TABLE OF CONTENT

- Introduction
- Foundations

- How to Read DSI Tables
- Damage Calculation
- Healing Calculation
- Damage Reduction

- Strategy Planning and Execution

- Stage Analysis
- Stalling and Bursting
- Rune Spinning and Stacking
- Diamond Usage
- Case Handling In a Pinch

- Resources Management

- Level
- Skill Level
- Amelioration
- Resources Distribution

- Miscellaneous

- Seal Card Drawing

- Seal Card Drawing

1. INTRODUCTION

Hello everyone, I am a fellow TOS player. Being a close to F2P player (6 dimes top up for the new dragons), I personally never skip a single SM/NM from my second month of playing onward. I deliberately skip Saruman and Lunar Sirius which are too early for me and Solar sirius is my first SM which I clear using 2 dimes.

So, how I do so? How I come up with strategies to face different kind of stages? Being an almost F2P player, how I manage my resources? All these have to do with mathematics. I plan my strategy and do the calculation before I ever attempt the stage so that I know exactly what to do like how many combo/runes I need to dissolve to kill the enemy, when to use my skill, when should I stall etc. With all these planning, even being restricted by resources as a F2P player, I still can find my own way to attempt stages based on what I have in my inventory.

So, how I do so? How I come up with strategies to face different kind of stages? Being an almost F2P player, how I manage my resources? All these have to do with mathematics. I plan my strategy and do the calculation before I ever attempt the stage so that I know exactly what to do like how many combo/runes I need to dissolve to kill the enemy, when to use my skill, when should I stall etc. With all these planning, even being restricted by resources as a F2P player, I still can find my own way to attempt stages based on what I have in my inventory.

Therefore, I am going to compile my knowledge as a guide.

2. FOUNDATIONS

First of all, I am going to teach your guys the necessary knowledge and mathematical equations required for strategy planning.

2.1. HOW TO READ DSI TABLES

In order to plan any strategy, it is important to learn about your enemy first. In forum, we have DSI sections whereby OP will list out the details of enemies in a stage in table form. All new DSI should be done in table form while some older DSI does not as forum does not have table function supported last time.

A general DSI table should have the following format which is similar to what we have in wiki.

Wave | Enemy | ATK | CD | HP | DEF | Skill Effect | Note |

Wave No. | Enemy Name | x | CD(cd) | y | z | Description of enemy skills | Anything not from skills but worth mentioning |

Indicates which round the enemy will appear. If it is left empty, it means that it is a mob whereby it appears in any round that is not mentioned in the subsequent rows.

Enemy

Usually just the enemy's name but some hardworking poster will use picture / coloured font which will tell you the attribute of enemy.

ATK

Indicates the base damage of enemy. For certain enemy with trojan/berserk/hp reduction skills, please refer to skill description

CD

As you can see in the table above, there are two values, one is within bracket and one doesn't. The value within bracket is what we called initial CD that is the enemy's CD when you enter the stage. The other value is the CD the enemy will become every time it makes an attack. So, an enemy with CD 2 (5) means he will have CD of 5 every time you enter the stage but after he make his first attack, he will attack again after every alternate turn (CD2).

For enemy without the value in bracket, it means that its initial CD is within x+-x/2 whereby x/2 is the integer division. For example, for a monster with CD3, its initial CD can range from 2(=3-1) to 4(=3+1) while a monster with CD4 can have initial CD range from 2(=4-2) to 6(=4+2).

Another important fact about CD is for enemies with two hp bars. The initial CD of the enemy in 2nd hp form is directly inherited from the 1st hp bar when it is killed.

HP

It tells you the enemy's hp which will decide how much damage you need to deal in order to kill him.

DEF

It tells you the defense value of the enemy, which will be deducted from your damage to get the actual damage. Usually, the value will be ignored as it does not affect your damage much. But there are enemies with really high defense which can be an annoyance. The detailed calculation will be covered in the next section.

Skill Description

The most important sections in a DSI table. It tells you the skill effect of the enemy which sometimes can be really sadistic and most of the strategy planning are done to counteract the enemies' skill. Please read the description carefully so that you won't get screwed by it.

Note

Used for any miscellaneous information like drops, raid cards, 2 hp bar etc

2.2. DAMAGE CALCULATION

The primary objective of any stages in this game is to kill your enemy. That's why it is important to be able to know how much damage you can deal and the way to do it is via mathematical formula.

First of all, if you are observant enough, you should know that a value will be shown on each card's icon. That's your card damage before it undergoes any modification and I call that your base damage.

Base Damage = Base Attack x Rune Factor x Combo Factor x Skill Multiplier x Amelioration x Dragonic Compulsion

I know that the formula is rather long but that's what happens in the game's mechanics. However, in general, we can ignore amelioration and dragonic compulsion in our calculation unless you are looking for a super massive burst then you would like to include them as they are often used for burst only.Base Attack

Base Attack is simply the attack of each cards. During a battle, you can hold on any card and you can see the base attack of the cards.

There are multiple ways to increase/decrease a card's base attack other than leveling:

- Absorption

There are only two cards capable to do so in the current version which are Michael Lucifer and Novalis. They deduct the base attack from the team members and add to their own base attack. This is by no mean a damage booster as it does not change the total base attack of team at all. However, when they are paired with Libra or Ursula respectively, it makes their skills much more powerful. - Transfer from Recovery

There are 4 cards currently capable to do so. The first one is Cassandra whereby her active make your recovery 0 while add 2.5 times of the deducted value to your base attack. The other 3 cards are the PR RGB ED whereby their leader skill add the recovery to your base attack. - Hidden Passive

When certain cards are used together, we can have additional boost to the base attack. There are too many of them for me to list out. - Fusion

When two cards fuse together, their stats change to the one based on fusion stats.

Rune Factor

The value of rune factor depends on the runes you dissolve and each attribute have a seperate rune factor.

Rune Factor for X attribute = (No. of X rune dissolved + No. of group of X runes dissolved)*0.25 + No. of enchanted X rune dissolved * Enchanted Bonus

Lets do some sample calculation.

Lets say for dark rune factor, you dissolve 3 non-enchanted dark rune in 1 group, so your rune factor will (3+1)*0.25 = 1

Now, lets say you have 11 non-enchanted dark runes to dissolve,

if you dissolve as group of 3, 3 and 5, your rune factor will be (11+3)*0.25 = 3.5

if you dissolve as group of 3, 4 and 4, your rune factor will still be (11+3)*0.25 = 3.5

However, if you dissolve them as a single group of 11, your rune factor will be (11+1)*0.25 = 3

So, it is optimal to split your runes to be dissolved as many as possible in order to maximize the rune factor.

Next, lets move to enchanted bonus, for any default team, the value of enchanted bonus will be 0.15. So, each enchanted rune contributes 0.4 to rune factor as compared to non-enchanted rune's 0.25. Therefore, 1 enchanted rune = 1.6 non-enchanted rune.

For a dual Norse team, they have hidden passive whereby the enchanted bonus is increased from 0.1 to 0.25. So, each enchanted rune has rune factor of 0.5 which is twice the amount of non-enchanted rune. Therefore, for a dual Norse team, Norse leader's enchantment is effectively a 2x damage multiplier while it is only 1.4x for a Norse-Daji team.

Combo Factor

If you are new to TOS, you will often see people tends to dissolve as many combo as possible instead of dissolving the runes as one big group. Besides contributing to higher rune factor, it also contributes to higher combo factor.

Combo Factor = 1 + (No. of combo + Extra combo(Greek Only) - 1) * Combo Bonus

Finally, we have some much simpler formula. The only thing I need to explain here is the combo bonus. Combo bonus is the constant value increment of combo factor for every extra combo made. By default, the system set it to 0.25. However, there are a few cards that have the ability to improve it.

- PR Daji (The 5*/6* version does similar thing so I only talk about the PR version)

The most OP leader in the current game. Her leader skill increases combo bonus by 125% which is equal to 1.25. Furthermore, when she is used as leader/ally, the combo bonus is further increased by 25% which is 0.25. So, if you use PR Daji as leader/ally, your combo bonus will be increased from 0.25 to 1.75! - Circe

The green enchantress which was once very popular as damage booster due to the low risk accompanied by her active. Her active increases combo bonus by 0.25. - Wavel

Also commonly called as dragon daji which also increases combo bonus by 1.25 restricted to a pure dragon team but without the hidden bonus.

1) Just how OP PR Daji is as compared to other multiplier leaders?

From first glance, people may think that PR Daji is as effective as a 7x multiplier leader but that only happens at infinite combo. In fact, PR Daji's effective damage multiplication increases as your combo increases.

To compare PR Daji with other leader, I will show the result in table form:

Consider most players can make combo in between 5 to 7, PR Daji is effectively a 4 to 4.5x multiplier leader.

To compare PR Daji with other leader, I will show the result in table form:

No. of Combo Made | Combo Factor with PR Daji | Default Combo Factor | Effective Multiplier |

1 | 100% | 100% | 1 |

5 | 800% | 200% | 4 |

9 | 1500% | 300% | 5 |

21 | 3600% | 600% | 6 |

45 | 7800% | 1200% | 6.5 |

2) Since PR Daji is so OP, why don't we use it as both leader and ally?

First of all, we need to understand that Daji increases combo bonus by addition rather than multiplication. Therefore, using Daji as both leader and ally will never increases your combo bonus to twice the combo bonus when you use Daji as leader/ally only and there are so many other leaders which multiply your damage more than 2x.

3) Why people always say don't use Circe together with PR Daji?

The answer is actually very similar to the previous question. Again, Circe also increases combo bonus by addition, so using Circe in a team with PR Daji will only increase combo factor from 1.75 to 2. It is not like they do not stack, but the effective multiplier is less than 1.15 which increases overall damage by less than 15%. Therefore, it is often advisable to use some other booster besides Circe.

4) Why people don't use Circe in Greek Deck while Circe works well with high combo?

This is because MH make Circe's active does not work in greek deck. Blame MH for this.

Skill Multiplier

There are tons of skills in TOS that can improve your damage by simple multiplication as long as you fulfill the condition. In general, there are 3 kinds of skill multiplier:

- Leader Skill

As long as you fulfill the condition, leader skill will increases your damage by multiplication according to description. - Everlasting Active

As far as I know, only 1 card go to this category: Medea. They will increases your damage like leader skill forever once you activate them until you die or deactivate them. PR Yan and Xi does not go to this category as they make rune factor's accumulation easier rather than boost your damage. Similar for Cassandra and Circe as they belongs to base damage and combo factor respectively. - Active

There are tons of them available in TOS. I won't list them out here to save space and time. These skills will place a buff on the left side of the screen and there are be 4 buffs at most at one time.

- Hades (Leader skill)

1 + No. of attribute in the team * 0.5 - Jyu Yun (Leader skill)

2 + No. of human in the team * 0.25 - PR Nian (Leader skill)

1 + No. of attribute of beast in the team * 0.5 - Horned King (Active)

1 + No. of attribute in the team * 0.5 (Capped at 4 attribute) - Odin (Active)

1 + (Max HP - Current HP)/Max HP * 1.5 - PR Odin (Active)

1 + (Max HP - Current HP)/Max HP * 2

If you activates it, just multiply the corresponding value, nothing much to say.

Dragonic Compulsion

In this section, I will only talk about the damage increase from DC.

First, to activate the skills, you need to score

>=2000 for first skill

>=4500 for second skill

>=7000 for third skill

If you activates it, just multiply them to the damage accordingly.

Next, the score itself also contributes as damage multiplier. The formula is

1* craft:

1 + Score/10000 for Score <=5000

1.5 + (Score-5000)/40000 for Score >=5000

1.5 + (Score-5000)/40000 for Score >=5000

2* craft:

1 + Score/10000 for Score <=7000

1.7 + 1.5*(Score-7000)/40000 for Score >=7000

1.7 + 1.5*(Score-7000)/40000 for Score >=7000

3* craft:

1 + Score/10000 for Score <=10000

2 + (Score-10000)/20000 for Score >=10000

2 + (Score-10000)/20000 for Score >=10000

Damage Modification

With the base damage calculated, it is times for damage modification.

There are generally 4 factors that can modify your damage.

I am pretty sure some of you are already taunted by such a long process of calculation.

Don't be afraid, my friends. Even I don't do the calculation like this, only the system do so. What I usually do is like this:

1) Multiply your base attack with leader skill first to get a base value. These values are generally constant so we can reuse them over and over again.

2) Next, assume you need to do 5/7 combo, which gives you the particular combo factor (2 and 2.5 for default team, 8 and 11.5 for team with PR Daji, etc). Again, these values will be reused again and again.

3) Calculate the rune factors. Just remember 3 runes in a group gives you 1 and every additional runes in the group give extra 0.25. Ignore enchanted bonus as we don't mind to deal extra damage unless you are using dual norse whereby enchanted bonus is really significant.

4) Just multiply these 3 together with active's multiplier and apply modification, then you can easily get your expected damage.

Unless you find that you fall short of damage from your calculation, then you need to do the full calculation and add in whatever bonus that you can possibly achieve.

If you are going to apply DC, it is safe to assume it is a 1.5x multiplier since score beyond 5000 contributes very little to damage boost.

So, the key in simplify calculation is always take the lower bound, we don't mind to do extra damage. If your lower bound can actually meet the damage requirement, then you can be very assured that your actual damage will be enough to kill the boss.

As you can see, I did not include sky drop into my calculation. This is because it is very unpredictable. As I take lower bound to simplify calculation, I usually assume that there is no sky drop in my calculation. Therefore, sorry to say, greek's damage will be highly unpredictable as they rely on sky drop and that's also the reason I rarely play greeks as it is very difficult to numerically analyse them.

There are generally 4 factors that can modify your damage.

- Attribute

If your attack have attribute advantage, multiply it by 1.5.

Else if it has disadvantage, multiply by 0.5.

Else, multiply by 1. - Your actives

Take note that active of certain cards like Ursula, Luna, Hertz does not really fit into the skill multiplier session. For Ursula and Luna, replace the attack of specific members with the member with highest attack. (Often Novalis and ML). For Hertz, you can take it as times 2 but remember to do attribute mod. seperately. - Enemy's Skill

There are generally 4 kinds of enemy skill that can affect your damage.

1) Reduction

We often see enemies with skills like beast shield, water shield, etc. If you do not fulfill the condition, your damage will be divided by a particular factor. For general racist/mono racist shield, the factor is 4. The most extreme I ever seen is water XY extra whereby SSS divides light and dark attack by 20.

2) Condition

If you fulfill the condition, do damage without modification. If you fail to do so, damage becomes 1.

3) Ignore damage

Skills like initial shield/ambush shield/kamikaze states that they will not receive damage unless the condition is fulfilled. So, your normal damage will becomes 1.

4) Tumbler shield

It simply cap your damage based on percentage of enemy's hp. - Defense

After doing all the modification, we have the final value for our damage. Now, we can just minus off the defense from this value and we get our expected damage. If the resultant value is less than 1, the resultant damage is 1. Take note that I put defense as final modification because it is last in system's order. One good example to illustrate this is Path of Atavism boss with 900k defense and beast shield. If you are using non-beast to attack, it will be divided by 4 followed by minus 900k instead of minus 900k followed by division by 4. The prior one will need to do 3.6mil damage for defense break while the latter one need only 900k.

I am pretty sure some of you are already taunted by such a long process of calculation.

Don't be afraid, my friends. Even I don't do the calculation like this, only the system do so. What I usually do is like this:

1) Multiply your base attack with leader skill first to get a base value. These values are generally constant so we can reuse them over and over again.

2) Next, assume you need to do 5/7 combo, which gives you the particular combo factor (2 and 2.5 for default team, 8 and 11.5 for team with PR Daji, etc). Again, these values will be reused again and again.

3) Calculate the rune factors. Just remember 3 runes in a group gives you 1 and every additional runes in the group give extra 0.25. Ignore enchanted bonus as we don't mind to deal extra damage unless you are using dual norse whereby enchanted bonus is really significant.

4) Just multiply these 3 together with active's multiplier and apply modification, then you can easily get your expected damage.

Unless you find that you fall short of damage from your calculation, then you need to do the full calculation and add in whatever bonus that you can possibly achieve.

If you are going to apply DC, it is safe to assume it is a 1.5x multiplier since score beyond 5000 contributes very little to damage boost.

So, the key in simplify calculation is always take the lower bound, we don't mind to do extra damage. If your lower bound can actually meet the damage requirement, then you can be very assured that your actual damage will be enough to kill the boss.

As you can see, I did not include sky drop into my calculation. This is because it is very unpredictable. As I take lower bound to simplify calculation, I usually assume that there is no sky drop in my calculation. Therefore, sorry to say, greek's damage will be highly unpredictable as they rely on sky drop and that's also the reason I rarely play greeks as it is very difficult to numerically analyse them.

2.3. HEALING CALCULATION

Healing is another important mechanism in the game as it allows you to stall against enemy. It is often required when you need to stall for skills and not killing your enemy. Luckily, heal formula is similar yet much simpler than damage formula.

Heal = Base Recovery X Rune Factor X Combo Factor X Skill Effect X Amelioration X Dragonic Compulsion

Base Recovery

Similar to base attack, there are a few factors that can affect it:

Exactly the same as damage section except that nothing increase the enchantment bonus like dual Norse.

Combo Factor

Exactly the same as damage section except that nothing increase the combo bonus. So, PR Daji does not help you to heal extra except for her insanely high recovery.

Skill Effect

Again, the same as damage section, there are actives and leader skills that multiply your recovery.

Amelioration

Once again, same as damage section.

Dragonic Compulsion

Score does not contribute to recovery multiplier but there are elves craft whereby the skill increases recovery.

There is no additional modification so healing is much simpler to calculate. Just get your base recovery, combo factor, rune factor and skill factors, we are done in most cases.

Besides these healing, there are three more special kind of healing we have.

Similar to base attack, there are a few factors that can affect it:

- Cassandra/PR RGB ED

She makes your base recovery 0, as simple as that. - ED/Yuki-Onna

Add a constant amount of recovery to specific members. - Enemy Skill

There are sadistic enemy skill which makes your recovery 0.

Exactly the same as damage section except that nothing increase the enchantment bonus like dual Norse.

Combo Factor

Exactly the same as damage section except that nothing increase the combo bonus. So, PR Daji does not help you to heal extra except for her insanely high recovery.

Skill Effect

Again, the same as damage section, there are actives and leader skills that multiply your recovery.

Amelioration

Once again, same as damage section.

Dragonic Compulsion

Score does not contribute to recovery multiplier but there are elves craft whereby the skill increases recovery.

There is no additional modification so healing is much simpler to calculate. Just get your base recovery, combo factor, rune factor and skill factors, we are done in most cases.

Besides these healing, there are three more special kind of healing we have.

- Leeching

Exclusive to Ursula, Barbara and Wavel's active. You heal by 5% of damage you deal. Capped at 50% of max hp. - Percentage Healing

Although PR RGB ED make your base recovery 0, they do provide you another healing mechanism. You heal 2% of loss hp for every dragon members for every heart rune dissolve. So, you heal 36% of loss hp for 3 heart runes if you run a dragon mono. - Dragonic Compulsion

For certain crafts, one of its skill is heal 50% of your max hp if you have enough score to activate it.

2.4. DAMAGE REDUCTION

Besides healing, another important aspect in stalling is damage reduction as it helps you to reduce damage, therefore you can stay alive longer and stall longer. One important feature in TOS is as long you are alive, you can continue to deal damage. Therefore, the longer the time the enemy takes to kill you, the more chance of attack you have. If you can stall indefinitely, then you can kill the boss no matter how much hp he has (Unless he heals). This is also the reason why we can see a lot of teams with low damage capability can pass stages whereby team with much higher damage can't pass.

So, how does damage reduction works?

There are mainly 2 kinds of damage reduction:

1) Tumbler

Tumbler works as damage limiter. When you have tumbler in active, when an attack is supposed to kill you, the tumbler effect will make you have 1 hp remained no matter how high your opponent's damage is. Therefore, as long as you can heal back enough hp to activate the tumbler again, you will be immortal. However, there is one catch for tumbler that is it can only be activated once per turn with exception of IPQOW's active 1st turn. Therefore, against multiple enemy that attack together, tumbler is not that useful.

There is no complicated equation for tumbler. When your enemy's attack exceeds your current hp and your current hp is more than a certain percentage, then you will survive with 1 hp.

2) Direct damage reduction

This refers to many leader skills and actives. In general, when we talk about damage reduction leader, we have defensive dragon, certain zodiac, Penetrating Eye Fong Tian-Ling, and our mightly Wukong.

These leaders have leader skill that reduces attack from particular attribute by X%. However, we are not that interested how much damage we actually reduce, but the damage we receive after the reduction.

So, the formula is

Damage Received = Original Damage * (1-X/100)

The formula is kinda simple and most people should be able to derive this even without looking at this guide. However, very often, we have team that use damage reduction leader as both leader and ally. So, given one reduces X% and one reduces Y%, how much damage we receive in the end?

The formula is

The formula is

Damage Received = Original Damage * (1-X/100) * (1-Y/100)

So, don't go and sum up the 2 percentage because that's totally wrong. Imagine you have 2 defensive dragons that -50%, is it logical enough to have 100% damage reduction? In fact, 2 50% reduction will only gives you 75% reduction as you only receive (1-0.5)(1-0.5)=0.25=25% damage in the end.

By applying these formulas, we can easily get the compound damage reduction and determine whether we can survive the stage or not.

In general, reduction leader is good for stages with 1 or 2 attributes only since their reduction only works for specific element with exception of Wukong and I am going to cover him in the next section.

Mightly Wukong

By applying these formulas, we can easily get the compound damage reduction and determine whether we can survive the stage or not.

In general, reduction leader is good for stages with 1 or 2 attributes only since their reduction only works for specific element with exception of Wukong and I am going to cover him in the next section.

Mightly Wukong

Okay, this guy deserves a section just for him for two main reasons:

1) This guy has the highest reduction percentage which is 80% after amelioration and his reduction applies to all attributes unlike other reduction leader.

So, how much damage will you receive you run this awesome cards as both leader and ally?

The answer is

1) This guy has the highest reduction percentage which is 80% after amelioration and his reduction applies to all attributes unlike other reduction leader.

So, how much damage will you receive you run this awesome cards as both leader and ally?

The answer is

(1-80/100)*(1-80/100)=0.04=4%

That means it is a 96% damage reduction. If an enemy wants to kill you with normal damage, he has to deal 25 times your max hp in order to do so. A 100000 damage will only reduce 4000 hp from you. So, with this figure alone, I don't need to elaborate on how OP he is.

2) Another special trait of Wukong's reduction is that it is not constant and it decreases with its hp percentage. The question here is: How fast does the percentage drop with respect to hp?

The formula of the reduction percentage for Wukong is:

2) Another special trait of Wukong's reduction is that it is not constant and it decreases with its hp percentage. The question here is: How fast does the percentage drop with respect to hp?

The formula of the reduction percentage for Wukong is:

Reduction Percentage = X^3 * 60% (below amel II)

Reduction Percentage = X^(1/3) * 80% (amel II or above)

Reduction Percentage = X^(1/3) * 80% (amel II or above)

whereby X is your current hp percentage.

As you can see, there is a huge difference between the ameliorated and non-ameliorated version. Since X is always less than or equal to 1, X^3 has a much smaller value than X^(1/3). To illustrate this, lets say you have 50% hp left, the non-amel version will only have 1/8 of its max reduction left, that is 7.5% while amel version will have about 79% of its max reduction that is 63.5%. See the huge difference? Even at 10% hp left, the amel version will still have 37% reduction percentage. Again, the amelioration makes wukong overcome one of its old weakness, that is multiple attacks.

As you can see, there is a huge difference between the ameliorated and non-ameliorated version. Since X is always less than or equal to 1, X^3 has a much smaller value than X^(1/3). To illustrate this, lets say you have 50% hp left, the non-amel version will only have 1/8 of its max reduction left, that is 7.5% while amel version will have about 79% of its max reduction that is 63.5%. See the huge difference? Even at 10% hp left, the amel version will still have 37% reduction percentage. Again, the amelioration makes wukong overcome one of its old weakness, that is multiple attacks.

Available Cards:

ID: 43061313