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Breaking Point for Buildings to be Worthwhile

Discussion in 'Civ5 - Strategy & Tips' started by Blatc, Jan 16, 2018.

  1. Blatc

    Blatc Prince

    Joined:
    Feb 24, 2015
    Messages:
    449
    I think this is a useful topic for any player looking to improve their game, up to those looking to optimize finish times: what is the breaking point at which a given building becomes worthwhile or not? There is certainly some necessary context to the question. For example, in pursuing a Science Victory, a Library is required in every city; however, back in the days of the Deity series I formulated an 'Illiterate' strategy that proved successful in some fast Domination games. For simplicity, I'll assume the pursuit is a Science Victory.

    Buildings that impact production and food should be the easiest to quantify. So, to gauge interest in the topic, let's first consider the stable, as there was a post in a recent thread that caught my eye:

    Stable
    Cost 100 hammers
    Maintenance 1 gold/turn
    Value +1 production per horse, sheep, and cattle
    *need a pasture on one of these resources to build, but the +1 production is based on the resource, not the pasture, so the bonus does not rely on further worker action, only tile expansion

    At what point does this building 'break-even' with regards to it's main output? (Note, this is a slightly different question than whether it's worthwhile, focusing only on 'getting back' the production invested)
    At 100 hammer cost, you 'get back' the production costs in:
    1 resource = 100 turns
    2 resources = 50 turns
    3 resources = ~33 turns (34th turn. I'm rounding off on these for simplicity)
    4 resources = 25 turns
    5 resources = 20 turns
    6 resources = 17 turns

    The 1 gold/turn is not prohibitive, but maintenance should be considered in this analysis. If we consider a gold to hammer value ratio of 4:1, the 1 gold maintenance reduces the stable value by an equivalent of 0.25 hammers per turn. As such, the return value becomes:
    1 resource = 0.75 hammers/turn = 133 turns (134th turn)
    2 resources = 1.75 hammers/turn = 57 turns
    3 resources = 2.75 hammers/turn = 36 turns
    4 resources = 3.75 hammers/turn = 27 turns
    5 resources = 4.75 hammers/turn = 21 turns
    6 resources = 5.75 hammers/turn = 17 turns

    The intangible consideration is the 'missed value', had you instead put this production into another building. This is where the player needs to make the best in-game decision for themselves. The number of turns cited above will have a different relative valued based on the estimated length of the game: a 300-400 turn game gives a lot more turns to derive value from the Stable, whereas a 200-250 turn game will see 'essential' buildings (ex. University) become available to build sooner.

    At this point I am going to estimate whether or not the building is worthwhile based on whether it can return it's equivalent production cost 1, 2, or 3 times over before the game ends. I will suggest that 1x is a definite 'no' (because of the missed value in building something else), 2x is a maybe that should be carefully considered, and 3x is a definite 'yes':

    # of resources: turns required to reach 1x, 2x, 3x equivalent return
    1 resource: 133, 266, 399 turns (note this is turns from completion of building, not total game length)
    2 resources: 57, 114, 171 turns
    3 resources: 36, 72, 108 turns
    4 resources: 27, 54, 81 turns
    5 resources: 21, 42, 64 turns
    6 resources: 17, 34, 51 turns

    I currently view having 3 resources and being able to start production before Education as the necessary requirements to build a Stable in my games. A common scenario involves reaching Education before finishing the Stable. When this happens, I evaluate how many hammers remain to build the stable, how quickly I'll get those hammers back (i.e. not the full 100, just the remaining amount), and whether finishing the stable will actually delay the University, and if so by how many turns. Usually, if I can get over 50% of the stable built before hitting Education, it's worthwhile to finish the stable before starting the University.

    My estimate is that the breaking point for building a Stable is having either 2 or 3 resources available by the completion of the building*, depending on game length and the point at which you can start production. If there is interest in this topic, I could cover some other buildings or related questions. Input from other players is of course welcome.


    *you can also estimate an average, if perhaps there will only be 1 such resource available upon completion, but 4+ resources later in the game. We can also further complicate things by factoring in the cost of buying a tile to get a 2nd/3rd/+ stable resource, which I'll mostly leave alone except to suggest that if you're going to purchase such a tile, buy it earlier rather than later to get more return value.
     
    Last edited: Jan 16, 2018
  2. mbbcam

    mbbcam Prince

    Joined:
    Apr 7, 2012
    Messages:
    460
    Location:
    Cambridge
    Errr ... I think you mean "break-even point" (which is when costs and benefits balance out) rather than "breaking point" (which is when something snaps or collapses). Sorry, but I used to be an English teacher. Otherwise, what a phenomenal piece of work! Now, if only I could work out whether it is better to work a food tile or a hammer tile ... :)
     
  3. Blatc

    Blatc Prince

    Joined:
    Feb 24, 2015
    Messages:
    449
    Thanks mbbcam, you are correct - I do mean the 'break-even' point.

    I bet we could get a decent set of guidelines on food vs. hammer; I'd suggest the first step would be to break the game (or at least city size) down into stages, i.e. early growth (pop 1-5), and so forth.
    As an example, even in recent games with Shoshone (great expanse) and first two policies opening tradition and liberty (maximum cultural tile expansion), I still bought tiles with 3-food because of how highly I value early growth.
     
  4. raider980

    raider980 Warlord

    Joined:
    Sep 27, 2010
    Messages:
    239
    I had this exact question yesterday in my current game. Should I build that stable if I only have one sheep? Should I build that forge if I have only one iron?

    I didn't build them. But primarily because I didn't think it was worth a gold for the maintenance. However, later in the game when I had more gold and some +% production buildings, I did build them. I figured that it may help get one fewer turn for building something. I didn't do any math but I'm not sure that the value of building them can be simply calculated by how many turns it takes to break even. Aren't there other factors that come into play? Like a forge plus a stable (maybe others) that gives +2 but then you have other buildings that give a +% production?
     
  5. Blatc

    Blatc Prince

    Joined:
    Feb 24, 2015
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    Part of the intangible consideration I mentioned is missed value in building other buildings; these other buildings can also be impacted by their respective modifiers. As an example, you could chose between building a forge or a mint. That the production from the forge is impacted by a modifier must be weighted against the fact that the gold from the mint is also impacted by a modifier - not to mention the science bonus from Mercantilism.
    Of course, you'd only be choosing between those two buildings if it would actually be worthwhile to build a forge: at 120 hammers for +1 production per iron tile, minus the 1 gold maintenance, I expect you'll find that many of the posters on here seldom build forges.
    I acknowledge that there are other factors that can come into play. My OP was meant to help provide a general guideline and start discussion on the topic, should posters be interested in getting into the details, including related math, of some of the buildings.
     
  6. BlackWizard

    BlackWizard King

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    Dec 14, 2010
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    649
    One must remember that forge and stables also lower build time for certain units. These however doesnt matter much in pure science game but in domination they do
     

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