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Wide Play for Fast Victory: Theory

Discussion in 'Civ5 - Strategy & Tips' started by Manpanzee, Jun 10, 2015.

  1. Manpanzee

    Manpanzee Prince

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    I've been fascinated with Wide play for a long time now, and I've finally gotten to a point where I believe that Wide empires are competitive with Tall empires for fast science/culture/diplo victory. I have yet to personally get a sub-200 science victory with a Wide game, but I believe it's only a matter of time. Somewhat recently, Acken achieved a sub-200 Deity science victory with an 8-city Korea game. So we know that it's possible. But "possible" doesn't automatically equal good. A better question is, "is going Wide desirable?" I think it is, for reasons outlined below.

    Definitions: "Tall" = four or fewer self-founded cities, finishing Tradition. "Wide" = five or more self-founded cities, finishing Liberty.

    There are a lot of nuances to Wide play that differ from Tall, but that's a whole discussion unto itself. Here, I just want to explain the important theoretical concepts that I think support Wide play as an idea. There are two main ones I want to talk about here.

    ~~~~~~~~~~

    1. Food/Growth. Conventional wisdom has it that Tall play gets superior growth. After all, it's right there in the Tradition finisher: "+15% growth in all cities". Obvious. Liberty doesn't have anything like this. However, this only means that Tall has more growth PER CITY than Wide. An empire with more cities can actually overcome this bonus and generate more total growth.

    Let's assume, for the sake of argument, that base growth is the same in all cities -- call this value x. An empire with six cities and the Tradition finisher would generate a total of (6x * 1.15) growth, or 6.9x total growth. An empire with seven cities and no Tradition finisher would generate 7x total growth. Here, the seven-city empire comes out slightly ahead. But this isn't a realistic comparison. A more realistic comparison is a four-city empire with Tradition and a six-city empire without. Here, the Tall empire generates (4x *1.15) = 4.6x total growth, while the Wide empire generates 6x total growth. Wide is way ahead now. It's really no comparison.

    Furthermore, we have to account for the fact that food requirements for growth go up as population rises. Going from 10 to 11 pop costs a lot less food than going from 30 to 31. Compare a four-city empire with four 20-pop cities to a six-city empire with six 13-pop cities. The latter empire needs significantly less surplus food in a city to increase its population.

    Take these two things together: 1. A Wide empire can have more total growth than a tall empire. 2. A Wide empire gains more population per unit of growth than a Tall empire. Combined, the outcome is this: A Wide Empire can gain population significantly faster than a Tall empire.

    For an example, here's a screenshot of my most recent completed game, a seven-city science victory with Egypt. None of my cities are particularly large -- my capital is size 25, which is downright small for a science victory endgame. But my total population is 157. Across four cities, this would be equivalent to an average size of 39 population, which is actually pretty massive for this point in the game. I've been able to gain a ton of total population by making many cities.

    Spoiler :


    2. Happiness. Again, we're fighting conventional wisdom here. Consensus says that the global happiness mechanic discourages wide play. But this isn't actually true, for the reason that per-city happiness sources more than offset extra unhappiness for founding more cities.

    Consider: One point of population generates one point of unhappiness, and each city adds an additional three unhappiness on top of that. Let's take two hypothetical empires, Tall and Wide, each with 160 total population. The Tall four-city empire generates 160 unhappiness from population, plus 12 unhappiness from number of cities, for a total of 172 unhappiness. The Wide six-city empire generates 160 unhappiness from population, plus 18 unhappiness from number of cities, for a total of 178 unhappiness. Tall is indeed ahead.

    But let's see what happens when we add in some local happiness sources. Let's say you have a Coliseum and a Pagoda in every city. The Tall empire above gets 16 total happiness from these buildings. The Wide empire gets 24 total happiness from these buildings. Add these to the numbers above, and the Tall empire has a total unhappiness deficit of 156, while the Wide empire has a total unhappiness deficit of 154. Wide is actually ahead! And this is only with Coliseums and Pagodas. Add in other sources of per-city happiness, and Wide pulls further and further ahead. Zoos, Circuses, and Stone Works all contribute, as can many other buildings via religious beliefs and social policies. And the more cities you add on to the Wide empire, the farther ahead Wide gets under this math.

    So, why the common belief that happiness penalizes Wide play? There are two main reasons, I think. The first is fairly obvious -- without these happiness buildings, the Tall empire is ahead, and newly founded cities have no buildings. So Tall does start out ahead, and Wide doesn't catch up until it has its buildings. The second reason is more interesting.

    As discussed above, Wide empires can gain population more quickly than Tall empires. This means that Wide empires spend their happiness more quickly, even with more happiness to work with. It's thus more common to encounter a visible happiness crunch with Wide play. But this is something that feels like a problem more than it actually is a problem. Happiness is first and foremost a limiter on population. It does contribute to Golden Age points, but that's a minor consideration. For the most part, it doesn't matter how much positive happiness you have -- you either have enough to keep growing, or you don't have happiness and need to stop growing.

    Consider two scenarios: In Scenario A you have 10 happiness to spare. Scenario B is exactly the same, but you instantly have 10 more population, putting you at zero happiness and forcing you to stagnate/avoid growth. Scenario B is clearly better, but it feels like you have a problem. If you haven't carefully thought it through, being in Scenario B feels like something you should try to avoid. But it's actually perfectly ok. You have a stronger empire in Scenario B than in Scenario A, and you can simply focus on non-food tiles until you find more sources of happiness.

    ~~~~~~~~~~

    There are a lot of other considerations that come into play for Tall versus Wide. Policy costs, national wonder costs, building maintenance costs, road maintenance costs, more efficient rush-buying, aggressive expansion penalties, defensibility, and faster early science may all tip the balance toward Tall play. On the other hand, faith, great person points, and more specialists provide additional edges to Wide play. It's a complicated system, and there's a lot to consider. But hopefully you can see that there is actually some theoretical basis in support of going Wide.
     
  2. Tabarnak

    Tabarnak Cut your lousy hairs!

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    Definition of ''wide'' isn't exclusive to Liberty. I count many games where i had 7-8 cities founded from my own using Tradition.

    Maybe you talk about pre NC? 4 of less pre NC for Trad and 5 or more pre NC for Liberty would be a better statement.

    Maps favourising Liberty are tough to find too. You need a lot of unique luxs to make Liberty working under no mods.
     
  3. Manpanzee

    Manpanzee Prince

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    Good point. I don't mean to be reducing the strategic options -- just needed to choose some kind of arbitrary definitions for the sake of discussion. I've done everything from 10-city Tradition to 3-city Liberty. I also specified "self-founded", which was totally unnecessary in hindsight. No real reason to differentiate between founded cities and captured/gifted cities.

    My main reason for choosing those definitions was to allow me to compare total growth with and without Tradition finisher, in order to make the argument that an empire with the Tradition finisher doesn't automatically get more growth than an empire without.
     
  4. Acken

    Acken Deity

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    I've yet to see 6+ tradition or 3 city liberty be better than the two other options so for the sake of the discussion I find the definition reasonable.

    Good opening post but it looks like an introduction.
    It would benefit to nuance the idea by the fact that growth is rarely equal between the two playstyles. Faster aqueducts, landed elites and often more caravan food on average per city.

    Then factoring in happiness sources from the policies themselves. And finally making a comparison by factoring in the tech penalty and additional science slots and how the "smaller" total growth of tradition compares.

    Finally it's important to talk about the money. Liberty having a ton more to pay in maintenance and no bonus from the tree directly.
     
  5. Illianor123

    Illianor123 Warlord

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    Most discussions I have seen here previously put tall as 6 or less, and wide as 7+.

    Tall has an easier time with national wonders, and all their cities are good, and thus able to build those happiness buildings. Also monarchy is a huge source of happiness for tradition.

    You are also confusing local and global un/happiness. IIRC correctly, collesuems and stuff won't fix the 3 unhappiness per city, you need luxuries or wonders for that. Not to mention the gold costs.

    Wide also requires more science and culture (though it does generate more, the questions is whether is overcomes the increase, as well as each city being slower to produce thebuildings when they become available).

    So each new city, spends some time being a tax, then after a while catches up before finally contributing. It just takes too long to reach the point of usefulness compared to tall.

    Discounting golden ages is a bad thing, they can contribute a lot and especially important for cultural victories.
     
  6. noonex

    noonex Chieftain

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    Win is not only about growth.

    Even science is not only about growth, because you theoretically have 4 more science slots for every additional city. With good great person bonuses it is more Great Scientists
    You can work as many specialists as you need without sacrificing growth
    You have more faith and theoretically may buy more GS later on (and can manage religion much easier in overall)
    You can achieve better defense going wide and choosing defensive locations for cities on borders of empire. Some cities near mountains/lakes/marsh or even rivers are just extremely hard to capture even with 20 to 1 advantage. (especially if cities are close and able protect each other from surrounding)
    Your empire is safer overall against sneak attacks
    You have much better chances for strategic resources.
    You have less chances that strong AI will settle close to your core cities which usually rises tensions.
    AI in general will not covet land with many low population cities (maybe it isn't true, but it is what my experience tells)
    Even human players will hate to try take land with many close low population cities. In contrast, high population developed city looks very attractive for warmongers.

    Bot NO - Tall empires give faster victories in general, even if you depend on luck sometimes.
    Jut Wide may give more consistent/enjoyable results.
     
  7. vanatteveldt

    vanatteveldt Emperor

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    In terms of happiness, monarchy (.5 happy per cap pop) is a huge boost for trad. In your 160 pop in 4 vs 6 cities example, liberty gives 5 happy for the 5 connected cities, while trad will give 20 happy for the 40 pop capital. In reality, the capital will be bigger than the other cities, so it gives even more.

    Another interesting comparison is the early game. Liberty has cheaper settlers and free settler+worker, but also needs more of them. Assuming 4 vs 6, trad needs 3 settlers, liberty 4, but (at least) 3 of those will be half cost. In my experience, liberty probably needs to self-build one or two workers (or the pyramids), while trad can generally steal all workers.

    On the other hand, liberty needs to build monuments and aqueducts, and also has an extra tech priority in engineering to get aqueducts, necessitating a choice between getting CS, edu, and engineering first. As acken said, growth is boosted for trad by landed elite and the finisher, and the earlier and free aqueducts.

    But forget the theory, play one of the maps in the recent wide vs tall threads using both playstyles and see which ends up faster/bigger/better.
     
  8. Acken

    Acken Deity

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    People rooting for tradition are free to play the current King science HoF game or GotM 111.
    Like many similar threads on CFC, claiming stuff and dismissing OP with no observable comparative results is useless.
     
  9. wayneb64

    wayneb64 Prince

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    I think you need to include the affects of Monarchy and Meritocracy in your happiness comparisons between tall and wide. That -1 unhappiness per two citizens in the capitol is huge and not countered by the +1 happiness per connected city. The +1 gold per two citizens is also quite noticeable if you play tall correctly and keep your capitol well fed with a caravan or two.
     
  10. Smirk

    Smirk King

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    While I agree with the overall picture painted there are a lot more variables. The free aqueducts alone will account for a significant growth increase for those going tradition. That is, with out liberty taking a sidetrack to get this tech early and then the required production to build them. Some of the ideal growth curve for smaller cities is balanced by this increased need for production.
    And to touch on gold, the empire wide gold should scale up per city, which things such as trade routes does not scale up (although you do get +1 by going Construction earlier). This is almost a non-issue as potential rush buying targets also scales per city (libraries, universities etc). So the most important difference is the need to buy/build aquaducts per city.

    Adding in the other food and happiness bonuses from tradition should be important for this comparison. The +2f and +10% in the capital is pretty great, alongside the additional happiness gained in cap. (And of course the somewhat small but still important long term +1 per 10 pop.)

    Although, a comparison is unfair since for the bulk of the game it seems completely one sided in favor of tradition and has since the policy rework. You didn't even touch on the 5% penalty per city which can really grind things down mid-game.
    Just considering some mid to end game tech where base cost is anywhere from 1-4k to set an optimal goal of say 4 turn techs, you need to generate 12.5-50 bpt per additional city, and thats with a total bpt from 250-1000 which is quite feasible. I think the conversation and really the strategy here is about getting those numbers in the cities which is more a balancing act of production and growth versus the tradition(al) method which is all about growth.

    Where this pays off is total science generation and where that pays off is bulbing great scientists. And naturally generating more due to more cities. I'm sure this drops off completely at a certain city count.

    So ignoring the aqueduct issue which is just a task that has to be done at some point the big difference seems to be GS management and use. All my attempts at this sort of SV have just ground down and seems to flounder mid game. (For context this was a few games with Inca and Babylon, which seem like perhaps the best civs suited to this sort of approach.)


    So was there any difference in your Egypt game with regards to GS use? I'd think based on the raw value of a GS late game the academy equation is completely changed from a tradition game.
     
  11. Manpanzee

    Manpanzee Prince

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    I think the local/global unhappiness difference is only an issue for ICS style games. The purpose of that mechanic is to prevent cities from being net positive in happiness. For a normal game, where you're actually growing your cities, every city's local unhappiness will far outweigh the amount of local happiness generation. I.e., each city's population will be larger than its happiness output. So local/global happiness shouldn't be an issue, and you can analyze everything in terms of total happiness vs total unhappiness. I think.

    I used to think this -- I remember posting things like "Monarchy is the most OP policy in the game" back in the day. But I really didn't have any idea of how to play wide then. Now that I have a better grasp on the concept and some completed games to look at, it turns out that Monarchy isn't actually significantly ahead of Meritocracy in raw happiness output for this style (although the gold is nice, of course). If you look at my screenshot, I have a 25-pop capital, which means Monarchy would save me 13 happiness. I also have 7 cities and 157 total pop, meaning than Meritocracy saves me 14 happiness (the capital counts as a connected city, I believe).

    Tradition does get Aristocracy, too, so pure Tradition is ahead of pure Liberty in happiness. It's definitely something to be aware of, and something that benefits Tall. My preferred build of Wide involves dipping into Tradition for Aristocracy, which evens things out, but that obviously does have opportunity costs.


    There are indeed a lot of variables. :) I'm not really trying to make a convincing argument that "Wide is the best". I'm more just trying to point to a couple things and say "Hey, maybe there are actually good reasons to go Wide".

    I'm still figuring out usage of Great Scientists in Wide games. My current feeling is that you don't want Academies and can bulb a bit more freely in the midgame. Your late game science will get extremely high and you'll have strong endgame bulbs, so you can spare a bit more GSes in the midgame to start catching up on the faster start Tall tends to have. For this game, I bulbed one for Scientific Theory, bulbed another to grab Chemistry and Fertilizer after that, then bulbed yet another for Plastics. I then bulbed three more post-Labs in order to jump all the way to Rocketry and get started on Apollo. Totally ignored the top of the tech tree -- I didn't even have Navigation yet!
     
  12. consentient

    consentient Domination!

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    I know it's not a typical example because the map was so OP but my CV on the Russia DCL shows that a wide empire can produce a LOT of science once you have public schools in them. Basically, because I had a huge army, no one DoW'd me, and I could concentrate on only building science and growth stuff. Sure, there were luxes aplenty on that map, but as you said in the OP, with happiness buildings, everything is OK after a while. If you hit ideologies in good time, sub-T200 science wins are probably possible with a really good player using 8 cities on most feasible maps, I feel, provided they played slowly and made a lot of really good choices.

    It's not like social policies are ever a bottleneck in a peaceful game. I generally have 1 spare before Rationalism and 2 spare minimum in the last 30 turns. Trad opener is usually my go-to for Liberty games where I've not got enough allies to head for Scholasticism, and there is not going to be as much quick return by opening Aesthetics.
     
  13. Acken

    Acken Deity

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    GS management for liberty:
    -There are already doubts it's worth settling with Tradition. With a wide game there are none. So don't settle any GS beyond the one you get out of the finisher if you chose that option.
    -I'm fairly convinced you should always bulb ST and Plastics. Contrary to tradition I find it really unlikely you'll be able to get enough money to buy all your science buildings. So hard building them to start them sooner is worth it.
    -Other midgame bulbs maybe. I found that it may be a little hard to wait long after plastics to get to rocketery at the right time so maybe adding a bulb somewhere before plastics is also worth it (fertilizer/chemistry) as it will allow you more time post plastics to wait for other bulbs to grow in strength.
    -The end should be fairly similar to tradition.
     
  14. BBMorti

    BBMorti Warlord

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    Well even with Trad I don't see a reason to plant more than the first GS, if you go for fast win times. I would aim hard for a religion with tithe for a fast liberty finnish, to upset the gold issues.
     
  15. budweiser

    budweiser King of the Beers

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    I believe the key to wide play is extra culture per city beyond the base amount.
     
  16. Bleidraner

    Bleidraner King

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    Well I pretty much agree with what Manpanzee is saying. I have been playing wide Liberty massively in the HOF lately, inspired by Manpanzee's games and the interesting discussion here in S&T. I still have not got to the point where I can offer an mathematical explanation and probably never will, as there are too many variables, but from the practical standpoint I can usually get with good maps 220-230 with 4 cities tradition and with insanely good maps 210. After a few tries with liberty wide (on maps that allow it of course) I am at the point where I am getting very similar results (220-230) with 7 cities Liberty, and it feels I am leaving turns at the table. I had an awesome 8 cities Liberty game with Acken's Korea map, for a t208, which basically is better than my fastest science ever by 3-4 turns (not is a HOF environment, I replayed the first 100 turns, so I had previous map knowledge).

    So based on empirical evidence I believe on some maps, Liberty wide can compete with Trad 4 cities. I am finding that wide games a lot harder to play, so much micro to do, and they are very unforgiving, you really have to pay attention to diplomacy, scouting, CSs, everything, if you screw something up, especially in the first 100 turns, you destroy your chances for a fast finish.

    On Deity/Immortal I am still experimenting, I go to engineering for aqueducts then Edu, Acken does metal casting for workshops before but I am not sure what's best. On lower levels like King and. Emperor I am at a loss, wonders are available, specially GL, so my higher levels carefully crafted BO does mot really have gaps early on for GL, so I am still trying to figure out what's optimal, there are not too many resources about this approach in the forums. It's fun to experiment though.
     
  17. TheMeInTeam

    TheMeInTeam Top Logic

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    At the conceptual level, there is a point in time where wide will necessarily surpass tall in terms of yields/strength, based on the numbers. The OP touches on that pretty soundly, but if you think about it for any setup where city :) can overpower global penalties and given how city growth scales, wide will EVENTUALLY produce more.

    The more difficult question to answer is whether it has a chance to catch up to the short-term returns of running a tall setup. If the tech tree were 5 times longer, the answer would be "no question", if it were 1/2 the length it's hard to picture wide strats possibly paying back in time. How close is a given start to the margin? Do you even care, are you just going to go massacre everything if you get your hands on a tech lead, etc?
     
  18. Mutineer

    Mutineer Deity

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    IN my past I did develop 8-10 city liberty/piety strategy. It never going to be fastest finish and it had glaring weekness at one point (fall behind tech and no army yet), but useally it was able to build army just at time and after that garanty win more or less try shear production power of 8-10 cities. But untill end of game it never become tech leader.
    There were multiply variation of this strategy, like getting sci from religious spread if situation warant it (strong opponent religion near by), or multiply other situational variations like borrow religious building from 2-3 near by neybors(spread there relidion or let them spread it, buidl there buiding and the convert back to own.) But in every strategy one of biggest problem were gold. Wide empies have to use any possible trick in book to get gold.
     
  19. chumchu

    chumchu Warlord

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    In principle it might work but it is so hard in practice if you play for the fastest times. It takes time to establish your additional cities and catch up.

    - The most important downside of wide empires (apart from finding the good land and luxes for it) is that you to build the same buildings in every city which is a ton of hammers. More maintenance is bad, but money problems can be solved by midgame. The hammers costs are worse since you need every hammer early on. You can skip watermills/hospitals/amphitheaters and some others but the point still stands as you need those % modifiers and specialist slots in every city.

    - The most important upside (after the food savings) is that you have more specialists slots for each city as which means more science for secularism (and Korea) and more great people generated.

    My repeated tries have yielded a number of lessons:

    - Conquering a neighbor with strong cities is a good shortcut to getting many developed cities and a good use of liberty's mid game hammer advantage. 4/5 city NC around turn 75-80 and then conquering as many cities as you can support before turn 125 seems optimal.

    - Freedom is the way to go with many small cities as every city of 15 pop can work max specialists and you do not have the problem of building parts or generating engineers (you will get too many). If you work max specialists your happiness issues will disappear with 6 happy per city. You only need 3 in freedom until late so you are free to fill in rationalism quickly.

    - Any city can get to 15 pop with fertilizer and a trade route but the faster the better. Luxes and hammers is more important than food.

    - Religious buildings (and jesuit education if you can get it) are top priority. Without a good religion you will not be competitive.

    - Temple of Artemis is stronger than the tradition finisher for food and might be worth competing for. Petra, Pyramids and Oracle are the only other Early wonders that seems achievable/worthwhile.

    - Korea/Persia/Egypt

    - Piety or commerce are the best side trees until rationalism
     
  20. Redaxe

    Redaxe Emperor

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    1) I find the problem with religion/Piety in Diety is that the AI is really attracted to Piety now and consistently I'm seeing Jesuit Education and To The Glory of God being chosen by AI. That has made me very wary of Piety and if you can get one of those 2 reformations after Liberty I don't think Piety is worth it.
    I tend to to think Tradition opener and Aristocracy is more worthwhile now or just putting more policies into Commerce.

    2) Regarding Temple of Artemis are we talking Diety? It's a great Wonder sure but if you want to play wide I can't see how you can get an early wonder like this and still be able to settle a tonne of cities quickly before the AI claims them all.

    I agree on Pyramids and Oracle though - both of those Wonders are definitely beneficial for a wide civ. And I think there is realistically no way on Diety you can get both Temple of Artemis and Pyramids so I tend to think Pyramids is the winner as playing wide is most likely to run you into happiness problems so you really make full use of the growth bonus.

    Regarding teching to Engineering for early aqueducts would we agree that this is the best tech order for wide...
    Pottery > Mining > Masonry (Pyramids) > Animal husbandry > Archery > Philosophy (Oracle) > Engineering (Aqueducts) > Metal Casting (Workshops) > Education etc....
     

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