Clash of Clans Math – Using Linear Inequalities to Save Elixir

This is quite a nice video on Clash of Clans and Math. Only got 70 views so far, but it is definitely a well prepared video.

Another video:

Farming in Clash of Clans has just gotten harder, due to nerf on Town Hall not granting shield, and very powerful defenses for TH10 and TH11. Watch these videos and you may gain some idea on a better way to farm.

Giant VS Golem: Clash of Clans Math

My previous posts on Clash of Clans Math (on Mortar damage, and Gold mine) were fairly popular, so I have decided to write one more post! This shows that Math can be applied to almost everything, even games!

Giant VS Golem: Clash of Clans Math

Giant lvl7 Vs Golem5

Recently, players of COC will know that the Level 7 Giant has been released. For fans of the Giant (I am one of them), this is great news. The Giant is a cheap substitute for tanking vs the Golem, and can be used in many strategies for instance Giwipe (Golem, Wizard, Pekka), Garch (Giant archer), among many others.

In this post, I will use Math to concretely compare the Level 7 Giant and the Level 5 Golem. For fairness sake, we will compare 6 Giants with 1 Golem (since they take up 30 spaces). Sources are taken from http://clashofclans.wikia.com/.

Health

  • Level 5 Golem has 6300+2×1260=8820 HP (We have factored in the 2 golemites)
  • Six Level 7 Giants have 6×1100=6600 HP

Conclusion: Golem is around 30% better than Giants in term of HP.

Calculation: (8820-6600)/6600 x 100%=33.6%

For pure tanking, nothing beats a max level Golem.

Golemite 1 and 2 cut out photo of Golemite Ssfang

Damage per second

  • Max Golem has 54 Damage per second + a 550 damage upon death. (We have ignored Golemites damage since it is really negligible)
  • 6 Max Giants has 6×50=300 DPS

Conclusion: Giants are 450% better than Golems in terms of DPS!

This can be quite significant, for example, when using Giants in Giwipe, often one does not even need to use wallbreakers, since the giants can break through the walls on their own. This frees up more spaces for wizards/other troops.

NewGiantTroopInfoImage

Against Spring Traps

Spring Traps are the ultimate nemesis of Giants, since each Spring Trap can bounce 15 Housing spaces, or 3 Giants.

  • Golems are unaffected by Spring Traps. (1 Golemite can be bounced by each Spring trap though)
  • Each Spring Trap can bounce 3 Giants. Town hall 10 has 6 Spring Traps, potentially bouncing a whopping 18 Giants.

To avoid Spring Traps, place a few barbarians before sending out your giants. Hopefully the barbarians will activate (and waste) a few spring traps.

Conclusion: Golems are more resistant to Spring Traps.

Against Inferno Towers (Multi-mode)

  • A Level 3 Inferno Tower does just 42 DPS to a Golem
  • It does 42×6=252 DPS to 6 giants.

Conclusion: Superficially, it seems good that Golems take 80% less damage than giants from Multi-mode Infernos. However, a bit of thinking reveals that the inferno in multi-mode will be attacking your other troops (for example wizards) instead, together with the 1 Golem. Hence, in other words, Golems also tank 80% less damage than giants from Multi-mode Inferno towers.

Inferno3

Against Inferno Tower (Single Target)

This calculation gets a little complicated. The inferno (Level 3) has 36 DPS initially, then 140 DPS after 2 seconds, then a whopping 1400 DPS after 5 seconds.

  • To kill the initial Golem (6300 HP), the inferno tower needs to take around 9.1 seconds. The first two seconds will pump out 36×2=72 damage, next 3 seconds will pump out 140×3=420 damage, while the remaining 4.1 seconds will deal the bulk of 4.1×140=5740 damage.
  • To kill 1 single giant (1100 HP), the inferno tower needs around 5.5 seconds. (36×2+140×3+1400×0.5=1192) Hence to kill 6 giants, 5.5×6=33 seconds is needed.

Conclusion: Giants survive 260% longer than Golems under Inferno (Single Target) Fire!

Inferno3

Other last points to note are that everytime a giant dies, there is a switch of targets, potentially attacking weak but crucial units like wizards or witches. This is a downside of giants.

So, who do you think is better? Giants or Golems? Leave your comments below!


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Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

CoC_titlescreen_2013

We can learn some mathematics from the popular game, Clash of Clans!

Lets look at the Building Cost and Production Rate of the Gold Mine.

Source: http://clashofclans.wikia.com/wiki/Gold_Mine

Gold Mine11clash of clans gold mine ap gp

We see that the Build cost actually follows a geometric progression(approximately) as each time, the build cost approximately doubles.

The formula for the n-th term of a geometric progression is \boxed{ar^{n-1}}, where a is the first term, and r is the common ratio.

The above formula works well for the first 2 terms, for example the second term is 300=150(2^{2-1}).

However, the Production Rate follows an arithmetic progression, as per level, the production rate increases by 200/hr.

The formula for the n-th term of an arithmetic progression is \boxed{a+(n-1)d}, where a is the first term, and d is the common difference. The formula works for all the 5 levels: for instance at level 5 the production rate is 1000=200+(5-1)(200).

Thanks for reading, and do “like” this post if you enjoy reading it! Hope you learnt some mathematics along the way.