Mana

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Revision as of 09:25, 31 March 2008 by Groentje (talk | contribs) (→‎Base node yield formula)
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Turns | Mana | Geld | Population | Land | Items | Spells


Basics

Magic Power (MP, m.p.) is also known as mana.

MP is generated and stored using your nodes.

  • The efficiency at which your nodes generate mana is controlled by the % of land that nodes occuppy.
  • The capacity for MP storage that your nodes provide, is 1,000 mana per node. You cannot have negative MP storage. You can have an temporarilly overfilled MP storage, e.g. when an enemy is destroying nodes - spending a turn will top-off that excess storage.


  • MP is consumed by many army units and heroes, by magic (spell casting, enchantments upkeep, defense assignment), by barriers. Your status report breaks down the total upkeep.
  • On most servers (except ARCH), summoning is restricted by your m.p. income:
    • when your income is negative, you cannot summon, recruit or buy more troops and your enchantments will no longer yield units.
  • There are also game features that alter the efficiency of your nodes: when items, heroes or enchantments reduce your MP production, that is called 'Hidden upkeep'.

Game features affecting M.P.

Items

  • Mana Crystal (lesser item) generates MP for your kingdom (random amount).
  • Mana Vortex (lesser item) destroys MP in target kingdom (random amount).
  • Efreeti Bottle (unique item) can refill your MP on using.
  • Some Uniques reduce your nodes MP generation (e.g. hidden upkeep)
  • Some Uniques boost your nodes MP generation (e.g. hidden bonus m.p.)

Enchantments

  • The Holy Light reduces your nodes MP generation (e.g. hidden upkeep)
  • Black Sabbath makes your MP generation fluctuate, but on average increases production in exchange for 666 population.

Spell

  • Earthquake will destroys part of targets MP, as well as a LOT of your own.
  • Wish can make you lose MP (100k) or give you Efreeti Bottle which can give you MP.

Heroes

  • Shaman ability 'channeling' increases node MP generation. The higher the hero level, the more efficient the channeling but also the more the upkeep for the hero. As a result there is shifting a break even point where the hero's channeling produces more extra MP than its upkeep, causing it to only be paying off on big land (>5,000 acres).
  • Devil Prince after Contract of Soul reduces your nodes MP generation (e.g. hidden upkeep). Devil Prince and Black Sabbath effects even out about.

Gods

  • Getting favour of any god, may refill part of your MP storage
  • Moon god favour and most favour increases node MP generation (by 10% resp. 20%)
  • Moon god disfavour and hatred decreases node MP generation (by 10% resp. 20%)

The number of nodes

  • Because of rounding in the m.p. formula (see text and chart below),
    • it is better to have e.g. 44.99% than to have 45.0% nodes.
    • depending on the number of nodes and the amount of land, destroying one can be more benefitial than building one.

MP charging

MP charging generates MP based on your "Income": it doubles what your nodes generate normally.

  • MP charging a good part of the turns in your turn cycle is essential for day-to-day oversummoning, and in upkeeping a huge army on relative small land, and an important part for strategies for many colors.
  • MP charging for an amount of turns that would overfill your nodes, is NOT a good idea: MP charge yield is accounted for early in the order of calculations, then topped off, and after that the m.p. upkeep for the amount of turns is calculated - resulting in underfilled nodes, even though you would have charged them full if you charged turn-by-turn.

zero m.p.

'Zero m.p.' is the case of fully depleting your magic power, complete stacks of m.p. consuming units may disband themselves (in random order: you may be able to keep supporting some of your smaller stacks); maintained enchantments may cancel themselves; and ultimately you may lose the barriers that you build.

More?

UBB thread of interest: http://ubb.the-reincarnation.com/viewtopic.php?t=12718


Turns | Mana | Geld | Population | Land | Items | Spells


Node yield / effectiveness of mana generation

The graph below illustrates that the more nodes you have, the less each individual nodes generates, and that above it is usually not worth building any more nodes: it will make you able to store more m.p., but per turn it will lower your m.p. generation, meaning you can support less m.p.-eating army with 70% nodes than you can on 50% nodes.

  • Stepped decreasing linear lines on the graph show decreasing gain-per-node above 10% node land use (LEFT axis) for normal and moons-favour situation.
  • Saw-tooth parabolic-like curves on the graph show what the m.p. yield for a given %percentage of nodes (RIGHT axis) for 2K, 3K, 4K, 5K and 5K+moon's favour situations.
  • the saw-tooth makes that for your m.p. income, sometimes it is better to destroy 1 node than to build 1 node (because of rounding). On 2K land it is a trivial effect, on 5K land between 25 and 55% nodes it becomes significant: you better check if your nodes are 'just below a whole %' right after each landrun.
  • Side note: having over 45% nodes on your land enables you to store more m.p. after charging a lot of turns than e.g. 45% nodes, but you will not produce more m.p. each single turn. You should only use >55% nodes if you have special need for lots of m.p. (eg casting Armageddon, or preparing a VE-bombardment or prepare to Earthquake a big mage or whatever).

Base node yield formula

After some investigation, i found out the REAL node yield formula.

Yield = XL/100 + N(100-X)/10 with X=floor(100N/L)

For full percentages this gives:

Yield Y = (10XL+100XL-X²L)/1000 = (110XL-X²L)/1000 = XL(110-X)/1000

In this formula:

  • Rndd= Rounded down function
  • N = amount of nodes
  • L = amount of land


Example1: Land=5000, N=1000, X=20

  • Yield = 20x5000/100 + 1000(80)/10 = 1000+8000 = 9000.


Example2: Land=5000, N=2000, X=40

  • Yield = 40x5000/100 + 2000(60)/10 = 2000+12000 = 14000.


Example3: Land=5000, N=1990, X=39, N/L=39.8

  • Yield = 39x5000/100 + 1990(61)/10 = 1950+12139 = 14089.
  • Max gain is thus when the first derative of this formula is 0: (for full percentages)
    • Max Yield for X: (110L-2X)/1000 = 0
    • <=> 2X = 110
    • <=> X = 55
  • Max gain in total is thus indeed at 55.99%.
  • Yield Y is your base income. It can now be influenced by:
    • Alchemist : - 0.10 Y
    • Moon's Favour : + 0.10Y
    • Holy Grail : - 1000
    • The Holy Light : - 0.25 Y
    • ...


AMNodebreakdown.jpg

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