquire and start to reduce the 'time cost' of any quest (mainly Arcana but also others) requiring that cube type. So good for you if those are the quests you have been taking!
2. Second, when you build it stops someone else doing so (except for the building that bypasses placement ) so it can hinder their ability to facilitate their own quest development.
3. If you are aiming at a narrow set of quests (say just your Lord bonus), then getting the right buildings can be tricky. However, if the Lord bonus 'directive' is only followed when convenient, a more flexible approach is more likely to interact favourably with buildings in play. I don't know how well this works having not played enough (i.e. I'm not sure how much you can ignore your lord), but there are quests that give you 2vp per a particular quest type (half a Lord bonus), which can help you go outside your usual quest remit.
4. If you flood Waterdeep (!) with buildings that nobody uses (too many) then this is wasting your actions and resources. Your buildings need to be appealing.

I guess this boils down to making your actions more efficient and matching your efficiency resource gains to your quest ambitions whilst spreading any resulting gains to other players between them.
 
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Morten Friis
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So, after reading this thread I decided to do some math (yay!). The calculations below are obviously overly simplified, but hopefully they'll help shine some light on the whole thing. Fist of all, in all calculations I assume that the first player will buy a building as his first action (with the assumption that early building is the optimal strategy) and that no more buildings will be built for the remainder of the game (the benefit of the building should be even clearer with just a single one in play). Second of all, I assume that the building is a basic 4 cost, 1 agent to 1.5 units benefit building. Third of all, I'll assume that there will always be spaces available that provide 1 unit for each agent placed. Following are the calculations for a 2 player game that will take into account three different scenarios:

Quote:
Round 1
A: Build; 1 agent + 4G (2 units) -> .25 unit
B: Use building; 1 agent (unit) -> 1.5 unit (and +.5 for A)
A: Any resource space: 1 agent (unit) -> 1 unit
B: Start; 1 agent (unit) -> .5 unit
Remaining actions in this round are even propositions - 1 agent -> 1 unit. At the end of the round, A will have 3.75 units and B will have 5.25 (including the 5G he started with).

Case 1: A never takes back start player, no more building built
The remaining actions will be even propositions. Player B will have a slight advantage of 1.5 units.


This obviously indicates that A should try to reclaim the start player token - we'll consider case 2:

Quote:
Case 2: A takes back start player, no more buildings built
Round 2
B: Use building; 1 agent (unit) -> 1.5 (unit) (and +.5 for A)
A: Start; 1 agent (unit) -> .5 unit
Remaining actions in this round are even propositions - 1 agent -> 1 unit. At the end of the round, A will have 7.75 units and B will have 9.75.


We now consider two sub-cases:

Quote:
Case 2.1: B never takes back start player
Starting from round 3 and onwards, A will get .5 extra units compared to B per turn, 3 in all over the remaining 6 rounds. A will have a slight advantage of 1 unit at the end of the game.


From case 1 and case 2.1 we see the importance of being first player in a round, when a building has been built. As a result, we assume the optimal strategy for both players is to take back the start player token if the building has already been taken, so we consider case 2.2:

Quote:
Case 2.2: A and B will take turns taking the start player.
Round 3
A: Use building; 1 agent (unit) -> 1.5 unit
B: Start; 1 agent (unit) -> .5 unit
Remaining actions in this round are even propositions - 1 agent -> 1 unit. At the end of the round, A will have 12.25 units and B will have 13.25.

Round 4
B: Use building; 1 agent (unit) -> 1.5 (unit) (and +.5 for A)
A: Start; 1 agent (unit) -> .5 unit
Remaining actions in this round are even propositions - 1 agent -> 1 unit. At the end of the round, A will have 16.25 units and B will have 17.75.

This pattern continues (For simplicitys sake, I assume there will still be enough 1 agent -> 1 unit placement even after each player gets an extra agent, though there won't. This doesn't matter since they take turns being the starting player with an even amount of turns remaining).
Round 5: A will have 20.75 units and B will have 21.25
Round 6: A will have 24.75 units and B will have 25.75
Round 7: A will have 29.25 units and B will have 29.75
Round 8: A will have 33.75 units and B will have 33.75


All in all, buildings seems pretty balanced in a two player game, from a purely mathematical point of view. Lets consider a 3 player game instead. In the first case, we'll assume that it is always best to be the first player:

Quote:
Round 1
A: Build; 1 agent + 4G (2 units) -> .25 unit
B: Use building; 1 agent (unit) -> 1.5 unit (and +.5 for A)
C: Start; 1 agent (unit) -> .5 unit
Remaining actions in this round are even propositions - 1 agent -> 1 unit. At the end of the round, A will have 2.75 units, B will have 4.75 and C will have 4.

Case 1: First player takes the new building, second player takes start player (remaining actions are even propositions)
Round 2
C: Use building; 1 agent (unit) -> 1.5 unit (and +.5 for A)
A: Start; 1 agent (unit) -> .5 unit
At the end of the round, A will have 5.75 units, B will have 7.75 and C will have 7.5.

Round 3
A: Use building; 1 agent (unit) -> 1.5 unit (and +.5 for A)
B: Start; 1 agent (unit) -> .5 unit
At the end of the round, A will have 9.25 units, B will have 10.25 and C will have 10.5.

Round 4
B: Use building; 1 agent (unit) -> 1.5 unit (and +.5 for A)
C: Start; 1 agent (unit) -> .5 unit
At the end of the round, A will have 12.75 units, B will have 13.75 and C will have 13.

This pattern continues, and as before I assume there will be enough 1 agent -> 1 unit spots on the board (though there obviously won't, and this time it won't even itself out)
Round 5: A will have 15.75 units, B will have 16.75 and C will have 16.5.
Round 6: A will have 19.25 units, B will have 19.25 and C will have 19.5.
Round 7: A will have 22.75 units, B will have 22.75 and C will have 22.
Round 8: A will have 26.25 units, B will have 25.75 and C will have 25.5.


Again, it seems pretty balanced, but with a slight advantage to player A. Lets now consider the cases where player A (who owns the building) and one of the other players (in this case C) fights for the start player token while B plays his own game:

Quote:
Case 2: A and C takes turns taking the start player (similar to the 2 player game). Even rounds, A gains 3 units and C gains 3.5 units. Odd rounds, A gains 3.5 units and C gains 2.5 units. B gains 3 units each round.
Round 2: A will have 5.75 units, B will have 7.75 and C will have 7.5.
Round 3: A will have 9.25 units, B will have 10.75 and C will have 10.
Round 4: A will have 12.25 units, B will have 13.75 and C will have 13.5.
Round 5: A will have 15.75 units, B will have 16.75 and C will have 16.
Round 6: A will have 18.75 units, B will have 19.75 and C will have 19.5.
Round 7: A will have 22.25 units, B will have 22.75 and C will have 22.
Round 8: A will have 25.75 units, B will have 25.75 and C will have 25.5.


Almost too close to call. Lets consider a final case where player A lets the other two players fight for the start player token:

Quote:
Case 3: B and C takes turns taking the start player. Even rounds, B gains 2.5 units and C gains 3.5 units. Odd rounds, B gains 3.5 units and C gains 2.5 units. A gains 3.5 units each round
Round 2: A will have 6.25 units, B will have 7.25 and C will have 7.5.
Round 3: A will have 9.75 units, B will have 10.75 and C will have 10.
Round 4: A will have 13.25 units, B will have 13.25 and C will have 13.5.
Round 5: A will have 16.75 units, B will have 16.75 and C will have 16.
Round 6: A will have 20.25 units, B will have 19.25 and C will have 19.5.
Round 7: A will have 23.75 units, B will have 22.75 and C will have 22.
Round 8: A will have 27.25 units, B will have 25.75 and C will have 25.5.


I know I've made some crucial simplifications, but overall it seems to me that buildings are actually pretty balanced - even from a purely mathematical point of view, which would require the building to be taken every single time, without exception, and that fact that players would most likely have to completely disregard their actual adventurer needs and miss out on great quests available.
 
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Jeff Hannes
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Okay, I know I'm late to the party here, but I'll give you one very simple example of why math alone cannot tell the whole story. I'll use your math to help illustrate it.

Here's the situation. Let's say it's a 5-player game. On turn 1 I build a House of Good Spirits (costs 3 coins, gives the occupier a Warriors and any other adventurer, gives the owner a Warrior). I've spent 1.75 actions to get the building into play.

Let's assume the other four players each use my building twice each. I gain 8 extra warriors, or 4.00 actions. So my net gain is 2.25 actions. Assuming every player who uses my building takes a cleric or a mage to go with their warrior (the better deal), they get a net gain of 2 warriors, or 1.00 actions. Let's say I even put all eight of those bonus warriors I received to use to complete quests. So strictly speaking, that building puts me 1.25 actions ahead of every other player. HOWEVER...

In this case you MUST take into consideration the availability of clerics and mages in the game from other sources. Suppose this is the ONLY building that comes up which provides Clerics (other than The Plith, which is printed on the board). By building this building (and never using it), I have injected as many as 8 additional clerics into the game for the other players. This is going to make it much easier for players to complete quests requiring clerics, and will be a serious boon to someone who has a Lord that gets bonus points from those quests.

So in that case I've gained 1.25 actions on every single player, but they are now completing quests that they would have had no shot at completing otherwise. With 24 buildings to choose from, an average of 8-10 coming into play and the order in which they enter play being completely variable, the varying requirements of drawn quests, and whether or not players have lords which lean more heavily towards quests requiring clerics or mages... there's absolutely no way to quantify the value of a building just using straight action value.

Now all that I said, I will agree that more often than not, the best play for the starting player at the start of the game is to buy a building. Because it will almost certainly get used 8 times (by you or other players), so you will get a good return on investment. However, consider that you will only get 1 VP for building it, whereas whoever builds the second building (assuming it's on round 2) could get 2 VP, and whoever builds the third could get 3 VP. Also consider the offset that the starting player starts with less money.

So while I do think early buildings are a very wise and reliable investment, they are hardly game-breaking. And in a 4+ player game, using your first action to build a building could cost you the opportunity to play an Intrigue card that turn.

Also, by limiting yourself strictly to math, you are ignoring the relative value of action spaces. The whole point of worker placement games is that not every space has equal value. Some are better than others at certain times, and the keys to doing well in almost any worker placement game are: 1. recognizing which spots are better and 2. getting to them before the other players. So even if it bears out that the building spot is the best action in the early game, you have to make the decision to go there, and if you're not first and want to build on turn two, you'll then have to spend one of your first-round actions to take Start Player. And even then you're going to have to weigh the decision of when to take start player versus when others might take it. This could lead to suboptimal actions, and it may end up bearing out that the person who just focuses on resource collection gets off to a better start and is able to parlay that start into an advantage throughout the game. But as I mentioned above, because of all the random variables, these decisions are going to be different every game.

I think the real problems people are having with this thread is the title. First, it should be "Are EARLY buildings too strong?" Since I think everyone can agree that we're only talking about the effectiveness of buildings built in the first few rounds. Second, the title poses a question, but you're not really asking. You're posing a theory as near fact.

But either way, I feel comfortable enough in my opinions to give an answer to your question:

No, I don't think buldings OR early buildings are too strong. Strong? Yes. Too strong? No. If the ONLY winning strategy required the first turn start player to buy a building with his or her first action in every game played, you'd have an argument. But I have a very hard time believing you'd be able to ever prove such a hypothesis.
 
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David
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Hey Morten,

Thanks for the analysis, but could you please avoid using the C(ode) markup on long lines with no line break? It really screws up the formatting of the whole page.
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Morten Friis
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ScoobyG wrote:
Hey Morten,

Thanks for the analysis, but could you please avoid using the C(ode) markup on long lines with no line break? It really screws up the formatting of the whole page.
Sorry mate, didn't think about that as it wasn't a problem on the monitor I used. Changed it to quotes instead.
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David
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Much better thank you
 
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jgsugden wrote:
RE: Prisoner's Dilemma.

It is not exactly a true PD situation, but the decision making situation is similar. Some people would say it is in the PD family. Although the decision making is not simultaneous (so few are), there are similar incentives and similar levels of unknown information when people make decisions.

Example: Player 1 builds a 4 cost building that provides 6 VP worth of resources when you use it and 2 VP of owner benefit. When it is player 2's turn, he doesn't know what players 1, 3, 4 or 5 will do over the rest of round 1. Even if they promise not to use the building, he doesn't know that to be true.

If all players pass on the building, player 1 loses out on the owner benefit and player's 2 through 5 gain a relative advantage to player 1.

However, every person looking at that board sees the same thing: If I use the building I get more resources than any other option on the table. As such, it is the best option for each player. The chances of all players passing on using it are slim. Thus, the owner and whoever uses it will come out ahead of the other players as they each get surplus value and the other players do not.

As such, player 2 might as well use it as there is little chance that it isn't going to be used by someone. Not true PD, but from the persepctive of a player decising what to do, the core argument of PD is there: If I can get collusion by all the players we can get a good situation (for all the players except the builder), but if someone breaks I'll suffer - unless I am the one that breaks. Either the owner loses out and everyone else gains an advantage relative to the owner, or the owner and whoever uses the building get an advantage.

The payouts are not quite the same as in PD, either, but the payout ratios have similarities to true PD:

If I use the building I know I am going to end up on the winning side fo the equation. If I do not, I could end up being one of the ones that is disadvantaged. Thus, even though the better relative advantage is found in nobody using the buildings (and we significantly undercut the value of the building if the owner uses it all the time), the individual incentives drive one of the other players to use it.


It's a stretch to call this a PD. Before continuing I want to make a few claims; they are general, and therefore will not apply to every situation in a game, but moreso to an average game state.
1) There are 3 cases for a buildings payout: Building is not used, building is used by owner, and building is used by non-owner.
2) There is always a "town owned" building available.
3) A building gives a similar benifit to its owner and its user, usually 1/2 the buildings cost (ie a 4 cost building gives a R/W/2c/2VP benifit to its owner, and a similar bonus over a "town owned" building to the user)

If a building is not used, the owner gets nothing, and the other player(s) also don't get the benifit. If the building is used by a non owner, that player and the owner gets a benifit, while the other players get nothing. If the owner uses his own building, he gets the building payout at the cost of the ownership payout, and the other players get nothing.

ie
case 1: 0 benifit to anybody
case 2: .5 benifit to owner and user, 0 to rest
case 3: .5 benifit to owner only

Just looking at this in a very micro (1 action) fashion, the correct conclusion is that taking my own building is always the best action, followed by taking an opponents building. No PD at all.

From a macro fashion (1/8th of a game) there's a little bit more delema, but not a whole lot. If it is my turn and I have less buildings available than pawns left to place, I may want to place in an opponents building that gives a better benifit, knowing that I will still get the benifit from all my buildings. Otherwise I will want to place in my own, to secure the benifit.

Assuming that a building will be used, taking a building with the greatest benifit over a town owned action is always best, regardless of the owner. In addtion, it is always to the owners benifit to have all of his buildings used, preferably by himself (this supports the assumption that any building that provides a benifit above a town owned will be used).

 
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John Sugden
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OP here:

RE: PD label - I have no further comment on it. I used it as a reference concept, not a technical label. As such, the details do not matter to me and I apologize for offending anyone with such lose labeling.

RE: Thread title - Yes. It should have said EARLY.

Regarding the underlying math: I'm now over 20 games in plus simulations. I've logged 7 games to analyze them (as I find that type of analysis enjoyable). I stand by the core of my earliest arguments, although my understanding has been refined a bit. There are a lot of 'average' moves you can make in the game. There are relatively few ones that provide 9 or more VPs worth of bonus resources. The players that take advantage of those situations and efficiently convert them into VPs are the ones that generally win.

Going first and building on turn 1 generally provides a substantial advantage and is almost always the best move to make. There are exceptions (specifically when a particularly good quest card is available), but the general rule is true an overwhelmingly large amount of the time.
 
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Chris Berger
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jgsugden wrote:
Going first and building on turn 1 generally provides a substantial advantage and is almost always the best move to make. There are exceptions (specifically when a particularly good quest card is available), but the general rule is true an overwhelmingly large amount of the time.


I think this is generally true when there is a 4 cost "good" building available, which I think should be true most of the time (I don't own the game myself, have been playing a friend's copy, so I don't know the distribution of building tiles). The ones I would not consider "good" are the progressive buildings that only provide 1 unit of benefit per turn, or 2 units of benefit if they are used every other turn - getting your building used only half the time (especially if you aren't able to keep the rook and use it yourself) isn't fantastic.

So, I don't think that means that buildings are too good, but that going first is pretty strong. Going 2nd is also strong in that you get the first chance to use that building for 1.5 units of benefit, or you can build first if p1 doesn't, or you can be first into Waterdeep Harbor, which is also a good position to be in where you get 1.5 units of benefit (-.5 for spending an intrigue card which seem to give 1 unit of benefit on average (though possibly helping others, but not that much), and you should still be able to reassign for a full unit of benefit when you are there early). Also, if the rook doesn't change hands (and if you think it might, you're in the best position to be the one to take it) and p1 doesn't get enough gold, you can probably have the first option to build on turn 2.

That's why I fully support the idea of drafting quests in reverse turn-order - because p1 is a very strong position, and p2 is weaker by probably slightly more than 1 gold, etc... Having a better chance at getting the quest you want should help to even that out a bit. Still, in the games that I've played, p1 has not won or been in very close contention yet, in any game. I think that's down to chance and the fact that the first-player advantage is decent but not so huge that it can't be overcome, but a few data points that say to me that it's not all that unbalanced.

Also, buildings are stronger with more players. Partly because of a more crowded board ensuring that they get used more (but note that 4p is starts out less crowded than 3p), but also because the benefits that you're giving out to other players who use your buildings are diffused more. Instead of 1/2 of the other players getting the same bonus as you when they use it (in a 3p), only 1/4 of the other players get it in a 5p.
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John Sugden
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arkayn wrote:
...
Also, buildings are stronger with more players. Partly because of a more crowded board ensuring that they get used more (but note that 4p is starts out less crowded than 3p), but also because the benefits that you're giving out to other players who use your buildings are diffused more. Instead of 1/2 of the other players getting the same bonus as you when they use it (in a 3p), only 1/4 of the other players get it in a 5p.
Another aspect to this is the percentage of your final score that this initial move represents. The resource advantage of buying a typical 3 or 4 cost building on that first turn is 9 VP. In a 2 player game the final score will likely be in the low 200s. In a 3 player game you're looking at scores above 170. In a 4 or 5 player game you're likely looking at scores a little above 140. The advantage in resources is a greater portion of the final expected scores.

The 'flip' side of this is that buildings that provide resources are harder to fully utilize in a 4 or 5 player game than in a 2 player game. You'll be completing about half as many quests in a 4 or 5 player game as in a 2 player game, and you'll be fighting to get quests that might provide uses for multiples of the same resources. As a result, it is much easier to get stuck with the wrong resources, although I have found it is still something that can be managed well with planning and careful play in a 5 player game.

With regards to the chances that you won't have a good 3 or 4 cost building in the starting 3:

There are 24 buildings. 5 are 8 cost buildings. 6 are progressive buildings. The Stone House, Heroes Garden and Palace of Waterdeep are all unlikely to be played every turn. That leaves 10 of 24 'good' buildings.

The chances the first building will not be a good building are 14 in 24. The chances of the the second one not being one is 13 in 23 if the first is no good. The chances of the third (assuming 1 and 2 are bad) is 12 in 22. We multiply those chances to gether and subtract them from 100% to get the chance that a least 1 good building appears: ~82%.

However, 82% is just the chances that the first player has a good option. In that ~18% of games where no good buildings appear in the starting 3, Palace of Waterdeep and Heroes' Garden are still pretty good and will be used for 6 or 7 turns in most games. Further, if there were two bad buildings and an 8 cost building on the board, it is possible that a player will get gold and then build the 8 cost building during round 1. The only potentially bad 8 cost building is the Zoarster, but that is mainly a factor of the low owner benefit. So, the chances that a good building will hit the table in round 1 is likely closer to 95%.

When one of those 10 'good' 3 or 4 cost buildings (or an 8 cost building) hit the table on round 1, it has been my experience (with 4 different groups of LoW players) that the first building gets used on average MORE than 8 times in a game. In one game, a first first round Yawning Portal was followed by a round 2 Zoarster. The Yawning Portal was used 14 times that game, resulting in a theoretical +49 point gain for the player that put the YP out - although he clearly couldn't make use of 14 clerics or wizards in a 5 player game.
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Chris Berger
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jgsugden wrote:
The resource advantage of buying a typical 3 or 4 cost building on that first turn is 9 VP.


And here I thought you had come around a bit, but it seems you are still laboring under the misconception that a (4 cost) building gives you +.5 units of benefit per activation regardless of who activates it. Whereas it only gives you +.5 if you activate it. In a 3p game, it gives you, on average, +.25 units of benefit when someone else activates it. In a 5p game, it gives you +.375 when someone else activates it.
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Everett Scheer
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jgsugden wrote:
Regarding the underlying math: I'm now over 20 games in plus simulations. I've logged 7 games to analyze them (as I find that type of analysis enjoyable). I stand by the core of my earliest arguments, although my understanding has been refined a bit. There are a lot of 'average' moves you can make in the game. There are relatively few ones that provide 9 or more VPs worth of bonus resources. The players that take advantage of those situations and efficiently convert them into VPs are the ones that generally win.

Going first and building on turn 1 generally provides a substantial advantage and is almost always the best move to make. There are exceptions (specifically when a particularly good quest card is available), but the general rule is true an overwhelmingly large amount of the time.


I agree with most of the above, that buying a building first turn is usually the correct move. However, you don't see the hidden cost (or rather the hidden benifit to your opponents) of your building. You may get the 9VPs with the one action, but you are also adding 16VPs (2VP*8 actions) to be distributed amongst other players when they use your building (you could deny these at 2VP per your own action). This means that in a 2 player game, it is much less benificial to buy a building than in a 5 player game.
 
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John Sugden
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arkayn wrote:
...
And here I thought you had come around a bit, but it seems you are still laboring under the misconception that a (4 cost) building gives you +.5 units of benefit per activation regardless of who activates it. Whereas it only gives you +.5 if you activate it. In a 3p game, it gives you, on average, +.25 units of benefit when someone else activates it. In a 5p game, it gives you +.375 when someone else activates it.
Yes, opponents effectively undercut your advantage when they use it - in theory. In a 2 player game, if I build a typical 4 cost building and my opponent uses it 8 times, he comes out with 16 vp of surplus resources for his 8 activations while I only come out with 9 vp from buying the building.

HOWEVER, that was one of my agents compared to his eight. What did I do with my other 7 activations? Does buying a building prevent me from using other buildings? From using intrigue cards?

Buying a round 1 building gives me a huge advantage in exchange for 1 agent and 4 gold. It gives my opponents a *chance* to fight over 8 small boosts by using 8 of their agent placements.

The real underlying analysis of round 1 buildings is this (to me):

1.) I give up an agent placement and 4 gold.
2.) I get a VP.
3.) I get a reliable "income stream" of resources. For most buildings, I know that I'll likely be getting a lot of a certain type of resource in the game. That can help me plan. I know that I can take the five wizard quest if if I am getting a bonus wizard every turn in a five player game. Other players may look at the 25 points and say, I may or may not be able to get to those 5 wizards in 20 agent placements if I already have to pay X wizards for my current quests.
4.) I know some other player is likely to get the building benefit of that building. I will be down 2 agent placements of resources in turn 1 for a 1 vp score and 1 owner benefit. That pute me behind the 8 ball when trying to complete early quests.
5.) On rounds 2 through 8, either I use the building or someone else does. Using the building itself is not better for me than using a board standard building, but it does prevent other players from getting any advantage from the building that round. If another player uses the building, that player also gets a surplus benefit that round, but I'm free to seek other surplus values by using buildings or intrigue cards.

Which is better for me? It depends upon the turn order, what surplus value plays are out there, and which of my opponents are most likely to use my building. If the person most likely to use my building is unlikely to win for other reasons, the fact that he is getting any advantage out of my building is irrelevant.

This is a simple game at the core. Agents -> resources -> points. The player with the most efficient average resources gained per activation and most efficient conversion of resources to points is going to win. Every time. And building a building gives you a very efficient exchange of resources for

Buying a building gives you a significant boost in resources. It also gives opponents an opportunity to get 8 small boosts in resources. If If I can use my other 7 activations to get surplus resources, then I'm going to be far ahead. If I can't, I'll only come out ahead if my opponents and I split up the use of the building amongst a lot of players or I use it most of the time. However, I see no reason to assume my other 7 activations will not generate surplus resources.

I'm winning a lot of games when I build buildings. It isn't the ony high surplus value early game strategy, but it is a great one and one that should not be passed upon if available, generally.
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John Middleton
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In comparison, how many other early game strategies are present besides building buildings, gathering a few resources, and possibly gaining a preferred quest or two. You could play some intrigue cards or seek first player status, but need a good reason this early in. It is a bit early to start playing Mandatory Quests and most intrigues will be resource gathering or one sort or another. Even the reallocation from the Harbor is very limited in since most valuable spaces will have agents on them.

The amount of playable spaces are limited strategically until several buildings are constructed.


So building early buildings then becomes not so much a player strategy, but a possible preferred action if the player order happens to allow it.

The strategy then is actually gaining first player status if you decide construction is important to you.
 
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Part of early (decent) buildings being the obvious choice is the lack of other options that provide surplus resources - that is true.

However, there are times when I will not go for the building as my #1 action. These generally surround the quest card options. There are a few quests, especially in 2 player games, that dwarf the value of the building. I have also been known to let an opponent build a weaker 4 cost building on round 1 if I can guarantee that I'll be able to build an awesome 8 cost one on round 2. Finally, if the 3 buildings in the builder's hall all suck (which I've only seen once in 25+ games), I won't build them.
 
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