Chaos Reborn

### Chaos Reborn

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Order in Chaos: The Battle-Math of Chaos Reborn
By Random Reference #98
A guide for players to help understand the math and risk management of Chaos Reborn as it relates to combat

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Introduction
(This guide is current as of 1.4. Some numbers might be out of date due to possible changes in creature stats but the concepts remain the same. Will look into whether the numbers need updating soon and if anyone notices any that are off from the current version of the game please let me know in the comments.)

This is a basic guide to help better understand the math involved in the combat of Chaos Reborn and to help improve player's risk management skills.

This is meant to be as easy to follow and apply as possible so I will only be covering attacking, defending and height considerations as they provide a good foundation to build on. I will also cover two special cases for creatures that have unique abilities.

It's recommended that you keep a calculator handy unless you are good at multiplying decimals in your head. Also to practice these concepts I suggest asynchronous games and/or single player against the AI offline or in realms as those offer the time needed to run numbers to your heart's content.
READ BEFORE CONTINUING
Before we get into things I need to point out that the values given in this guide apply to classic and don't factor in things like talismans and totems which give buffs to creature stats. If you play equipped you may need to adjust to the new values however by the end of this guide you should have no problem applying these concepts with all kinds of different percentages.

Also important to note is that all of these scenarios exist in a vacuum where only the specified creatures are in play, you will need to factor in other things such as positioning/other creatures and should not simply take moves that offer mathematical advantages for the sake of that advantage alone. Some creatures are worth allot more than others so it's acceptable in many situations to take a mathematically disadvantageous shot if the creature you are risking is worth less than the creature you are trying to kill, again circumstances should be taken into account.

There is a formula I will use throught the guide to determine a creature's chances of dying if they attack an enemy first. Remember that if a creature has for example a 75% chance of dying that is the same as having a 25% chance of survival and I will often use these interchangeably so please keep this in mind or later sections could be confusing.

Lastly this guide is meant to be read in order if possible as later sections assume you have read the ones before them.
Quick Explanation of ATK/DEF Values
Since the in-game guide doesn't really explain this well unless you're already familiar with the concept this section will briefly cover how the kill percentage is calculated when one creature attacks another.

Every battle in this game comes down to two values for deciding the kill percentage: The attacking creature's attack value and the defending creature's defense value.

In a battle where one creature has 10atk and the target has 10def the kill chance is 50%. This is because each value essentially represents the number of times a creature would kill/survive in the encounter if it played out multiple times. With the 10vs10 scenario the attacking creature will succeed 10 times and the defending creature will survive 10 times which is 10/20 total attacks ending in a kill or 1/2= 50%. If we do 10atk to 20def then 10 attacks will result in a kill while 20 will result in the defender surviving so 10/30 = 1/3 = 33%.

With that in mind the easiest way to figure out kill percentages on the fly is to simply add the attack value to the defense value then divide the original atk value by the new number. Dropping the zeros from each makes things easier as well.
For example: With 20atk to 30def we do 2+3=5 then do 2/5 = 0.4 or a 40% chance to kill.
For 30atk vs 50def it's 3+5=8 then 3/8 = ~0.38 or 38% to kill.
Attacking
At first glance this seems like the most obvious part of the game- My creature has x% of killing the enemy creature and that's that. But is it?

Let's look at an example:

In a rat vs rat mirror match both rats have a 50% chance to kill the other one. This seems like an even fight however by attacking first with our rat we are actually increasing the chances of our own rat's survival compared to our opponent's rat.

We can see why using a very basic formula that I will be using throughout most of this guide-
Our rat has a 50% chance to kill the enemy rat when it attacks and a 50% chance to die the next turn if the enemy rat survives. We already know the enemy rat has a 50% chance of surviving so let's see what our rat's chances of survival are by finding out the enemy rat's chance of killing it if we decide to attack first.
To do this simply multiply the enemy rat's chance of surviving(50% or .50) by the chance of it killing our rat(also 50%). So we do .50 x .50 = 0.25 or a 25% chance of our rat dying to the enemy rat if we choose to attack first.
Our rat has a 25% chance of dying vs the opponent rat's 50% chance of dying which means that if nothing else is in a position to help out the enemy rat we are mathematically correct to attack it with our rat first and the opponent was incorrect to offer our rat the first attack.
This also means that in mirror matches in general the advantage usually goes to the attacker if there aren't also height considerations though there are a few exceptions which are covered in the next section.

That one was easy right? So let's look at a scenario where the percentages are a bit more complicated:
Goblin vs Dwarf

A goblin has a 33% chance to kill a dwarf while a dwarf has a 40% chance to kill a goblin(directly). Our goblin is in a position to attack an enemy dwarf so let's find out if that's a good idea.
We already know the dwarf has a 67% chance of surviving so let's see how our goblin's odds look.
Again we multiply the enemy creature's chance of surviving(67% or 0.67) by its chance of killing our attacking creature(40%). So 0.67 x 0.4 = ~0.27 or a 27% chance of our goblin dying to the dwarf if we attack first.
In this scenario we see that the enemy dwarf has a 33% chance to die vs our goblin's 27% chance to die making it a mostly even matchup with a slight edge for the attacking goblin. Since the odds are so close this call will depend on the board but all other things equal the goblin gains a slight edge by attacking first.

If we reverse the scenario and give the dwarf the first attack we can see using the formula(0.6 x 0.33) that the dwarf's chances of dying are ~20% to the goblin's 40% which gives the dwarf a very clear edge.

Defending
As we saw in the last section getting the first attack tends to be advantageous for the attacking creature but let's look at some scenarios where the opposite is true and the defender is at an advantage.

Dwarf vs Rats

A rat has a 14% chance to kill a dwarf while a dwarf has a 66% chance to kill a rat directly. Using the formula from the previous section and applying these new values to it- 0.86 x 0.66 = ~0.57 we see that the dwarf's chances of survival are 86% compared to the rat's 43% if the rat attacks first. To put it another way the rat has a 14% chance to kill the dwarf and a 57% chance of dying itself. In this scenario the rat is actually at a large disadvantage even though it has the first attack.

Of course when there's one rat there's usually more so let's look at an entire rat pack vs a dwarf.
The chances of a dwarf surviving a rat pack if they all bite on the same turn are 0.86^3 or 0.86 x 0.86 x 0.86 = ~0.64 or a 64% chance of survival vs all the rats. With this new survival percentage we can now calculate any one rat's chance of surviving this encounter- 0.64 x 0.66 = ~0.42 or a 58% chance for any one rat to survive this encounter.
Even with the entire pack the chance of the dwarf dying is only 36% compared to a 42% chance of losing a rat however this isn't much of a difference and is close enough to be considered roughly even. Since there are multiple rats though the advantage goes to them because each individual rat is worth less than the dwarf. If the dwarf survives and kills a rat the advantage will shift to the dwarf and it would then be less favorable to continue pressing with only two rats, try using the formula with the given values from above to see why. :)

Dwarf vs Dwarf
A dwarf has a 14% chance to kill another dwarf when using its ranged attack and a 25% chance to kill directly. As we know from the previous section attacking first usually gives a creature the edge in a mirror match however because the dwarf has a ranged and direct attack the dwarf mirror is different.
The first dwarf to get into range will very likely have to use its ranged attack while the defending dwarf will be able to use its direct attack on its own turn if it suvives. Lets use the formula to see what this matchup looks like. The first attack is going to be ranged and the counter-attack direct so we do 0.86 x 0.25 = ~0.22 or a 22% chance for the attacking dwarf to die compared to a 14% chance for the defending dwarf.

In this case because the attacker in the mirror match had to start with a weaker ranged attack and would then be subject to a more powerful direct attack the advantage shifts to the defender. This same rule applies in the manticore mirror as well with a manticore that starts the confrontation by moving in with a ranged attack being at a disadvantage(20% to kill vs 40% to die).
The sapphire dragon mirror breaks this rule because if one moves in to attack with ranged first it is almost exactly as likely to die as it is to kill the defending dragon(29% to die, 27% to kill).
Keep in mind this isn't factoring in height considerations which are covered in the next section and it also assumes the defending creature in the mirror would move in to do a direct attack if it survives. If there is a reason it wouldn't or couldn't retaliate with a direct attack the advantage would be with the attacker.

Hydra vs The World
I'm not going to go into details on any one matchup but the hydra has by far the highest defense in the game and it's generally unfavorable for most creatures that aren't undead to attack it directly with one exeption being another hydra in which case the previous section shows that the hydra that gets the first attack will have the advantage all other things being equal. The giant having the highest attack value in the game when it has its boulder also allows it take on a hydra directly, again gaining an advantage from getting the first attack. Since the hydra is such a valuable and dangerous creature however it is generally worth sacrificing a lesser creature or two to try taking it out(keep its multi-attack in mind) if you don't have an undead creature or magic attacks to deal with it. This same idea applies to any dangerous creature with lesser odds being acceptable in many circumstances due to the value of eliminating such threats if successful.
Height Advantage
Creatures with height advantage gain a 50% boost to their attack rating when battling creatures directly below them and creatures attacking from below suffer a 50% attack reduction. For ranged attacks creatures get a 25% boost to attack for every one tile higher they are than the target and an attacker suffers a 25% penalty to attack for each tile higher the target is. Because the boost is percentage based certain creatures benefit much more from height than others because their base attack values are higher and some creatures suffer more when attacking something with height advantage for the same reason.

Let's look at two examples where this changes the dynamics of creature battles.

Elf vs Elf
Elves have a ranged attack of 20 and a defense of 20 so an elf mirror match is the same as the rat mirror match from the "Attacking" section with both having a 50% chance to kill the other on the first attack and only a 25% chance of dying themslelves if they are the first to get a shot.
What happens though when one has the high ground?
An elf with a full two tile height advantage will have a defense of 20 against an elf on the ground level while the elf on the ground will only have 10 attack against the higher elf. This means the elf without height will have a 33% chance to kill the elf on high ground because it has a ranged attack of 10 with the penalty which makes a ratio of 1/2 which is 1/3 times or 33%.
This also means the elf with height will have a 60% chance to kill the other.
If we use the formula from before for the elf on the ground attacking first(0.67 x 0.6 = 0.4) we see that the elf on the ground only has a 33% chance of killing the enemy while also having a 40% chance to die itself.
By taking the highest ground one elf has gained a dominant advantage over the other to the point where the elf on the lowest ground is actually more likely to die from attacking first than the elf on highest ground is from being attacked first.

Eagle vs Elf
An eagle with one tile height advantage on an elf will have a 33% chance of dying to the elf's ranged attack and with its swoop bonus will have a 50% chance to kill the elf. If an elf were to move in to take a shot on an eagle with one tile of height advantage we can see using the formula(0.67 x 0.50 = ~0.34) that it would have a 34% chance of dying itself to the eagle's 33%. This is basically even however since an elf is generally more valuable than an eagle this would actually be disadvantageous for the elf.
Note that in the screenshot the eagle has actually moved directly into range to attack the elf allowing the elf to take a shot at the eagle then back out of the eagle's range instead of the eagle forcing the elf to come to it. In that scenario the elf is at an advantage because it has a free shot without any risk of counter-attack.

Always keep height in mind when calculating risk/reward and remember that it not only hurts your attack rating to attack from below but also boosts the counter-attack of the enemy as well.
The Paladin: A Special Case
Because the paladin counter-attacks any enemy that attacks it directly the formula we've been using only gives the chances of our creature surviving a direct attack on that paladin the turn we attack but doesn't factor in the innevitable second attack the following turn if our creature survives the counter. To do this simply use the same formula from before then take your creature's chance of surviving the counter-attack and multiply that by it's chance of surviving the attack the following turn.

For example let's make this easy and pretend a rat has a 25% chance to kill a paladin and a paladin has a 75% chance to kill a rat. If the rat attacks first we see that 0.75 x 0.75 = ~0.56 giving the paladin a 56% chance of killing the rat the turn it attacks or a 44% chance of survival for the rat by attacking first. We then take the chance of the rat surviving(0.44) and multiply it by the chance of it surviving a second attack the following turn 0.44 x 0.25 = 0.11 or an 11% overall chance of the rat surviving if it attacks first aka 89% chance of dying. In this case the rat is more likely to die if it attacks than it is if it were to move next to the paladin and not attack. Keep in mind these numbers are made up and only for demonstration, a rat actually has a lower chance to kill a paladin than 25% and the paladin a higher chance to kill a rat.

It's worth mentioning that because you are actually increasing the rat's chance of dying by attacking one possible tactic is to move a rat or two next to a paladin but not attack and instead use the rat(s) to block it from attacking something more valuable. For example park some rats in front of a paladin then move a hound in behind them to try paralyzing it. The paladin in this situation would be prevented from going after the hound if it were to avoid the paralysis and if the paralysis is successful the rat(s) could then safely attack.
The Spider: A Special Case Pt2
The spider is unique in that not only does it have two different attack values but it also has a web that halves enemy defense and the web has a defense value of its own.

The spider's first attack on a creature is its web which has a value of 90 while its actual killing attack has a value of 30. When a creature is webbed it will have one turn where it can break free before the spider can attempt to kill it and its chance of freeing itself is its attack measured against the web's defense of 70.

Spider vs Wizard
A spider has a 69% chance to web a wizard and once webbed a 60% chance to kill. A wizard that has been webbed has a 22% chance to free itself(20 attack vs 70 defense) in the turn before a spider can attack it. Let's find out what the chances of a spider catching and subsequently killing a wizard in two turns are.

First we need to find out what the chance of the wizard getting and then staying webbed is. To do this we multiply the chance of the spider webbing the wizard(69%) by the chance of the wizard staying webbed(78%) so 0.69 x 0.78 = ~0.54 or a 54% chance of the wizard being trapped by the web and not freeing itself the following turn.
Now that we have that percentage we multiply that by the spider's chance of killing a webbed wizard(60%) so 0.54 x 0.6 = ~0.32 or a 32% chance overall for the spider to trap and then kill the wizard by itself in two turns.

As we can see from the numbers even though the spider has a 69% chance to trap a wizard its overall chances of actually killing the wizard(in two turns) are 32%. This is why it's best(when possible) to back the spider up with another creature which can attack the turn it webs something. This greatly reduces the chance of an enemy surviving in most cases by giving you a chance to attack the webbed creature/wizard before it can attempt to free itself.
Creature Value
This section is short because it treads somewhat subjective and very circumstantial territory. Certain creatures are clearly more dangerous and therefor valuable than others so it is often the best play to take bad odds when attacking a valuable creature if the creature you are risking isn't worth as much or if the enemy creature is a clear threat to your wizard in the present or near future. This is going to come down to circumstances and judgement calls which is the beauty of this game after all.
Final Considerations
At this point you should now have a good idea of how creatures can gain advantages from attacking first and height as well as an awareness that attacking first isn't always preferable. This last section will be to address some extra things to consider besides just whether you have a mathematical advantage on any one attack.

The Wizard:
Attacking an enemy wizard with any creature is usually the correct play if given the opportunity regardless of the chance you will lose that creature if it fails because wizards are the highest value piece on the board and killing the enemy is of course your only goal. There are circumstances where it wouldn't be the best play such as having an extremely low chance to kill combined with a reasonable chance of your wizard dying the next turn but in general if you have a random creature with a shot on the enemy wizard it's usually worth the potential sacrifice.

Other Creatures:
If you are deciding whether to move in to attack with a creature you need to not only consider the possible counter-attack from the target but also guaranteed counter-attacks from other enemies nearby as it's fairly uncommon for a creature to not be backed up by another. To do this simply apply the formula from earlier to find the chance of your creature surviving the target creature when your creature has the first attack(chance of the target surviving x their chance of killing your creature = your creature's chance of dying) then multiply their chance of survival by their chance of surviving any other enemies that can attack.

Final Thoughts
Hopefully this guide has been helpful to give you a better understanding of how to apply math to the combat in Chaos. Remember that this is only meant to show you how to determine your odds when deciding whether to attack or to put a creature in harm's way and there are many, MANY circumstances in the game where the mathematically correct play is not always best.
TLDR
Disregard this section if you have already read through the guide.

This is fairly wordy so if you don't really want to read a bunch of examples or maybe you just hate math then if nothing else know this one formula:
When your creature attacks an enemy creature its chance of dying itself when making that move is the enemy creature's chance of surviving the attack multiplied by their chance of killing your creature when they attack it the next turn. For examples see the "Attacking" section.
17 Comments
Random Reference #98  [author] Dec 15, 2016 @ 6:06am
Thanks Glassjaw, I'm happy to see players are still finding my guide helpful after all this time. :)
Glas Masv Dec 1, 2016 @ 4:01am
Very useful to think about. I think I'll use rats differently and the tips for elf vs. elf are helpful too. I also didn't know spider web attack value.
Random Reference #98  [author] Feb 1, 2016 @ 12:32am
Welcome to the game knowbody, I'm glad you found it helpful. :)
LawdHammerC Jan 31, 2016 @ 11:16am
I"m just getting started with this awesome game. TYVM for this great guide!
Random Reference #98  [author] Jan 15, 2016 @ 2:33pm
Thanks Pitzotl, glad you found it helpful. I'll see if I can clean up some of the earlier sections and interesting idea about the tables, that would probably be helpful to alot of people so I'll see what I can put together on that front when I have some extra time.
Sus scrofa Jan 15, 2016 @ 1:06pm
Very useful guide albeit it was a bit confusing in the beginning, at least to me. Nonetheless the confusion passes in a couple of paragraphs so it's no biggie. The guide really gives some sense of order to the Chaos in the head when you play. What I would like to see in the future are some tables of various creature match-ups, maybe later make even height tables of the same purpose. It's a just a grunt work and basically even I can do it for myself, but I think it would look nice in your guide.
Random Reference #98  [author] Dec 25, 2015 @ 12:18pm
Thanks dans. I added a section addressing atk/def ratio since you aren't the first player I've seen mention that they found that part of the game confusing. Sounds like you've got it figured out now but hopefully that will help other players in the future.
dans Dec 25, 2015 @ 2:35am
First off, good post. Thanks.

However I'm feeling fairly dumb in the math department because it's taken forever (it seems) to figure out how the percentage to kill is calculated from the attach and defense ratio of just two creatures. And searching numerous points provided no illumination of the topic.

In various places I've seen stated that an attack defense ratio of 2:1 is 66%, or that a 4:6 ratio is 40%, or on this forum page for a webbed wizard that 20:70 is 22%. I mean, really, how do you get 0.66 out of 2 to 1???

Well, this is how. Attack 2 plus defense 1 equals 3; or 2 out 3 is 0.66 or 66%.
Attach 4 plus defense 6 equals 10; 4 out of 10 is 40 percent.
Attach 20 plus defense 70 is 90; 20 of 90 is 0.22; or 22%.

Bah! Humbug! It's simple once pointed out, but why hasn't any one done so? Or perhaps I really am math challenged.
necross.san Oct 30, 2015 @ 2:16pm
@ MattyRasker

It can
Random Reference #98  [author] Oct 15, 2015 @ 11:07pm
Thanks Azzo, glad to hear you found it helpful. :)