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Cost of Social Policies (Updated)

Discussion in 'Civ5 - Strategy & Tips' started by Dethrin, Nov 16, 2011.

  1. Dethrin

    Dethrin Chieftain

    Joined:
    Nov 6, 2011
    Messages:
    3
    Because every google search returned old information (as well as the Number Crunching Thread in the archives), I just wanted to post an updated version of the formula used to calculate the cost of Social Policies, since it appears to have changed.

    So let's assume the following:
    pb(k): The base cost of policy k. Depends only on the number of policies already purchased.
    n: The number of cities in your empire. (settled and annexed cities count towards n but puppeted cities do not)
    p(n,k): The total cost of policy k. Depends on cities you control and policies already purchased.

    And because policy cost is also dependent upon map size, difficulty, and game speed:
    pm: map size modifier for cities (0.15 for Standard and below, 0.1 for Large, 0.075 for Huge)
    pd: map difficulty modifier (0.5 for Settler, 0.67 for Chieftan, 0.85 for Warlord, 1 for Prince and above)
    ps: game speed modifier (0.67 for Quick, 1 for Standard, 1.5 for Epic, 3 for Marathon)

    base cost of next policy = speed modifier * difficulty modifier * (base policy cost + (3 * number of policies)^2.01)
    pb(k) = ps * pd * (25 + (3k)^2.01)

    imprecise cost of next policy = base cost of next policy (1 + map size modifier * number of non-capital cities)
    pc(n,k) = pb(k) * (1 + pm(n - 1))

    And now to round that off to a nice even multiple of 5:
    final cost of next policy = 5 * round down (imprecise cost / 5)
    p = 5 * floor(pc(n,k) / 5)


    Summary:
    Formulas
    pb(k) = ps * pd * (25 + (3k)^2.01)
    pc(n,k) = pb(k) * (1 + pm(n - 1))
    p = 5 * floor(pc(n,k) / 5)

    Modifiers
    Map Size (pm)
    Duel: 0.15
    Tiny: 0.15
    Small: 0.15
    Standard: 0.15
    Large: 0.1
    Huge: 0.075

    Difficulty (pd)
    Settler: 0.5
    Chieftan: 0.67
    Warlord: 0.85
    Prince: 1
    King: 1
    Emperor: 1
    Immortal: 1
    Diety: 1

    Speed (ps)
    Quick: 0.67
    Standard: 1
    Epic: 1.5
    Marathon: 3


    Table of Social Policy Costs (num. cities over num. policies, assuming Standard size, speed, and a difficulty of Prince or above)
    Code:
    	n = 1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
    k = 0	25	25	30	35	40	40	45	50	55	55	60	65	70	70	75
    1	30	35	40	45	50	55	60	65	75	80	85	90	95	100	105
    2	60	70	80	85	95	105	115	125	135	140	150	160	170	180	190
    3	105	120	140	155	170	185	200	220	235	250	265	285	300	315	330
    4	170	195	220	250	275	300	325	350	375	405	430	455	480	505	535
    5	255	290	330	370	405	445	485	525	560	600	640	675	715	755	790
    6	355	410	465	515	570	625	680	730	785	840	895	950	1000	1055	1110
    7	475	550	620	695	765	835	910	980	1055	1125	1195	1270	1340	1410	1485
    8	615	710	805	895	990	1080	1175	1270	1360	1455	1545	1640	1730	1825	1920
    9	775	895	1010	1125	1245	1360	1475	1595	1710	1825	1945	2060	2175	2295	2410
    10	955	1095	1240	1385	1525	1670	1815	1960	2100	2245	2390	2530	2675	2820	2960
    11	1150	1325	1495	1670	1840	2015	2190	2360	2535	2705	2880	3050	3225	3400	3570
    12	1365	1570	1775	1980	2185	2390	2595	2800	3010	3215	3420	3625	3830	4035	4240
    13	1600	1840	2080	2320	2560	2800	3045	3285	3525	3765	4005	4245	4485	4725	4965
    14	1855	2130	2410	2690	2965	3245	3525	3805	4080	4360	4640	4915	5195	5475	5750
    15	2125	2445	2765	3085	3405	3720	4040	4360	4680	5000	5320	5640	5955	6275	6595
    16	2415	2780	3145	3505	3870	4230	4595	4960	5320	5685	6045	6410	6775	7135	7500
    17	2730	3135	3545	3955	4365	4775	5185	5595	6005	6415	6825	7235	7640	8050	8460
    18	3055	3515	3975	4435	4895	5350	5810	6270	6730	7190	7645	8105	8565	9025	9480
    19	3405	3915	4430	4940	5450	5960	6475	6985	7495	8005	8520	9030	9540	10050	10560
    20	3775	4340	4905	5470	6040	6605	7170	7735	8305	8870	9435	10000	10570	11135	11700
    21	4160	4785	5410	6030	6655	7280	7905	8530	9155	9780	10400	11025	11650	12275	12900
    22	4565	5250	5935	6620	7305	7990	8675	9360	10045	10730	11415	12100	12785	13470	14155
    23	4990	5740	6485	7235	7985	8735	9480	10230	10980	11730	12475	13225	13975	14725	15470
    24	5435	6250	7065	7880	8695	9510	10325	11140	11955	12770	13585	14400	15215	16030	16850
    25	5895	6780	7665	8550	9435	10320	11205	12090	12975	13860	14745	15630	16510	17395	18280
    26	6375	7335	8290	9250	10205	11160	12120	13075	14035	14990	15945	16905	17860	18820	19775
    27	6880	7910	8940	9975	11005	12040	13070	14105	15135	16165	17200	18230	19265	20295	21330
    28	7400	8510	9620	10730	11840	12950	14060	15170	16280	17390	18500	19610	20720	21830	22940
    29	7935	9130	10320	11510	12700	13890	15085	16275	17465	18655	19845	21040	22230	23420	24610
    30	8495	9770	11045	12320	13595	14870	16145	17420	18695	19965	21240	22515	23790	25065	26340
    
     
  2. binhthuy71

    binhthuy71 Emperor

    Joined:
    Nov 3, 2003
    Messages:
    1,887
    Location:
    Southern California foothills
    That's one heck of a first post! Thank you for the breakout of the actual cost-by-progression for SPs.
     
  3. Ickey

    Ickey Chieftain

    Joined:
    Jun 19, 2009
    Messages:
    36
    So, broadly speaking, with 8 cities SPs cost double what they cost with 1 city?

    That's not as bad as I thought, actually. Your next 7 cities taken together should generally be able to produce a similar amount of culture as your capital, right?
     
  4. wannabewarlord

    wannabewarlord Prince

    Joined:
    Mar 26, 2008
    Messages:
    408
    Location:
    Switzerland
    This is good stuff. Thank you!
     
  5. vexing

    vexing knows

    Joined:
    Dec 24, 2010
    Messages:
    2,668
    the number crunching thread does contain the updated formula later in the thread, though the original post is obviously out of date.
     
  6. Schalke 04

    Schalke 04 Knappe

    Joined:
    Dec 10, 2002
    Messages:
    429
    Location:
    Münster, Germany
    If you just compare 1 city vs 8 cities:

    Your next 7 cities should produce the amount of culture you generate in your capital + what you get from cultural CSs. With Representation even less.
     
  7. Dethrin

    Dethrin Chieftain

    Joined:
    Nov 6, 2011
    Messages:
    3
    Well, given that your capital is probably constructing a majority of the wonders and utilizing most, if not all, of the Landmarks (and most likely the Hermitage as well), I doubt the rest of your cities will individually equate. However, as Schalke 04 mentioned, Representation will ease the burden of 7 additional cities on the final cost of your Social Policies, as will the extra gold they generate help maintain cultural CS alliances.
     
  8. Dethrin

    Dethrin Chieftain

    Joined:
    Nov 6, 2011
    Messages:
    3
    Yeah that had occurred to me, but doing it out will probably save time from having to scroll to a specific post every time I want to check the updated formula. Plus it was more fun :p
     

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