Gilmoy's 0.42 Journal: Cultural "Influance" 101

B. Nomenclature and Summary (so far)

Cultural influence (or Influence for short) has several parameters, which form a pipeline.  These data are somewhat dispersed, so you must do the database join by click-drilling every turn.

Every planet has these parameters (in pipeline order).  Below each, I list some of the things that affect them.

1. Influence Growth (leftward-flag icon) (Planet cornerbar: public for enemy planets in sensor range)
• I will abbreviate this to "igrowth" hereafter, to distinguish it from population growth.
• This is further split into two types of awards: base points gb and percentage +hb%.
1. Anything that says "Influence Growth +gb" gives you base points.  It is not a formatting error for "+100%"; it really is distinct.
• +2: Civilization Capital
• +1: Colony Capital
• +2: Financial, Manufacturing, Technological Capital (each!)
• +1: Consulate ==> (upgrades to) +2 Cultural Center ==> +3 Outreach Center
2. Anything that says "Influence Growth +hb%" gives you a % bonus to your base igrowth.
• up to +50%: previous turn's Approval bonus%
• +5% each: Influence levels for improvements (e.g. tile and adjacency bonuses)
• +25% Cultural Forum
• ==> +50% Information Hub
• ==> +75% Interstellar Exchange
• ==> +100% Interstellar Embassy
• ==> +150% Interstellar Ministry
• +25% Franchise Center
• Total igrowth is then (Σ gb) * (1 + Σ hb).  This is shown next to each planet's leftward-flag icon.
2. Current Influence (Planet Manage, Influence hovertip, above the total line) (private)
• This is an unbounded(!!) accumulator, which increases monotonically, for the duration of the game.
• It seems to preserve full floating-point precision internally.  For display, it truncates (not rounds) to 0.1 precision.
• Initialization: current influence = 30.  This applies to:
• your homeworld on turn 0
• every new colony, on the turn of colonization
• Capturing a planet preserves(!) its current influence.  It doesn't reset it to 0 or 30!
• [x] by invasion [eviator]
• [_] by influence-flip: ??
• Every turn: current influence += (previous turn's influence growth/10).
• No limit.  eviator reports that on turn >400 he has a planet with current influence >2800.  I'm still putzing around in the low-100s.
3. Influence bonus (upward-radar waves icon) (Planet Manage, Influence hover tip: private)
• Anything that says "Influence +%" gives a percentage bonus to the Current Influence.  These include:
• Racial traits: Influential +2 = +25% (Terran, Altarian, Iridium)
• Planet specials: Serene +25%; Twin Moons +50%
• Colonization events: Funny Tasting Food B+10%, Ruins B+20% (where B denotes the Benevolent choice)
• Ideology choices:
• Benevolent:
• +05% for tier-1
• +10% for the 1st tier-2 (nothing for the 2nd)
• +15% for the 2nd tier-3 (nothing for the 1st) -- this popped my entire ZOC-perimeter!  that was fun
• [_] Pragmatic?
• [_] Mercilevolent?
• +10%: Passionate Representation, Influential Voice
• +50%: Diplomatic Outpost
• +150%(!!): Innovation Complex
• Some have reported this as a bug, thinking it should be +150% Research.  But after you read this thread -- you might appreciate it the way it is!!
• Total influence is then current influence * (1 + Σ influence bonus).  This is shown next to your radar-waves icon.
• It also increases with current influence, but it can jump suddenly whenever your bonus changes from one turn to the next.
4. Zone of control (ZOC),  in radius of space hexes.  This is drawn as the blue border around every friendly planet, and as the light shaded area on the mini-map.
• ZOC radius = f(total influence), for an unknown function f.  In a later reply, I'll tabulate empirical data for the thresholds of f.
• ZOC is (usually) much greater than your planet's sensor range.  As your current influence grows without bound, your ZOCs will all creep outward until they collide with non-friendly ZOCs.
• Adjacent friendly ZOCs merge.  N.B. GC3's graphics engine makes this quite beautiful -- you must play an influence game once just to watch your map as art.
• Adjacent non-friendly ZOCs compete, and create a Voronoi-like partitioning of the (galactic) plane.  I'll elaborate this below.
• ZOCs affect:
• tourism income
• [_] anything else?

C.  Confound: Starbases

The above is for planets only.  Starbases add their own twist.  Keep in mind that starbases are missing many planned features, e.g. the crew and module effects tabs on the Starbase Manage screen.  Surely starbase influence UI will be part of a future Beta release.

• [_] Starbases do(?) have their own Influence Growth.  We just can't see it yet.
• I infer this because some starbase modules add Influence Growth with a <Target>Starbase</Target> tag.  These apply to:
• [_] the starbase itself
• [_] friendly starbases in starbase effect?
• [x] not to friendly planets in starbase effect
• =0(?): naked or non-Culture starbase.  Datum: 61 turns, no growth.
• =0(?) (despite its text saying "+1"): Culture Ring.  Datum: 54 turns, no growth.
• [0.42 bug?] I now suspect that the <Target>Starbase</Target> tag is a typo for <Target>Planet.
• "+1": Diplomatic Outpost
• Current influence: Initial value unknown.
• [_] 30?  (but then it would have range 7 hexes)
• [_] whatever value exactly gives range 5?
• [_] Influence bonuses: none?
• Zone of Control of 5 hexes.
• [_] Does it ever grow?  Experiment: mining starbase, watch its ZOC for 100+ turns.
• Datum: Starbase, no ring, 61 turns, no growth.  Hypothesis: Base influence growth of 0.
• Datum: Starbase, no ring for 5 turns, Cultural Ring for 54 turns, no growth.
• [x] Conjecture: It is simply the starbase's effect range.
• Partially confirmed.  Datum: Support Field Stabilization (effect range +2), effect range and ZOC both increased to 7 hexes.
• [_] 2nd module: in Age of War ...

A starbase affects igrowth and influence bonus for all friendly planets in starbase effect.  (I'm already benefiting from it in my test game.)

• [_] For a culture-flip "attack", it is not clear (to me!  I'm a noob) whether you should put your starbase effects around the enemy planets (i.e. build them close to the enemy), or around your own.
• [_] If you put them near the target enemy planet, whose current influence do they project?  Their own?  Your nearest planet's?  Something else?
• [_] Do +influence% starbase modules amplify your "decayed influence waveform" in all space hexes in starbase effect?

That's what I test when I'm not trying to win 

D.  Influence-to-Radius: Function and Data

Math interval nomenclature:

• Square brackets [, ] denote closed endpoints.  I use these when I'm nigh-certain of a breakpoint.
• Parentheses (, ) denote open endpoints.  I use these when my data are too coarse to be sure of a breakpoint.
• Total influence UI display seems to round nearest to 0.1 precision.  However, current and total influence both seem to preserve full precision internally.  When I "know" an endpoint to 2+ digits of precision (based on the above pipeline), I'll write it as "x.x" x.yyyy.

From my notes, here's what I have so far.  I'll edit as new data (and hypotheses) arrive.  Update: Turn 111.

• 05 hexes: (???, ???) -- whatever initial value a starbase gets
• 06 hexes: (???, ???)
• 07 hexes: [??.?, 30.0)
• 08 hexes: (30.3, "38.1" 38.15)
• 09 hexes: (38.3, "46.8" 46.8195]
• 10 hexes: [46.9, 56.4]
• 11 hexes: (56.4, 66.6]
• 12 hexes: (66.7, 77.3)
• __ dunno: (77.4, 77.6)
• 13 hexes: ("77.7" 77.7375, "89.1" 89.154)
• 14 hexes: ("89.9" 89.9325, "101.5" 101.52)
• 15 hexes: ("102.2" 102.2625, "114.7" 114.672)
• 16 hexes: ["114.8" 114.835, "127.4" 127.448)
• 17 hexes: ("128.5" 128.496, "142.9" 142.896)
• 18 hexes: ("143.3" 143.289, "157.9" 157.872)
• 19 hexes: ("159.2" 159.216, "173.5" 173.496)
• 20 hexes: ("175.4" 175.419, ...)
• 21 hexes: ("191.8" 191.856, "204.0" 203.9603)
• 22 hexes: ("207.4" 207.441, ...)

wow, that's a read for tomorrow, thanks for posting.  I want to digest it fully, no can do while half asleep.  I prefer never starting the fights. I love to win the hearts and minds.

D2.  Influence-to-Radius: Notes and Comments

• Consider a new game.
• Homeworld ctor initializes current influence 30.
• Civilization Capital gives igrowth +2 base points.  Assume we keep Approval 100% = +50% bonus tier.  Then igrowth = 3.
• T/A/I all have the Influential (+2) racial trait = Influence +25%, so their total influence = (30 + 0.3t) * 1.25.
• Turn 0: 37.500 => 8 hexes.
• Turn 1: 37.875
• Turn 2: 38.250 => 9 hexes.  Their ZOC always pops on turn 2!
• I had to play Drengin =0% to test for total influence values < 37.5.  They have no trait, so their equation is simply 30 + 0.3t.
• Turn 0: 30.0 => 7 hexes.
• Turn 1: 30.3 => 8 hexes.  Drengin's ZOC always pops on turn 1!

Raise your hand if you've noticed this!  Else hie thee hence, Start Game, scrap your ships and click Turn

Corollaries:

• The influence pipeline seems to be entirely deterministic.  Plug and chug.
• Two identical colonies (same Influence bonus, or lack thereof) that were colonized on the same turn, with identical Influence-affecting things (same improvements/starbases, or lack thereof), will always have identical current influence and total influence.
• If they were colonized on different turns, the later one will exactly repeat the same influence progression of the earlier one.
• From this, we can predict the ZOC-growth times for typical colonies.  Let's assume +50% Approval bonus throughout.
• Hex 7, 8, 09, 10, 11 hexes: For these radii, I'll tabulate the turn(s-after-colonization) on which they occur, and their equations.
• Naked planet, i.e. with no Influence bonus, events, improvements, or starbases:
• Turn ~, 0, 02, 26, 051: (30 + 0.30t) * (1.25): T/A/I homeworld
• Turn ~, 0, 04, 51, 101: (30 + 0.15t) * (1.25): T/A/I colony (Colony Capital +1 gb)
• Turn 0, 1, 28, 88, 123:   30 + 0.30t: Drengin homeworld

Hypothesis:

• Consider the series given by k_n = SUM{i=1}{n} (i) = n(n+1)/2.  Tabulate its values, and compare to the (fuzzy) radius upper breakpoints:
• k_01 = 01
• k_02 = 03
• k_03 = 06
• k_04 = 10
• k_05 = 15
• k_06 = 20
• k_07 = 28 (07 hexes = 30.0)
• k_08 = 36 (08 hexes = 38.0625)
• k_09 = 45 (09 hexes ~ 46.8)
• k_10 = 55 (10 hexes = 56.3)
• k_11 = 66 (11 hexes ~ 66.3)
• k_12 = 78 (12 hexes ~ 77.2)
• so close, but ... what's the rule?  Can somebody do a better curve-fitting?
• [_] Customize a race with influence penalty racial traits to test current-influence scores < 30 ...

E.  Epiphanies

I was startled at some of these results.  They're non-intuitive ... so we must retrain our intuition.

1. Current influence is a clock.  This is ... a ginormous concept, which should cause you to completely re-assess the worth of Influence improvements.  It sure flip-flopped my estimate of "lowly" Consulates!!
• Current Influence is unbounded(?), and appears to be immune to damage or reduction(?).  Hence, it increases monotonically, for the duration of the game.
• It follows that, in an influence-war, the mightiest "weapon" is the clock.  It's a Time Cannon, with game turns as ammunition.  (Insert Scottie in J. J. Abram's Star Trek Reboot: I did think of time as the thing being fired!!)
• More specifically, your weapon is simply how early you started to pump your Influence Growth.  The unbounded nature makes influence-racing fundamentally different from all other arms-races.  If you fall behind early, you may never catch up.  Just ... never.
2. Contrast this to the standard military conquest, or economy.
• Manufacturing-based clocks are capped by the pop limit.  Eventually, your planets fill up.  Hence, even if you get a head start in birthing and conquesting, I can catch up later.  Eventually, both of us will have maxed out our planets.  Your advantage is then simply the area between our two manuf curves, for the time interval in which you had the gap advantage, in total manuf.  If you spent that surplus on ships that got destroyed as you slogged across the galaxy to get to me ... then when we meet, I might still be equal to you in terms of manuf-turns of stuff in play.
• Ship techs are "clockless".  If you research Large 60/48s on turn 100 (and then freeze tech while you do other stuff), and I get them on turn 250 ... mine are still exactly as strong as yours.  Stalemate.  So I can just wait, and research them later.  All I have to do is match your fleets in size, and your earliness gives you zero advantage.
• [_] An economy strategy is also (potentially) unbounded.  If you get a $ lead, I might never catch up.  But ... can you buy a tactical win with that?  Is there a way to convert bc to planet-ownership?  (Beta 2+ will surely add more cool stuff to do with your $.)
• [_] Diplomacy, e.g. United Planet votes: ???
  
3. ZOC never shrinks.  It strictly grows outward (as long as you hold the planet).  It never shrinks or decays.
• Obviously, losing a planet to conquest or flip also flips its ZOC from friendly to enemy.  We will disregard this hereafter.
• You can safely destroy a Consulate or other Influence improvement without affecting your ZOC.  Your ZOC does not shrink; it only grows more slowly.

Let's doodle some numbers.  Hypothesis: Enemy AI's homeworld H is its last surviving planet.  You create a new planet Q next to it, and colonize that.  (Maybe you have Extreme Colonization tech, and it didn't.)  How do your Influences compare?

• It is turn 380.
• H had some stuff for Influence Growth 6.5 (which you can see).  Let's say he averaged 6.4 over the entire game.
• H's current influence = 30 + (380 * 6.4/10) = 273.2.
• You can't see this, but you can easily compute an upper bound for it: 30 + visible igrowth * turn number.
• You cannot see H's Influence bonus of +22%.  N.B. Influence bonus is non-cumulative, so it is also memory-less: this turn's value is the only one that matters.
  
• H's total influence = 273.2 * 1.22 = 333.3.
• Your new colony Q starts at current influence = 30.  Disregarding distance decay, and assuming you can instantly surround Q with influence-boosting starbases (and carrier ships with influencer bays, if GC3 unveils that feature -- plz oh plz), what Influence +% do you need:
• to keep Q: Let's assume that the flip-threshold is 4x.  Then H is clobbering Q by 11.11x.  Then you need +278% just to get your nostrils above that 4x waterline.
• to tie H, so that hexes equidistant between Q and H flip a coin: +1,111%.
• to flip H: Let's assume that homeworlds flip the same as any other planet, i.e. no special rules.  Then you need 4x tie, so +4,444% (= 44.44x).  Maybe it's physically impossible to pack starbases into space at the required density levels to achieve that.
• Suppose Q can't flip H immediately, so you're going to grow into it.  What Influence Growth +% do you need to match H's inherent igrowth advantage over you?
• Q's naked igrowth = 1.5 (from Colony Capital and approval).  You need +433% just to tread water vs. H's igrowth of 6.5.  Otherwise, H is ahead of you, and pulling away.

More as I learn it.  Chime in with your (non-)war stories!

F.  Influence-in-space (hexes), Voronoi diagrams, flip-duels

I lack data here.  I'll edit this as I learn.

Your ZOC shows space hexes that are "within your influence" (or "sphere of control").  But ...

• [_] Do space hexes in your ZOC have Influence as a numerical attribute?
• Friendly ZOCs evidently merge via a simple max function, not add.  It doesn't matter how many overlapping ZOCs affect a hex; only the "strongest" one counts.
• [_] Influence decays with distance from its source.  What is the shape of the decay function?  Let r = distance to a hex, m = your influence radius.
• Conjecture: simple linear interpolation, total influence * (m + 1 - r) / (m + 1).
• Conjecture: It's convex downward, like an umbrella or cone head.  (Not a tent surface -- which can be concave due to gravity)  Hence, a hex closer to the source always has more influence than a farther hex.
• [_] Which came first, the radius function or the decay function?  i.e. does radius determine decay (equivalently: the staircase levels at each outward ring), or does decay naturally produce the radii?

When two non-friendly planets are near enough, their ZOCs intersect.  Let shared hexes denote the hexes in this intersection, i.e. in both ZOCs.  As we've all seen, the GC3 engine somehow assigns a winner to every shared hex, and then draws a wavy ZOC-boundary between the two ZOCs.

• Equidistant.  For shared hexes equidistant to two planets, the planet with higher total influence wins that hex.  Visualization: Umbrellas, with total influence as the length of the shafts.  Longer shaft wins, because it means the entire umbrella surface is higher by that amount.
• For "equally naked" colonies, this means: the earlier colony wins.  So colonization-racing is important.
• [_] Voronoi bisector.  If the two planets have identical total influence (e.g. they tied in the turn-of-colonization, and have same +% bonus), then ... I dunno!  Maybe the equidistant hexes become ZOC-free (which would be lovely).  Somebody post a screenshot?
• In graph theory, a Voronoi diagram is a partitioning of the plane such that every element (usually points, but it generalizes to line segments) is bounded by a cell of points that are closest to it (than to any other point).  It has obvious applications in the siting of any centralized physical service, e.g. hospitals, fire departments, airbases, Amazon drone fields.  The Voronoi cell boundary between two points is the perpendicular bisector of the line segment between them; between a point and line segment is a parabolic arc with the point as focus and line segment as directrix; etc.  If GC3's Manage and Govern windows are spreadsheets in space, then the main map is a Voronoi diagram.  Another way to envision it is that it's a "Venn-after-voting", i.e. a Venn diagram where you force every shared hex to commit, instead of showing them as being shared.
• I coin the term Voronoi ridge to be the (wavy) line of equidistant hexes that all go to the higher-influence planet.  This is the most common case; in fact, very rarely would you get a perfect tie.
• [_] r+1.  When both planets are "pretty close" in total influence, then all hexes with a 1-hex difference in range go to the closer planet.
• [_] I assume that the converse also holds: if I see two ZOCs where all of the r+1 hexes go to the closer planet (on both sides), then I infer that their total influences are "close".
• [_] r+k.  As one planet dominates the other in total influence, then it starts to win r+2 hexes (e.g. 8 hexes from me, 6 hexes from you).
• [_] Insufficient data.  Will edit later.

Finally, there is a pipeline(?) to influence-flip a planet.

• [_] Conjecture (from GC2): When hostile influence(-in-space) is 4x a planet's influence, the planet flips ...
• [_] ... immediately?  (i.e. next turn)

G.  The Influence Gambit: Consulates before Growth/Research/Expansion

With this in mind, I pondered an Influence Gambit (which I'm following in my test game).  The concept of current influence as clock has totally rearranged my priorities.

• End-of-game lifecycle pov.  Suppose the game shall last until turn 300.  What shall you build by turn 10?
• If you colonize 5 by turn 30 ... I can wait and catch up later.
• If you build weenies by turn 50 ... I can wait, and build just enough defense.  I hope!!  ok, speed weenie gambit is a wonderful confound, I hope the AI does it well
• If you pump growth and tech ... I can wait.
• But if AI #55 builds a Consulate on turn 8 ... then the only (easy) way for me to match that is to build mine on turn 7.  Current influence is the one thing I cannot just recoup later on.
• Homeworld builds:
• Consulate, for +1 gb = 3 gh = 4.5 Influence Growth.
• Part of my usual growth strategy: growth, manuf, 1 colonizer for Benevolence.
• Early detour for Diplomacy and the cultural techs.
• Go for Influence Growth things.  These add to your monotonic clock every turn, like a 401(k) match.  Even when you're doing other things, Influence Growth will keep adding, turn after turn.
• Don't worry about the Influence +% things.  These are non-cumulative, hence "clockless".  In the limit, you could wait until you're actually in a flip-duel, and only then splurge to pick up some Influence +% pumps.  They'll pay off in full on the very next turn.
• As for your subsequent colonies ... I'm still exploring that.
• [_] The obvious idea is: my interior and backfield planets (esp. in a safe corner or edge of the Large map) will not get into any flip-duels, so they can devote all tiles to the mainline growth strategy: growth, manuf triangle, then specialize.  I always build up manuf first, because it helps all subsequent builds, including later terraforming.
• [_] My frontier planets (toward the center, or large unexplored areas, or known AI sites) do as homeworld: Consulate first.
• Generally, whenever I make a strategic decision between influence growth, planet build-out, or colonization, I go for igrowth first.  All else can wait!!
• Proof sketch: Consider all permutations of those 3, and estimate their relative strengths at some future benchmark, e.g. by turn 100.
• Tech/manuf/ships may be exponential in power vs. time.  Hence, being behind by K turns may mean your net strength is only 70% or 50% (for a secondary-vs-primary prioritization match-up, or tertiary-vs-primary).  But that may suffice: my ships don't have to seek-and-beat yours, they just need to keep me alive, e.g. shoot down your transports and defend my Culture Ring starbases.
• Colonization (and conquests) is also somewhat exponential (but with a very small exponent?).  You're limited by pop growth rate to replenish losses, but the more sources you have running in parallel (which is somewhat clock-like, for many small clocks), the more frequently you can skim off a new wave of people.  OTOH, I might not care that you outnumber my planets 3-1, because I have a bat, you have some gold, now I have a bat and some gold.
• Current influence is linear in game turns x igrowth.  It may be the least exponential-like clock in the game(!).  Hence, you maximize the area by building up igrowth as early as possible, and running it for as long as possible.  Because of this strict linear nature and the decisiveness of influence-flips, it may be impossible to counter a large current influence lead except by spending an equal number of turns(!)
  
• First starbase (near homeworld, with 2+ planets in starbase effect) is Culture Ring, with all of the +Influence Growth modules ASAP.
• I do this even before I build an Economic Ring to pump production.
• [0.42] Pitfall: Research the cultural techs before the banking techs, due to cross-branch starbase module upgrade path:
• Gu4 Passionate Representation => Gu5 Cultural Exchange for Interstellar Exchange +75% before
• Gb4 Xeno Economics => Gb5 Interstellar Banking for Interstellar Embassy +100% (upgrades from Gu5 I.Exchange)
  
• In a less cut-throat style, you may choose to go for the banking techs first for other reasons.  Here I consider the influence-first gambit, so wealth must wait. (sigh)

In a previous thread, I gave my Technological Capital Gambit list of 17 techs in 30 turns. (scroll to top of that page)  That's fine for a mainstream conquest victory.  Here, I'll present an analogous list, but of Influence parameters, especially turns at which I achieved radius benchmarks.  All turns assume Approval +50% bonus tier.

• Altaria: default igrowth 2 +50% = 3, default influence +25% (racial) = 37.5 => 8 hexes.
• Turn 02: 9 hexes.  (This always happens for T/I/A homeworld; see above.)
• Turn 03: Consulate adjacent to capital (+1L), igrowth 3 + 55% = 4.65.
• Turn 10: Benevolence unlocked, influence => +30%.
• Turn 15: 10 hexes: 36.480 * 1.30 = 47.4.  (Compare to turn 26 for naked T/I/A homeworld)
• Turn 30: 11 hexes: 43.455 * 1.30 = 56.5.  (Compare to turn 51 above)
• Upgrade Consulate to tier 2 Cultural Center, igrowth 4 +55% = 6.20.
• Turn 31: Starbase with:
• Culture Ring ig +1 [_] does not seem to be adding, infl +10% => +40%
• Cultural Forum ig +25%, igrowth 4 +80% = 7.20.
• Turn 36: 12 hexes: 47.675 * 1.40 = 66.7.
• Upgrade Cultural Forum to tier 2 Information Hub ig +50%, igrowth 4 +105% = 8.20.
• Turn 46: 13 hexes: 55.875 * 1.40 = 78.225
• Turn 50: Mindfulness unlocked.  A tier-2 Ideology gives add'l Influence +10%?  Influence +40% => +50%.
• N.B. this can pop your ZOCs while you're in the Ideology screen.
• Turn 51: 14 hexes: 59.975 * 1.50 = 89.9625
• Turn 61: 15 hexes: 68.175 * 1.50 = 102.2625
• Turn 70: Passionate Representation, +50% => +60%.
• Turn 70: 16 hexes: 75.555 * 1.60 = 120.8
• Turn 76: 17 hexes: 80.475 * 1.60 = 128.76
• Turn 79: Upgrade:
• tier 2 Cultural Center ==> tier 3 Outreach Center ig +3
• tier 2 Information Hub ==> tier 3 Interstellar Exchange ==> tier 4 Interstellar Embassy ig +100% (yah, all in 1 turn)
• igrowth (2+3) + (100% + 50% +5%) = 5 * 2.55 = 12.75.
• Update:
• Turn 085: 18 hexes: 090.585 * 1.60 = 144.936
• Turn 092: 19 hexes: 099.510 * 1.60 = 159.216
• Turn 100: 20 hexes: 109.710 * 1.60 = 175.536
• Turn 108: 21 hexes: 119.910 * 1.60 = 191.856.  Before I could even count those hexes ...
• ... I colonized a planet, took Ideology tier-3 Breakthrough (which finished tier 3), and got Influence x => x+15% to all planets, instantly.  So all of my ZOCs popped while I was still in the Ideology screen!  I came back and ...
• 22 hexes: 119.910 * 1.75 = 209.8425

Watching my ZOCs pop exactly when predicted is half the fun (so far).  It feels totally different than my usual growth/tech/colony expansion style.

• I really want to try this with Iridium because the -25% growth racial trait makes it more of a challenge.  N.B. The current-influence clock is completely disjoint from population, so it's a great equalizer for races that don't have population to waste.

Thanks a lot! very impressive breakdown

This is great! I have some comments.

B.1. As you may recall, the approval production bonus is multiplicative, not additive. I believe for influence it is additive as you indicate in your formula (see C)

B.2. Here is a screenshot of my highest influence planet (turn 619). Note that my *current influence* is 1384.3, and my *influence bonuses* bring it up to 2491.7. I think you are right that there is no limit. Or rather, I haven't found it yet, it seems.

C. In my graphic above you can see 3 culture rings each adding a 10% *influence bonus*. I actually have 4 in the area, but only 3 cover my planet. So the initial "Culture Ring" starbase has that immediate effect.

The 3 starbases have been upgraded to Interstellar Embassies, each granting 100% *influence growth*. My planet has +10 gb (colony capital + 3 outreach centers). I have 100% approval (another 50%) and adjacency bonus gets me another 30% *influence growth*. So

10 gb * (1 + 3.00 + 0.5 + 0.3) = 48.0 *influence growth*

This is reflected in the map view:

Also you can see in the above screenshot the growth for the planet I'm hoping to flip. Since my growth per turn is over 7x the enemy's, assuming 4x is needed to flip and assuming starbases only affect *my* planet's influence, and assuming no decay penalty (lots of assumptions, some probably not sound), I would eventually flip this planet.

Culture Ring says it has "Influence Growth +1" in addition to the 10% planet bonus.

I also want to point out that while I have owned Embor II for a while, I only added the consulates within the last 100 to 200 turns. Embor III, however, has probably been colonized for around 500 turns, so it has built up a rather large bank of influence that I need to overcome.

F. The GC2 conjecture about planet flipping, I may be wrong but I believe the mechanics were once you hit 4x and maintained at least 4x for 10 turns, after that there is an independent non-zero probability of flipping on each subsequent turn.

Now here are some of my conclusions based upon your work and my experience:

* With the current available starbase modules it is neigh-impossible to culture flip using just starbases if I do not hold a nearby planet. I say that because starbases have, at best, very low base points, thus little for the starbase module *influence growth* bonuses to multiply. I could stack several around the nearest (but still far) planet, but because of decay I get diminishing returns.

* Even if starbase modules did give base points, it would have to be A LOT to culture flip in a reasonable amount of time.

* The larger the map, the less viable culture-flipping becomes, because the more distant planets will have built up influence for a long time.

* Based upon all this, I believe the "clock" idea is a bad one. At the very least the numbers are widely out of balance. The longer a game goes before you are able to start your culture bomb in a given area, the more time it takes to flip. This could make for some VERY long and boring games, which is out of balance with the other victory conditions.

Is there a Beta console command that will let us peek at a non-friendly planet's Manage screen?

• Edit: In [0.42-0911], the god console command, which "toggles the ability to manage all empires", does not let you peek at AI planets.
• In fact: it seems to have no effect at all.  I played 10 turns with god mode toggled on, and nothing changed.

Or, equivalently , flip a planet outright, so that I can just Manage it myself?  (I promise to flip it back to enemy!)

• Seriously tho ... that would be invaluable for reverse-engineering equations.  You could set up a 2-player game and flip Mars to enemy just to test your influence effect on it.
• Even better if a culture-flip (or invasion) clears current influence to 0 (or the default 30).  Then I could flip it repeatedly in the same game to test different gaps in culture.  (We must stipulate that a console command flip shall not reset current influence -- since the point is to peek at its value in the wild)

Except that you don't have to flip a single planet to win a culture victory. The culture victory conditions are to have x% of the galaxy inside your ZoI and don't be at war with anyone.

Fair point. Perhaps that's just the completionist in me that I want all your planets are belong to me.

What you say?!

Am I interpreting this right, that a given civ's culture value can't decrease but the rate at which it increases can, for example by eliminating starbases and influence buildings? And it is possible to catch up to and overtake another civ's culture in a given area by spamming culture buildings, even if it's increasingly difficult the wider the gap gets?

Not quite. A given source of culture's influence can't decrease, but if that source is eliminated or conquered a civ's influence can be decreased or eliminated.

Example: The Terrans have built a bunch of consulates on Earth and it is pumping out culture. The culture being put out by Earth will only increase. If they replace those consulates with research buildings the rate of increase will drop, but the Terrans' culture in the area around Earth will keep increasing. However, if the Drengin pull up with their transports and conquer Earth, all of that Terran culture that had come from Earth is gone. I am not totally sure, but I think that all the Terran culture becomes Drengin culture. For this reason, military conquest of a high-influence planet will often lead to a few flips the next turn. 

It is possible, but especially if you are trying to get to the 4x point to flip a planet a can take a loooong time. As long as you are putting out more culture in a given hex you are catching/pulling away from another civ, but because a civ's culture is always building, it isn't that hard to build up a lead that will take an impractically long time to overcome.

Ooh, so basically, you capture the palace and the less interested provincial governors just change the flags and get on with life? I like that :) 

Do you know if there will eventually be a visible  marker for a given tile/sector/planet's culture? 

There will be for planets, but I'm not sure about other tiles.

Aloha,

OK, I'm probably going to get ripped, but I'm going to ask anyway...

Where the heck are Consulate, Cultural Center, and Outreach Center?  I swear I have search the entire tech tree and the Ideology tree and I can't see where you get those.  I have invaded planets with them, so I know they are in the game, but I have never seen them anywhere.

thanks

Thanks

I dunno about the Cultural and Outreach Centers (I haven't searched the entire tech and ideology trees lol), but I'm pretty sure consulates are available at turn 1? :s

Ahhhh, I started a new game and there was the consulate.  The new game, I was Human...  the old one I was Iridium.  I didn't realize that the Iridium don't even have access to all that influence line.  I think this makes them far less than ideal for the Influence Gambit.

So I guess an Iridium player, especially in multiplayer against human opponents who understand this game mechanic, would be forced to go on the military offensive early in order to prevent themselves from falling too far behind in influence o.o

So,Build a Consulate,raise the planetary shield and lie back and watch the iridium fireworks!

The Iridium get their influence and economy together. It is gimped currently because the influence/economy buildings are 1/per planet and the top upgrade loses the influence bonus. They also have some influence buildings in the diplomacy tree that is currently locked.

Oh, ok I did think it was strange for the design of a faction that isn't typically portrayed as unusually militaristic would force it's players in practice to focus on militarism