4) Guts!

Author:    Leonard Dickens
Email:     leonard@dc.net
Date:      1998/07/17
Forums:    rec.games.computer.stars

Here is an improved version of Thomas Pfister's excellent recent post on
bombing.  Since it came time for Armageddon's in a game I am in, I took
the time to understand the post and brush it up to cover bombing in a
more complete manner.

Bombing and Defenses in Stars!


Each Defense type has a specific "base" defense coverage, which is
the value of Defense coverage _ONE_ Defense gives population:

SDI      0.99%
Missile  1.99%
Laser    2.39%
Planet   2.99%
Neutron  3.79%

The coverage of more than one Defense is calculated as follows:

(4.1.1a) For pop defending against normal bombs:

  Def(pop) = 1-((1-d)^n), where n is the number of Defenses.

e.g. 100 Neutron-Defs:

           = 1 - ((1 - 3.79%)^100)
           = 1 - ((1 - 0.0379)^100)
           = 1 - (0.9621^100)
           = 1 - 0.0208
           = 0.9792
           = 97.92%

This is the defensive coverage afforded to population versus normal
bombs (like cherry bombs; see list below) and versus packet hits.

(4.1.1b) For buildings (factories, mines, and defenses themselves) the
defensive coverage versus normal bombs is halved:

  Def(build) = Def(pop)*0.5

e.g. versus 100 Neutron Defs:

             = 97.92% *.5
             = 48.96%

(4.1.1c) For pop versus invasions the coverage is 75%:

  Def(inv) = Def(pop)*.75

e.g. versus 100 Neutron Defs:

           = 97.92% * .75
           = 73.44%

(4.1.1d) Versus smart bombs the coverage is calculated differently.  The
base coverage level of the defenses is halved.  Thus, the total
defensive coverage is calculated as follows:

  Def(smart) = 1-((1-(d/2))^n)

e.g. versus 100 Neutron defs:

             = 1 - ((1 - (3.79%/2))^100)
             = 1 - ((1 - (1.895%))^100)
             = 1 - ((1 - 0.01895)^100)
             = 1 - ((0.98105)^100)
             = 1 - .1476
             = 0.8524
             = 85.24%

(4.1.1e) The following table summarizes the effective defense percentage
obtained against each type of attack, using 100 defenses:

          pop   build   inv   smart
SDI      63.03  31.51  47.27  39.12
Missile  86.60  43.30  64.95  63.21
Laser    91.10  45.55  68.32  69.95
Planet   95.20  47.60  71.40  77.83
Neutron  97.90  48.95  73.43  85.24

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Each normal bomb type has a specific pop-kill percentage, as well as
building-kill number and a minimum kill number.  The values given by
_ONE_ bomb are summarized here:

            perc #inst  min
Lady Finger 0.6%    2   300
Black Cat   0.9%    4   300
M70         1.2%    6   300
M80         1.7%    7   300
Cherry      2.5%   10   300
LBU-17      0.2%   16     0
LBU-32      0.3%   28     0
LBU-74      0.4%   45     0
OrbtlColnyM 0       0  2000
Hush-a-boom 3.0%    2     ?
MultiContnM 2.0%    5     ?

Normal bombs add linearly; that is, adding another bomb always
increases the amount of stuff killed/destroyed the same amount.  (That
is, until the enough bombs are there such that the planet is wiped
clean, after which point additional bombs add nothing).

The effect of normal bombs is computed as follows:

(4.1.2a) Normal bombs versus pop.

In this case, you get the larger of the percentage kill sum (as
modified by defenses), and the minimum kill value (also as modified).
It is typically the case that a bomb kills more than its minimum kill
value.  If so, you should use this formula:

  Normalpopkills = sum[bomb_kill_perc(n)*#(n)] * (1-Def(pop))

e.g. 10 Cherry and 5 M70 bombing vs 100 Neutron Defs (97.92%)

                 = sum[2.5% *10; 1.2% *5] * (1-97.92%)
                 = sum[25% ; 6%] * 2.08%
                 = 31% * 2.08 %
                 = 0.31 * 0.0208
                 = 0.00868
                 = 0.868% of planetary pop will be killed

The minimum calculation does not give a percentage of pop killed, but
rather an absolute number.  It works as follows:

  Minkills = sum[bomb_kill_min(n)*#(n)] * (1-Def(pop))

e.g. the same bombs/planet as the previous example:

           = sum[300 *10; 300 *5] * (1-97.92%)
           = sum[3000; 1500] * 2.08%
           = 4500 * 2.08 %
           = 4500 * 0.0208
           = 93.6  minimum pop killed (probably rounded to 100...(?))

To determine whether the minimum kill value will be used, just
multiply the planet population by Normalpopkills and see which is
higher.  Whichever way gives more kills is used.

e.g. the same bombs/planet as before; assume the planet pop is 300000.
The amount of pop killed (via Normalpopkills) is 0.00868 * 300000 =
2604 (rounded to 2600 (?)), which will used since 2604 is greater than

(4.1.2b) Normal bombs versus buildings.

  Destroy_Build = sum[destroy_build_type(n)*#(n)] * (1-Def(build))

e.g. 10 Cherry + 5 M70 vs 100 Neutron Defs

                = sum[10*10; 5*6] * (1-(97.92%/2))
                = sum[100; 30] * (1-(48.96%))
                = 130 * (1- 0.4896)
                = 130 * 0.5104
                = ~66 Buildings will be destroyed.

Building kills are allotted proportionately to each building type on
the planet.  For example, a planet with 1000 installations (of all
three types combined) taking 400 building kills will lose 40% of each
of its factories, mines, and defenses.  If there had been 350 mines,
550 factories, and 100 defenses, the losses would be 140 mines, 220
factories, and 40 defenses.

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Each smart bomb type has a specific pop-kill percentage.  The values
given by _ONE_ bomb are summarized here:

Smart              1.3%
Neutron            2.2%
Enriched Neutron   3.5%
Peerless           5.0%
Annihilator        7.0%

Smart bombs do *not* add linearly; instead, they use this formula:

  Pop_kill(smart) = (1-Def(smart))(1 - multiply[ (1 - kill_perc(n)^#n) ])

Where "multiply[x(n)]" is the math "big-pi" operator, which means
multiply all the terms together, i.e.:
  multiply[x(n)] = x(n1)*x(n2)*x(n3)... *x(ni)

e.g. 10 Annihilators + 5 neutron vs. 100 Neutron-Defs(Def(smart)=85.24%)

                  = (1-85.24%) * (1 -  multiply[((1-7%)^10); ((1-2.2%)^5)])
                  = (1-0.8524) * (1 -  ((1-0.07)^10) * ((1-0.022)^5))
                  = 0.1476 * (1 - (0.93^10) * (0.978^5))
                  = 0.1476 * (1 - 0.484 * 0.895)
                  = 0.1476 * 0.56682
                  = 0.0837
                  = 8.37% of planetary pop will be killed.

Notice that the second term asymptotically approaches 1.0 as the
number of bombs increase.  Thus, with high bomb numbers, the maximum
kills will approach the first term (14.76%); that's the term
determined solely by the planet's defenses.  There are two results
worth noting of this behavior, one each for the attack and defense:

On the attack, you will note that it doesn't really take that many
bombs to approach the kill limit; i.e., a single B-52 carrying 16
Annihilators will, by itself, kill roughly 69% of the maximum killable
pop; adding a second such bomber boosts this to 90%, and a third to
97%.  Adding additional bombers above this point gains you almost no
additional pop killed.  Thus, fleets of smart bombers should be quite

But on defense, we note that there is a maximum kill percentage for
any given defensive tech, and that as defensive tech increases, this
value can fall below the pop growth rate.  Thus, with planetary pop in
the high growth zone (say 1/4 to 1/2 max. pop), but above the level
needed to operate all defenses (250K), the planet may grow more pop
than can be bombed!  Sometimes you can never bomb out a high defenses
planet with smart bombs alone.

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When you attack a planet using multiple types of weapons/bombs
(i.e. mixing normal and smart bombs), the effects are resolved in the
following order:
        waypoint 0 invasions
        in-space packets move, hit
        production (new installations built, new packets launched)
        population grows/dies
        normal bombing
        smart bombing
        waypoint 1 invasions

Each of the steps above is done for each player, before moving on to
do the next step.  Thus, allies bombing the same planet can therefore
overcome the smart bomb pop-kill limitation, as they are individually
limited but not collectively.  (And two players each knocking off 15%
of the pop will be able to clear any planet).  It is also possible to
use normal bombs to knock down a planet's defenses before destroying
the pop using smarts against the weakened defense.

(4.1.5) Credit

This file was created primarily by Thomas Pfister, who posted it to
r.g.c.s on June 6, 1998.  Leonard Dickens has cleaned up the English,
anglicized the numbers, and added extra analysis/details not found in
the original.  Credit is also due to SBPosey, whose useful work on exact
order of execution is excerpted here in section 4.1.4

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 You can gain tech from another player in 3 ways.
 1) Scrap, at one of your starbases, a ship with higher tech than you possess.
 2) Have an armed ship present at a battle in which a ship with higher tech than you possess is killed.
 3) Invade the planet of a player with higher tech.

For each event (battle, scrap, or invasion), there is a 50% that nothing
will be learned.  If that test is passed, then there is a 50% chance for
each tech category that is superior to yours that you will learn a tech.
For ways (1) and (2), the only techs that count are those that went into
building the ship.  For way (3), all techs that the invaded player has
are available.  Once you learn a tech, by any method, that is it for the
turn; only 1 tech from other players per turn.

 You have techs at all 10 and your opponent has techs at all 11.

 You destroy a Scout A (Tech 0) with a Trans-Galactic Drive (Tech 9),
a Dolphin Scanner (Techs 10, 5 and 4), and a Colloidal Phaser (Tech 10).
You chance of learning a tech level is 0 (no superior tech categories).

 You destroy a Scout B: the same scout, but with a Gatling Gun
(Tech 11) in place of the Colloidal Phaser.  Your chance of
learning a tech level is :
 (50% for learning ANYTHING times 50% for 1 superior tech category)=25%
 If you learn a level, it will be weapons (from the gatling gun)

 You destroy a Scout C: Scout B with a Cheetah Scanner (Tech 11)
in place of the Dolphin Scanner.  The ship has superior tech in two fields, so your chance of learning a tech level is
  .5 * (1 - (.5^2)
 =.5 * (1 - .25)
 =.5 * .75 = .375
 (50% times 50% for 2 superior tech categories)=37.5%
 If you learn tech, it will be either weapons (from the gatling gun), or electronics (from the scanner).

 You invade one of his planets.  You chance of learning a tech level
  .5 * (1 - .5^6)
 =.5 * (1 - .015625
 =.5 * .984375 = .492
  (50% times 98.4% for 6 tech categories)=49.2%
 If you gain tech, it could be in any of the fields your opponent leads in.

 You destroy 5 Scout Bs in 1 battle.  One Battle, so chance is the
same as for a single Scout B: 25%.

 You destroy 5 Scout Bs in 5 separate battles.  Your chances are
 (1 - (1 - 25%)^5)=76.27%

 For 5 Scout Cs in 5 separate battles, 90.46% (1 - (1 - 37.5%)^5).

 For 5 Invasions: 96.62% (1 - (1 - 49.2%)^5).

 For purposes of destroying ships, it doesn't matter if they are destroyed
in battle or scrapped.  It also doesn't matter if they are owned by you or
another player, or scrapped by you or another player.

 Remember you may only gain 1 tech level from another player per turn, via any method.  In terms of turn order, scrapping takes place first, then waypoint zero invasions, then battles, then waypoint one invasions.

(courtesy SBPosey, with minor editing by myself)

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 The wolf/sheep concept relies on the fact that a player with a warship (wolf) present at a battle in which a ship (sheep)with superior tech is destroyed stands a chance of gaining a tech level.   With scrapping, you can attempt to transfer tech to a single ally.  By arranging to have the ship killed, rather than scrapped, where 2 or more allies are present, each of them stands a chance of gaining tech.  Thus, this is often the tech trading technique larger alliances favor.
 Since, presumably, the parties involved in the scheme have each other set to friend, the wolf ships must have their battle orders explicitly set to attack the player providing the sheep.  For this reason, the sheep donor should take care not to have any ships present other than the sheep due to be destroyed.

 Example: races A, B, C, and D enter into a tech trading alliance.  Each race produces 6 'wolf' ships.  They each split these ships into two fleets of three, and send each fleet to an uninhabited planet near their homeworld.  Once there, the fleets are split, and one wolf from each fleet is given to each of his allies.  Now there are eight sheep/wolf sites; each player has a ship present at six of these sites, and prepares to send sheep to the remaining two.
 All players give their wolves orders to attack only the player who is about to start sending sheep.
 The players discuss amongst themselves who shall specialize in what fields, and start building two sheep per year, and sending them off to the nearby sites.
 Eventually, players may wish to send wolf ships of their own to each of the sites, so that they can clear up some ship slots.
 In this way, each player has 6 chances to gain tech, at the cost of two sheep, each year.
 This is cheaper and easier than managing scrapping.  On the downside, you don't have control over which field you try to gain in a given year.

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Tech Trading The Invasion Way

 What you want to do, of course, is set up a planet of which two of you can trade ownership, over and over.  Each ownership change has a chance of giving the invader a bonus tech level.  The chances of tech transfer depend on how many tech fields the invader is behind the defender in.  Nothing to do with how FAR behind he might be, just how many fields the other guy leads in.  Check out the article 'Guts of Tech Trading' for more detailed info.
 Of course, the more often you can trade the planet, the more chances for tech transfer.  You want to take advantage of the fact that there are two periods in each Stars! turn during which an invasion can take place.
 At the start of a turn, all ships with waypoint orders for the current location are carried out.  Then ships move.  Then the destination waypoint orders are carried out.(see 'order of events in a turn').  Thus, at the start of each turn, one of you is going to invade the chosen planet from a ship in orbit.  Then, later the same turn, the other is going to arrive with a freighter and invade right back.  Next turn, same deal.
 So one of you needs to have a freighter full of colonists at the planet, and each turn, manually drop 200 colonists.  You can't use repeating orders, as they only work when the ship moves each turn. And you can't move the ship each turn, 'cause then the orders will be carried out at the end of the turn, and you need them carried out at the beginning.  You HAVE to do it manually each turn.
  The other player needs 2 freighters, which can be on repeating orders, moving to the planet and invading with 200 colonists one year, moving away again the next, and repeating.  It's a two year repeating cycle, so you need 2 ships, so one can arrive like clockwork each year.
 Why 200 colonists each time?  Well, the smallest unit of colonists you can beam up or down is 100.  So you want no more than 100 colonists on the planet at all times, so it's as easy as possible to invade.  That means you have to invade with 200 colonists, 100 to be killed in the fighting, and 100 to remain for the next invasion.
 At this rate, a medium freighters worth of colonists will last 60 years.  That's cheap enough, dont'cha think?

 When you're setting this sort of operation up, you can run into problems if you forget that the pop count you see on another players planet is only an approximation (see the little +- in front of it?)  The lowest pop your scanners will EVER see on another players world is 400.  So you have to communicate with your ally.  Decide who's going to send the colony ship to get the invasion world up and running (with only 100 colonists, not 200, as none will be lost to invasion), decide which year you're going to start, and then trust the other guy to do the right thing, 'cause you CAN'T SEE how many colonists are actually on the planet when it's in his possession.

 It's nice to pick an invasion planet within one years travel of the guy using the 2 freighters.  There are several advantages to this.  First, it means the freighters don't have to be full of colonists sitting on their asses when they could be hard at work, generating resources.  The freighters can pick up 200 at a time on auto-orders, and ferry them to the invasion world.  It also means they will never run out of fuel, and they stay under protection of any forces you have defending the planet.  It also makes the process invisible to all but the most careful observer.  As the invasion planet is always in the same players possession at the end of the turn, it does not appear to others to be trading hands at all, unless they take note of the ships in orbit, and the low population, and deduce the truth.

 Another nice thing about this invasion method is that planets that are red to both races may be used.  The only thing to remember is that the guy who invades manually at the start of the turn will be in possession of the planet when 'die-off' occurs, so if the planet is red for that player, he should drop 300 colonists a turn... 100 to die invading, 100 to die off due to climate, and 100 to remain to be killed in the next invasion.

 For each invasion, your chances of getting tech can be quite low.  So to get maximum benefit, you have to do it on a lot of worlds at once.  Why not, if you've got red worlds just sitting there unused?  The initial costs are low, and the payoff just keeps coming.

 Check out the chart below.  It shows the percentage chance of tech transfer per year in different circumstances.  Note that since each planet yields one invasion per turn to each player, the transfers go both ways.

        Numbers show percentage chance of a tech advance in a turn

Tech levels
you lag in

     6   |  49     74     87     93     97     98     99
     5   |  49     74     86     93     96     98     99
     4   |  47     72     85     92     96     98     99
     3   |  44     69     82     90     94     97     98
     2   |  38     61     75     84     91     94     96
     1   |  25     44     58     68     76     82     87
             1      2      3      4      5      6      7
                                                 Invasion worlds used

 As you can see, the more worlds the better!  With 6 or 7 worlds operating, two players can split the research duties and virtually never need to duplicate the other's efforts.

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 The guts behind how and why scrapping works found in 'Guts of Tech Trading'.
 For practical purposes, these are the things to remember:
 1) You must scrap at a starbase belonging to the person receiving the tech.

 2) It makes no difference if your ally scraps the ships at your starbase, or if he transfers the ships to you, and you scrap them.

 3) Remember: scrapping is a waypoint zero task only; you cannot scrap the same turn the ship moves.(see sec 3.1, 'order of events in a turn')

 4) To gain tech in a given field from scrapping, the scrapped ship must contain an item requiring a higher tech level in that field the receiving player possesses.

 4) The odds of gaining tech from scrapping depend on the number of fleets scrapped, not the number of ships.  Scrapping a fleet of 5 ships has the same effect as scrapping a fleet of 1 ship.  Split the 5 ships into 5 fleets, then scrap, and the chance of transfer goes way up.
 Below is a small table showing the likelihood of tech transfer per fleet scrapped in a single turn, assuming the ship scrapped contains superior tech in one field.

 fleets scrapped     chance of transfer
               1                    25%
               2                    44%
               3                    58%
               4                    68%
               5                    76%
               6                    82%
               7                    87%

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  The cost of a tech level depends on four things:
 1) Your research setting for that field (cheap, normal, or expensive)
 2) The level you are researching (higher level, higher cost)
 3) The total number of tech levels you have already have in all fields (you can add it up yourself, or look at 'tech levels' on the 'score' screen).
 4) whether 'slow tech advance' was selected as a game parameter.

 in general,

 totalCost=(baseCost + (totalLevels * 10)) * costFactor

 where  totalLevels=the sum of your current levels in all fields
   costFactor =.5 if your setting for the field is '50% less'
                      =1 if your setting for the field is 'normal'
                      =1.75 if your setting for the field is '75% more expensive'

 If 'slow tech advance' is a game parameter, totalCost should be doubled.

 Below is a table showing the base cost of each level.

           Level   Cost            Level  Cost

             1     50              14    18040
             2     80              15    22440
             3     130             16    27050
             4     210             17    31870
             5     340             18    36900
             6     550             19    42140
             7     890             20    47590
             8     1440            21    53250
             9     2330            22    59120
             10    3770            23    65200
             11    6100            24    71490
             12    9870            25    77990
             13    13850           26    84700

It's a Fibonacci series up to level 12, then it levels out
quite a bit. To get all 6 categories to TL26: (at all normal cost):

This includes the 10/level additional cost, and assumes all tech areas
start at TL0.

(Courtesy Bob Martin, with some editing/formatting/additions of my own)

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continue to 4.4)