KrikkitTwo
Immortal
- Joined
- Apr 3, 2004
- Messages
- 12,418
Any number crunching been done on combat?
Like the damage expected when there is a certain Strength ratio?
Like the damage expected when there is a certain Strength ratio?
Any number crunching been done on combat?
Like the damage expected when there is a certain Strength ratio?
That said, I was wondering if anyone could put some of these calculations together into spreadsheets for relative ease of use to calculate some of the costs. I'm specifically thinking about something where you could input or just cross-reference the number of social policies you have with the number of cities you have founded/annexed to determine when you'll next be getting an additional SP.
Try this.View attachment 269750
k = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
n = 1 25 45 90 160 245 345 465 595 745 905 1075 1260 1460 1670 1890 2120 2365 2620 2885 3160 3445 3745 4050 4365 4690 5025 5370 5725 6090 6465 6845
2 30 55 120 205 320 450 605 775 970 1175 1400 1640 1900 2170 2460 2760 3075 3405 3750 4110 4480 4865 5265 5675 6100 6535 6985 7445 7920 8405 8900
3 40 70 145 255 395 555 745 955 1190 1445 1725 2020 2335 2670 3025 3395 3785 4195 4620 5060 5515 5990 6480 6985 7510 8045 8595 9165 9745 10345 10955
4 45 85 175 305 465 660 885 1135 1415 1720 2050 2400 2775 3175 3595 4035 4500 4980 5485 6010 6550 7115 7695 8295 8915 9555 10210 10885 11575 12280 13010
5 55 100 205 350 540 765 1025 1315 1640 1990 2370 2780 3215 3675 4160 4670 5210 5770 6350 6955 7585 8240 8910 9605 10325 11060 11820 12600 13400 14220 15065
6 60 115 230 400 615 870 1165 1495 1865 2265 2695 3160 3655 4175 4730 5310 5920 6555 7215 7905 8620 9360 10125 10920 11730 12570 13435 14320 15230 16160 17115
7 70 125 260 450 690 975 1305 1675 2085 2535 3020 3540 4090 4680 5295 5945 6630 7340 8085 8855 9655 10485 11345 12230 13140 14080 15045 16040 17055 18100 19170
8 75 140 285 495 765 1080 1445 1855 2310 2805 3345 3915 4530 5180 5865 6585 7340 8130 8950 9805 10690 11610 12560 13540 14550 15590 16660 17755 18885 20040 21225
9 85 155 315 545 835 1185 1585 2035 2535 3080 3665 4295 4970 5680 6430 7220 8050 8915 9815 10755 11725 12735 13775 14850 15955 17100 18270 19475 20715 21980 23280
10 90 170 345 595 910 1290 1725 2215 2760 3350 3990 4675 5405 6180 7000 7860 8760 9700 10685 11705 12760 13855 14990 16160 17365 18605 19885 21195 22540 23920 25335
11 100 180 370 640 985 1395 1865 2395 2985 3620 4315 5055 5845 6685 7570 8495 9470 10490 11550 12650 13795 14980 16205 17470 18775 20115 21495 22915 24370 25860 27390
12 105 195 400 690 1060 1500 2005 2575 3205 3895 4635 5435 6285 7185 8135 9135 10180 11275 12415 13600 14830 16105 17420 18780 20180 21625 23110 24630 26195 27800 29445
13 115 210 425 740 1135 1605 2145 2755 3430 4165 4960 5815 6725 7685 8705 9770 10895 12065 13280 14550 15865 17230 18635 20090 21590 23135 24720 26350 28025 29740 31495
14 120 225 455 785 1210 1710 2285 2935 3655 4440 5285 6195 7160 8190 9270 10410 11605 12850 14150 15500 16900 18350 19850 21400 23000 24640 26330 28070 29850 31680 33550
15 130 235 485 835 1280 1815 2425 3115 3880 4710 5610 6575 7600 8690 9840 11045 12315 13635 15015 16450 17935 19475 21070 22710 24405 26150 27945 29790 31680 33620 35605
16 135 250 510 885 1355 1920 2570 3295 4100 4980 5930 6950 8040 9190 10405 11685 13025 14425 15880 17395 18970 20600 22285 24020 25815 27660 29555 31505 33505 35560 37660
17 145 265 540 930 1430 2025 2710 3475 4325 5255 6255 7330 8475 9690 10975 12320 13735 15210 16750 18345 20005 21725 23500 25330 27220 29170 31170 33225 35335 37500 39715
18 150 280 565 980 1505 2130 2850 3655 4550 5525 6580 7710 8915 10195 11540 12960 14445 15995 17615 19295 21040 22845 24715 26645 28630 30675 32780 34945 37165 39440 41770
19 160 290 595 1030 1580 2235 2990 3835 4775 5795 6905 8090 9355 10695 12110 13595 15155 16785 18480 20245 22075 23970 25930 27955 30040 32185 34395 36665 38990 41380 43825
20 165 305 625 1075 1650 2340 3130 4015 5000 6070 7225 8470 9795 11195 12680 14235 15865 17570 19345 21195 23110 25095 27145 29265 31445 33695 36005 38380 40820 43320 45880
21 175 320 650 1125 1725 2445 3270 4195 5220 6340 7550 8850 10230 11700 13245 14870 16575 18360 20215 22145 24145 26220 28360 30575 32855 35205 37620 40100 42645 45255 47930
22 180 335 680 1175 1800 2550 3410 4375 5445 6615 7875 9230 10670 12200 13815 15510 17285 19145 21080 23090 25180 27340 29575 31885 34265 36710 39230 41820 44475 47195 49985
23 190 345 705 1220 1875 2655 3550 4555 5670 6885 8200 9605 11110 12700 14380 16145 18000 19930 21945 24040 26215 28465 30790 33195 35670 38220 40845 43540 46300 49135 52040
24 195 360 735 1270 1950 2760 3690 4735 5895 7155 8520 9985 11550 13200 14950 16785 18710 20720 22815 24990 27250 29590 32010 34505 37080 39730 42455 45255 48130 51075 54095
25 205 375 765 1320 2025 2865 3830 4915 6115 7430 8845 10365 11985 13705 15515 17420 19420 21505 23680 25940 28285 30715 33225 35815 38490 41240 44070 46975 49960 53015 56150
26 210 390 790 1365 2095 2970 3970 5095 6340 7700 9170 10745 12425 14205 16085 18060 20130 22290 24545 26890 29320 31835 34440 37125 39895 42750 45680 48695 51785 54955 58205
27 220 405 820 1415 2170 3070 4110 5275 6565 7970 9495 11125 12865 14705 16650 18695 20840 23080 25410 27835 30355 32960 35655 38435 41305 44255 47295 50410 53615 56895 60260
28 225 415 845 1465 2245 3175 4250 5455 6790 8245 9815 11505 13300 15210 17220 19335 21550 23865 26280 28785 31390 34085 36870 39745 42710 45765 48905 52130 55440 58835 62315
29 235 430 875 1510 2320 3280 4390 5635 7015 8515 10140 11885 13740 15710 17790 19970 22260 24655 27145 29735 32425 35210 38085 41055 44120 47275 50520 53850 57270 60775 64365
30 240 445 905 1560 2395 3385 4530 5815 7235 8790 10465 12265 14180 16210 18355 20610 22970 25440 28010 30685 33460 36330 39300 42370 45530 48785 52130 55570 59095 62715 66420
31 250 460 930 1610 2470 3490 4670 5995 7460 9060 10790 12640 14620 16710 18925 21245 23680 26225 28875 31635 34495 37455 40515 43680 46935 50290 53740 57285 60925 64655 68475
32 255 470 960 1655 2540 3595 4810 6175 7685 9330 11110 13020 15055 17215 19490 21885 24395 27015 29745 32585 35530 38580 41735 44990 48345 51800 55355 59005 62755 66595 70530
33 265 485 985 1705 2615 3700 4950 6355 7910 9605 11435 13400 15495 17715 20060 22520 25105 27800 30610 33530 36565 39700 42950 46300 49755 53310 56965 60725 64580 68535 72585
34 270 500 1015 1755 2690 3805 5090 6535 8130 9875 11760 13780 15935 18215 20625 23160 25815 28585 31475 34480 37600 40825 44165 47610 51160 54820 58580 62445 66410 70475 74640
35 280 515 1045 1800 2765 3910 5230 6715 8355 10145 12085 14160 16370 18720 21195 23795 26525 29375 32345 35430 38635 41950 45380 48920 52570 56325 60190 64160 68235 72415 76695
36 285 525 1070 1850 2840 4015 5370 6895 8580 10420 12405 14540 16810 19220 21760 24435 27235 30160 33210 36380 39670 43075 46595 50230 53980 57835 61805 65880 70065 74355 78745
37 295 540 1100 1900 2910 4120 5510 7075 8805 10690 12730 14920 17250 19720 22330 25070 27945 30950 34075 37330 40705 44195 47810 51540 55385 59345 63415 67600 71890 76295 80800
38 300 555 1125 1945 2985 4225 5650 7255 9030 10960 13055 15295 17690 20225 22895 25710 28655 31735 34940 38275 41735 45320 49025 52850 56795 60855 65030 69320 73720 78235 82855
39 310 570 1155 1995 3060 4330 5790 7435 9250 11235 13380 15675 18125 20725 23465 26345 29365 32520 35810 39225 42770 46445 50240 54160 58200 62365 66640 71035 75545 80170 84910
40 315 580 1185 2045 3135 4435 5930 7615 9475 11505 13700 16055 18565 21225 24035 26985 30075 33310 36675 40175 43805 47570 51455 55470 59610 63870 68255 72755 77375 82110 86965
41 325 595 1210 2090 3210 4540 6070 7795 9700 11780 14025 16435 19005 21725 24600 27620 30790 34095 37540 41125 44840 48690 52675 56780 61020 65380 69865 74475 79205 84050 89020
42 330 610 1240 2140 3285 4645 6215 7975 9925 12050 14350 16815 19440 22230 25170 28260 31500 34880 38410 42075 45875 49815 53890 58095 62425 66890 71480 76195 81030 85990 91075
43 340 625 1265 2190 3355 4750 6355 8155 10145 12320 14670 17195 19880 22730 25735 28895 32210 35670 39275 43025 46910 50940 55105 59405 63835 68400 73090 77910 82860 87930 93130
44 345 635 1295 2235 3430 4855 6495 8335 10370 12595 14995 17575 20320 23230 26305 29535 32920 36455 40140 43970 47945 52065 56320 60715 65245 69905 74705 79630 84685 89870 95180
45 355 650 1325 2285 3505 4960 6635 8515 10595 12865 15320 17955 20760 23735 26870 30170 33630 37240 41005 44920 48980 53185 57535 62025 66650 71415 76315 81350 86515 91810 97235
46 360 665 1350 2335 3580 5065 6775 8695 10820 13135 15645 18330 21195 24235 27440 30810 34340 38030 41875 45870 50015 54310 58750 63335 68060 72925 77930 83065 88340 93750 99290
47 370 680 1380 2380 3655 5170 6915 8875 11045 13410 15965 18710 21635 24735 28005 31445 35050 38815 42740 46820 51050 55435 59965 64645 69465 74435 79540 84785 90170 95690 101345
48 375 695 1405 2430 3725 5275 7055 9055 11265 13680 16290 19090 22075 25235 28575 32085 35760 39605 43605 47770 52085 56560 61180 65955 70875 75940 81150 86505 92000 97630 103400
49 385 705 1435 2480 3800 5380 7195 9235 11490 13955 16615 19470 22515 25740 29145 32720 36470 40390 44475 48715 53120 57680 62395 67265 72285 77450 82765 88225 93825 99570 105455
50 390 720 1465 2525 3875 5485 7335 9415 11715 14225 16940 19850 22950 26240 29710 33360 37185 41175 45340 49665 54155 58805 63615 68575 73690 78960 84375 89940 95655 101510 107510
Hmm.... this doesn't seem to line up with the calculations from the table here. It also doesn't seem to line up with a spreadsheet I have seen in this thread in the Hall of Fame section.
I checked it against my first five games and Alpaca's formula is accurate. I did round to the nearest five and this doesn't quite match. Alpaca did say, "rounded to the next multiple of 5," and I guess that means rounding up. There are more pressing things than chasing that five! When I first checked it I was confused by the count of social policies. The formula uses the number of the policy you are working on so that if you already have four, use '5' in the calculation.
Wow, that's some nice math, alpaca! May I suggest you start a new article for this in the Civilization Wiki? There you can use proper LaTeX markup to describe the formulas. As it is not a forum the good stuff also won't get buried under random comments or other threads but stays there in an accessible fashion.
But how many people read the wiki?
the good stuff also won't get buried under random comments or other threads but stays there in an accessible fashion.
Good point regarding the problem of this info getting buried. I certainly had trouble finding this thread until I was pointed in its direction by another forum poster.
Any chance the mods could sticky this incredibly helpful thread? This is some of the most fundamental/basic/core info for strategy in the game.
With alpaca's permission I could of course also copy the content of this thread into the wiki where you'd find it more easily.
Sure, I don't mind at all - I haven't updated things for the new patch, though
Interesting...
This is a pretty counterintuitive result. It means that, if you're getting zero culture from city states, then ANY increase in cities will reduce your time between policies, as long as cT is fixed. For example, even if all of your cities produce only 1 culture, adding a city will decrease your time, as long as the new city produces at least one culture and you're getting no culture from CSes.
[That's because cT is always positive, and pm is always greater than 0 and less than 1, so 1/pm > 1.]
For what it's worth, I differentiated the time function with respect to n, and found the exact same first-order condition, although I haven't checked my math closely yet. It's interesting that the condition doesn't depend on pB or n at all (except for the fact that pB must be positive).
I'd like to look at the derivative wrt n when cT is a function of n, but for now, it's time to play...
I have checked and confirmed that the new effects of Representation (according to the text, 33% reduction in the culture cost rise from founding cities) from the March patch (1.01.217) do reduce the current Culture cost of the next Policy. I have not yet been able to confirm how this is accomplished. My theory is that it applies retroactively to your existing cities. I think a simple test for this would be to start a new game, build no cities until after you build the Oracle in your only city (your capital) and check to see if it affects the culture cost of the next policy; if it does not affect it at all, then this would likely mean that the fact I see a reduction in the cost (using the Oracle's free policy as a simple test, since adopting that free policy does not trigger a normal new-policy rise in the cost of the next policy) is due to the Representation effect being applied retroactively to the cities you have already built (as opposed to only future cities you would build after adopting the policy).
Here is the progression of the Culture Cost of Next Policy in this game:
# Policies # Cities Culture Cost of Next Policy:
0 1 50
1 1 90
2 1 185
3 1 320
3 2 385
4 2 590
5 2 840
5 3 980
6 3 1310
7 3 1680
8 3 2095
8 4 2395
8 4 2080
(Sorry for the misaligned column titles; I'm too lazy to manually reformat from my spreadsheet). New cities were founded (as you can note) after the 3rd, 5th and 8th policy adoptions; the final row which decreased the culture cost of the next policy adoption by 315 points was the effect of adopting Representation from The Oracle's free policy adoption (which, since it is free, I did not ennumerate the policy count, though technically it is the 9th policy adoption).
OK, further testing on this and another save indicates that there is a tech cost discount based (at least in part) upon how many known civs have that tech. Whether the bug is the discount itself or the fact that the UI doesn't properly account for it (because TeamTechs:GetResearchCost() doesn't include it) I don't know.
Here is the evidence for this, spoiled because it's kinda long-winded.
Spoiler :
I am using TeamTechs:GetResearchProgress() and Player:GetOverflowResearch() to calculate the true cost of techs. Ending the turn on the OP save will result in Scientific Theory being awarded with progress of 2599 and 199 overflow, so the true cost is 2400.
On this save, 4 AI civs (all known to the player) already have Scientific Theory and a 5th (Siam) is researching it but is only about 30% done. Because of tests on another game I am pretty confident that Siam's progress doesn't significantly affect the discount, but it's something to watch for if someone else feels like investigating it.
If we start from the OP save and take Scientific Theory away from everyone, China will switch to it and get it on the in-between turn. With only 1 known civ having Scientific Theory, it takes the displayed 2 turns for the player to get it, but the cost turns out to only be 2700. (2836 spent and 136 overflow)
Once again starting from the OP and taking Scientific Theory away from everyone, but this time also resetting China's progress will result in the tech costing the actual displayed value of 2808 since the player does not know anyone with it. (2836 spent and 28 overflow)
Going the other way and giving Scientific Theory to all 6 living AIs on the OP save results in a tech cost of only 2247. (2599 spent and 352 overflow)
Some things to note on the tech discount:
- Only known civs count, which is part of why this is more noticeable in the later eras after you've met everyone.
- The discount applies to everyone. The AIs get it too if they know other civs with the tech they are researching.
- The discount appears to be affected by changes to the TECH_COST_TOTAL_KNOWN_TEAM_MODIFIER global define (30 by default) but not by changes to the TECH_COST_KNOWN_PREREQ_MODIFIER global define. However I don't currently know the exact formula as there does seem to be something else with a minor influence.
- A rough approximation is that it is 3-4% per known civ. Note that in the game from the OP the discount was about 3.85% when 1 known civ had the tech and nearly 25% when 6 known civs had it.
So how much is the discount? Well, it is determined at least in part by the global define TECH_COST_TOTAL_KNOWN_TEAM_MODIFIER (30 by default) and the numbers above do indicate approximately 3% per known civ. But the numbers don't exactly match either a Base*(1-.03k) or Base/(1+.03k) formula so there is either some complexity I haven't nailed down or some other modifier at play.