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Lilac Veritas

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About Lilac Veritas

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    Lilac Veritas
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    The Golden Horde

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  1. Lilac Veritas

    And So the Dust Settles

    The Field of Real Numbers We will now look at some axioms regarding the set of real numbers R. We will note that an "axiom" is a statement that isn't meant to necessarily be proven and instead, they're statements that are given. These axioms are rather straightforward and may seem trivial, however, we will subsequently use them in order to prove many simple theorems and build a foundation for the set of real numbers. The Axioms of the Field of Real Numbers Let R denote the set of real numbers and let +:R×R→R denote the binary operation of addition and let ⋅:R×R→R denote the binary operation of multiplication. Then for all a,b,c∈R, the following axioms hold: Axiom A1: a+b=b+a (Commutativity of Addition). Axiom A2: a+(b+c)=(a+b)+c (Associativity of Addition). Axiom A3: There exists an element 0∈R such that a+0=0+a=a (Existence of an Additive Identity). Axiom A4: There exists an element −a∈R such that a+(−a)=(−a)+a=0 (Existence of Additive Inverses). Axiom M1: a⋅b=b⋅a (Commutativity of Multiplication). Axiom M2: a⋅(b⋅c)=(a⋅b)⋅c (Associativity of Multiplication). Axiom M3: There exists an element 1∈R such that a⋅1=1⋅a=a (Existence of a Multiplicative Identity). Axiom M4: There exists an element a−1∈R such that a⋅a−1=a−1⋅a=1 (Existence of Multiplicative Inverses). Axiom D: a⋅(b+c)=a⋅b+a⋅c (Distributivity of Multiplication over Addition). We note that these axioms define a special algebraic structure known as a field, so we say that R is a field under the operations of + addition and ⋅multiplication.
  2. Lilac Veritas

    Yo Sheepy, what is this math

    Whoops seems I've made a duplicate thread:
  3. As the title suggests, the in game calculations of resource value in the Revenue tab, and the Profit per Slot calculations on the Resources tab are very much incorrect. First consider the raw resources. It gives the following for oil: Expected Daily Profit per improvement at a market value of $4,765 PPU: (3 Oil/day * 50% Bonus * 3784 PPU) - $600 Operating Cost = $22,104.00 I have 12 oil wells, so 4.5 per well. Firstly it gives 2 market prices, secondly the estimate is too high. Using the given prices we get 20842.5 for 4765, 16428 for 3784, and in my own person numbers where I use the lowest selling price (4220) I got $18,390.00. Note that ALL of these numbers are below 22k and that the actual profit is below 19,950. If it was 22k it would be profitable to cut Shopping Malls and Subways for Oil, at 18.4k it is not. Now consider the revenue tab. I have 19 cities following the same build of 72% commerce, maxed oil, gas and uranium production, and the projects for gas and uranium. I make no food and face 20/1 taxes. I make $1,700,429.78 in cash and the game says the total revenue with resources I make is worth $2,926,205.99. I wont break dowm the math here too much but with 1692 tons of gas per day thats 6.4 million alone, and whilst I lose 400k to food, by my math I make just over 10 million, with the market prices of the lowest selling offer. The given numbers spit in the face of mathematics at best, and at worst force nations into poor builds. I know you want nations to produce resources but lying about the profit isn't great, especially when the given equation doesn't even match the answer.
  4. Lilac Veritas

    3/6/2018 - Removal of Trial Changes

    Honestly shout out to ss23 for the hard work behind the scenes, often goes unappreciated
  5. Now this I can get behind, no unnecessarily complex maths formulas (seriously simplify this stuff, if you programmed it in like that with the factorials I'd have you head for wasting cpu time), its simple and to the point, anyone can get the idea without whipping out a calculator or a spreadsheet, and we can min-max to our hearts content within parameters. Also as the bonus caps out at 33% after 3, you get constant returns to scale after that so you still specialise but its not extremely broken and its not an all or nothing affair (go hard or go home)
  6. Also there's an error on your formula for b. You give it as 1 + m! / 2!(m-2)! but really it should be b = 1 + m! / (100 * 2! * (m-2)!) which is what you use in the examples but even that is wrong because 2! = 2, so its literally just b = 1 + m! / (200*(m-2)!) for those of you unfamiliar with factorial, the top and bottom cancel in such a way that it becomes: b = 1 + (m * m-1) / 200, which is a heckaton easier to read and doesn't involved unneeded numerical operations. The bonus production give as a multiplied increase to the base production for each level of improvement is as follows: m b 1 1 2 1.01 3 1.03 4 1.06 5 1.1 6 1.15 7 1.21 8 1.28 9 1.36 10 1.45 11 1.55 12 1.66 13 1.78 14 1.91 15 2.05 16 2.2 17 2.36 18 2.53 19 2.71 20 2.9 There's some interesting points to make First m = 5 is the max for refined resources, so you'd only increase production by 10% which is a little lackluster when the gas project doubles it but its not nothing Bauxite and Iron max at 6, 15% extra, Oil maxes at 66% extra so Gas production with project, especially importing oil as the increased oil production will make oil cheaper, will go from being the best possible resource production you can do thats even better than bank at 2k, to THE BEST GODDAMN RESOURCE PRODUCTION EVER WHY ISNT EVERYONE DOING THIS RIGHT NOW or until the gas market adjusts due tot high supply. Uranium only gets a 3% bonus. At 20 farms you get a 190% bonus, ie they are 2.9x better than normal. 20 farms at 2.5k land, no MI gives 290 (100 currently) and 20 farms at 3.5k land with MI (hardcore food guy) would be 507.5 PER CITY. The bonus goes insane the more improvements there is, its a quadratic as b = 1 + (m^2 - m) / 200. My opinion is the bonus is too weak for low slots and too big for high slots. A 3% bonus for uranium is bugger all, I'd expect more than a 10% bonus for full refined focus (thats 200 pollution for steel), and 190% extra for food at 20 farms is absolutely insane although I'm sure Fraggle would be very happy to run an overslotted low infra, 20 farm, high land build Edit: A way to make it not crazy is to have b depend on what % of the max you have you that resource ie make having 4/5 refined slots on a resource give the same bonus as 16/20 farms
  7. I'm always a fan for specialisation and all, but really what cuts me most about the update and its long term effect is how commerce has been impact. Now I know, you'll make the argument that upper teir should make commerce and lower tier should make resources etc etc Here's why that's not working under the current model: Commerce gives a flat bonus to income per citizen. This has some interesting effects: Commerce becomes better with infrastructure Higher commerce means the population lost to disease and crime hurts more Due to base upkeep, some higher commerce improvements are worse than lower commerce below 700 infrastructure But for the most part people are above 1k because you really can't do much. Consider 1.5k, 2k and 2.5k. To maximise the bonus from commerce and generally the bonus from any improvement you want to pick the ones with the highest profit per slot. At 1.5k there's a bit of a triple point between Subways, Shopping Malls and Stadiums at around 14k profit per slot. Subways are the best due to also reducing pollution, followed by Mall then Stadiums, then Banks. The benefit from Commerce is 0.725 * (1 + Commerce / 50) per citizen, using 8 slots at 1.5k (4 Malls, 1 Subway, 3 Stadiums) gives 80 Commerce, which is 2.6x more income per citizen than 0 Commerce. For 1.5k this is ~112k over the 8 slots. At 2k everything from 1.5k gets even better, more people to use it, and the size of the population is large enough to counter the larger upkeep on all commerce so Stadiums are the best at 22.6k pps, Malls at 20.7k pps, Subways at 19.95k pps, Banks at 12.7k pps. If you didnt get any more commerce you'd make very roughly 50k more from the 8 slots. Wow!~ 50k more! Everyone should build to 2k! And that's where infrastructure costs kill the dream. 0 to 1.5k infra, 6 million, 1.5k to 2k infra, 9 million. If your nation is going to be in a war you'll need to rebuild. You could build from 0 to 2k, or you could build from 0 to 1.5k and rebuild another 1.5 cities. Now there's other arguments to be made about infra paying off over the longer term (ie about 4 months, and you've got other slots which is why 2k is more or less the meta if you avoid war for 4 months or dont get completely destroyed, but realistically if you drop from 2k to 1.5k then thats more than half of your infra value gone so you should be crying) but on the margin its not great, even if it works out on the war cycle. Supermarkets still suck at this point (8.1k) so ITC is useless. If you've got 2.5k land like any self respecting person at 2k infra should (Land is cheap and cannot take damage) then under current market prices (151 ppu) farms win by 400 pps, and even banks are beaten by the current iron market. At 2.5k commerce is back, you get a huge 31.35k pps from a Stadium, thats most likely the best a single slot can do. Malls and Stadiums are above 25k, Banks at are 16.3k, Supermarkets are at 10.2k. oh oh dear the ITC is still useless, and 2.5k costs 16ish million just from 2k. You could build from 0 to 2.5k or you could build from 0 to 1.5k in 6 cities... If you've got the food project at 2.5k land or 3k land then food wins again! Sure an extra 16k from a bank could be nice at 105% commerce but its not worth a project slot, not when at 4.6ppu importing oil and producing gas gives a massive 19k pps. Commerce at 1.5k? Nope, sell gas with a project, although thats the only one that beats 14k right now. See the issue is, Commerce is both too good and too bad. At 1.5k which I'd still class as fairly lower or mid tier, malls, stadiums, subways beat any resource without a project. At the same time supermarkets and even banks in certain cases are trash so you NEVER want the ITC unless you have like 3k infra. If you have 3k infra you should feel bad for having $56,124,587.90 in infra value when 2k is only 15.2k. 1 City of 3k or 3.5 Cities of 2k? Losing 10% from beige at that level is over 16 million and thats only 300 infra vs 2k from nothing. See this sounds crazy but even with these insane market prices that have effectively killed global war as the investment is far too high, resources are still inferior to commerce at 1.5k infra. Now if prices went EVEN HIGHER to make it worth it (ie above 14k pps), what does that mean? It means every single rational player with a 1.5k infra build would cut commerce to produce, lowering their cash income by 112k per city for a higher amount in resources. But you buy resources with money, and these nations would want to specialise for project boosts and because you need to with continents. They still need to buy other resources to run a military with less cash and sky high prices. The supply of resources goes up BUT the ability for nations to purchase the resources goes down because commerce value is flat and not tied to the market. Anyway I've run out of steam for a bit, I hope I made some sort of point with these numbers. If you want trade to increase, buff commerce. If you want more nations to sell resources, buff production. Sounds a bit like something we had before no? I'm a fan of specialisation as I said before but its a bandaid fix on the wider issue that people dont have liquidity to buy so the market stagnates and cannot clear properly
  8. Resource prices are high, so people decide to produce for themselves and sell to take advantage of the market Due to the slot requirements and the profit per slot, supermarkets arent worth it so they get cut, leaving just 1 bank giving a boost over 100% commerce to 105%. This does not justify the use of a project slot so the bank is cut and the ITC is scrapped for further increases in production. You go to sell but people only buy because they must AND any rational consumer has done what you have done, ie the overall cashflow or liquidity has beenreduced as there's more asset value in resources, but its hard to exchange cause buying steel at 5k makes you feel dirty when you remember how it used to be.
  9. Lilac Veritas

    Bringing the New Hotness

    To loyal friends!
  10. Lilac Veritas

    Be the Change You Want to See in the World

    I admit I was confused for a while, people should just maintain a name smh, looking at you Qital/Noytal/Vack etc.
  11. Lilac Veritas


    My only response to all that I see here, of virtue signalling, genuine attempts, and people proving why such a thread was made is https://www.youtube.com/watch?v=cRoFXC4lCEU This thread is a shitshow, I'm going back to doing economics now, don't need to deal with sexism in PnW if communicate solely through spreadsheets
  12. Lilac Veritas

    Bring back color stocks

    Remember when colours meant things? Those were good days
  13. Lilac Veritas

    Progressive Taxation / Econ Suggestions

    as durmij said in another thread, I'm definitely getting the impression that Argotitan is like a captain vietnam reroll or something, or maybe they're just the same annoying breed of troll -- Now regardless of the irl merits of regressive, flat, or progressive tax rates, or whether its better in the middle cause we have brackets, I'm sure we can all agree that more freedom to set rates on alliances is a good thing, as this suggestion has come up many, many times before

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