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2010-02-04, 09:29 PM
Moving this guide over here. It's really the only guide I care about, since my other guides are either aimed at a very small audience, or are just simple point-me-in-this-direction guides. This one is the result of my full-scale effort, and I never really got the criticisms from it that I was looking for when I posted it on SW. So here it is. Fancy name for HP washing. For an introduction to what HP washing is, view this guide (http://www.sleepywood.net/forum/showthread.php?t=1611086). If you already know what HP washing is, continue reading to see how it will benefit your mage.
1. Introduction to Magic Guard
Magic Guard is the most fundamental survival skill in mages. In order to understand how a mage survives, one must first understand how Magic Guard works.
http://img188.imageshack.us/img188/2317/magicguard.jpg
The first sentence of the skill reads, “Temporarily replaces damage with MP instead of HP.” What this means is that damage is channeled from HP to MP, which means that MP is part of a magician’s HP.
The following is the skill table of Magic Guard:
Skill Level|MP Usage|% replaced by MP|Duration (seconds)
1|6|11|111
2|6|14|132
3|6|17|153
4|6|20|174
5|6|23|195
6|8|30|246
7|8|33|267
8|8|36|288
9|8|39|309
10|8|42|330
11|10|49|381
12|10|52|402
13|10|55|423
14|10|58|444
15|10|61|465
16|12|68|516
17|12|71|537
18|12|74|558
19|12|77|579
20|12|80|600
Notice that the most damage is channeled to MP at level 20. Thus, it is imperative that all magicians have Magic Guard maxed in order to ensure survival of the highest amount of damage possible. Many people are reluctant to do this because MP potions cost more than HP potions in the lower levels. If this is of concern, I still recommend washing because while MP costs more at lower level to replenish than HP does, in the higher levels MP potions will be cheaper than HP potions due to Mana Bulls and %-typed potions.
Here is how much HP and MP the average magician will have at various levels:
2nd Job
At level 30
image here to come
At level 40
image here to come
At level 50
image here to come
At level 60
image here to come
At level 70
image here to come
3rd Job
At level 80
image here to come
At level 90
image here to come
At level 100
http://img94.imageshack.us/img94/813/lv100.jpg
At level 110
http://img257.imageshack.us/img257/2208/lv110.jpg
At level 120
http://img340.imageshack.us/img340/7539/lv120.jpg
4th Job
At level 130
http://img257.imageshack.us/img257/2711/lv130.jpg
At level 140
http://img257.imageshack.us/img257/6151/lv140.jpg
At level 150
http://img338.imageshack.us/img338/7317/lv1501.jpg
At level 160
image to come
At level 170
image to come
At level 180
image to come
At level 190
image to come
At level 200
image to come
Notice that in these images, the magicians have quite a bit more MP than HP. In fact, the magicians have around six times the amount of MP as HP. This leads me to my next point.
The second sentence of the skill reads, “If MP reaches 0, the HP takes a full hit.” This concept is extremely important, since it is because of this that HP and MP must remain at a vital ratio in order to survive the maximum damage possible.
2. The Magic Ratio
At maxed level, which I will assume all mages have, Magic Guard channels 80% of the damage taken to MP. What this actually means is that the HP only takes 20% of the hit, which means that a magician can survive a damage equivalent to one damage point fewer than five times its HP, and its MP will absorb four times that damage taken to HP. Essentially, it means that the HP and MP should be in a constant, magic ratio of…
1 HP to 4 MP
… in order to capitalize on survival. Suppose a mage has 2000 HP and 8000 MP, which is just enough to survive a damage of 9999. This amount of damage will bring both his HP and his MP down to 1, which will allow him to survive the hit. Let us explore what happens when HP is not at this ratio.
Suppose a mage who has 1800 HP and 12000 MP is hit 9999 damage. According to the First Rule to Magic Guard, 20% of the damage is inflicted on the HP. This means that the mage will take 1999 damage to his HP, which is over the amount of HP she has, causing him to die. Suppose this same mage is hit 8999 damage. This will bring his HP down to 1 and his MP down to 4800; therefore, 4800 points of MP on this magician are wasted because they cannot be utilized by the HP.
This is the problem that most unwashed mages have, due to the nature of how HP and MP are gained upon level up within the game.
Suppose a mage who has 2200 HP and 6000 MP is hit 9999 damage. According to the first rule of Magic Guard, it would appear that this mage might be able to survive a damage of 10999, or five times his HP. However, this isn’t true. According to the Second Rule of Magic Guard, if MP reaches 0, the HP takes a full hit. Since 6000 MP will be drained completely from this 9999 hit, the rest of the 3999 damage not accounted for by the MP will hit the HP, which will cause this magician to die.
This generally does not happen unless a mage is completely loaded with many HP equips, doesn’t have MP Max maxed, is using an alternate AP skill build such as a STR mage, overwashed, or a combination of any of the above.
3. The Truth About Mana
To ensure the maximum amount of a survival on a mage takes an immense amount of planning and calculation, because washing a Mage is extremely different from washing other classes. In other classes, washing is a very simple and straightforward concept: its only rule is to wash until the MP hits the minimum point. The reason for this is that to other classes, MP is trivial; the only amount of MP necessary is the amount enough to cast all skills. Many physical classes at level 200 don't even use Sorcerer Elixers.
However, on a mage, MP is more important. Not only does it serve a major purpose in survivability through Magic Guard, it is a basis for attacking power. Skills like AMP double MP usage, easily causing each skill to take 50-100 MP per cast. In addition, ultimates such as Meteor can take up to 8000 MP to cast, which is only alleviated by having a higher MP base. It takes 11667 Max MP to have a Mana Bull completely recover one cast of Meteor at maxed level, which drains 7000 MP per cast.
Because of this importance of MP, some people are under the misconception that it's benefical to a mage to have as much MP as possible. Some people believe that it's necessary for all magicians to to hit the MP cap of 30000 with HB, or have 18750 MP without HB. This is complete BS. Meteor at maxed level costs 7000 MP per cast. That lame 8x MP washed out per point is hardly going to affect MP cost at all. Usually, the total MP lost will not exceed 3000, but even if it does, the following is a table shows that such a loss still won't put much of a dent in the amount healed by % potions.
Base MP|Ginseng (40%)|Mana Bull (60%)|Ginger Ale (70%)
15000|6000|9000|10500
15250|6100|9150|10675
15500|6200|9300|10850
15750|6300|9450|11025
16000|6400|9600|11200
16250|6500|9750|11375
16500|6600|9900|11550
16750|6700|10050|11725
17000|6800|10200|11900
17250|6900|10350|12075
17500|7000|10500|12250
17750|7100|10650|12425
18000|7200|10800|12600
18250|7300|10950|12775
18500|7400|11100|12950
18750|7500|11250|13125
As seen in the table, in an extreme example, even if 3750 MP is lost, which is more useful? A mage with 3000 HP and 15000 MP who can take a 15000 hit or a mage with 2625 HP and 18750 MP who can only take a 13125 hit? Neither of these two mages will be gaining any extra damage or usage for their Meteor, and no other spell in a Mage's skillset uses even a noticeable amount of MP due to MP Recovery and MP Eater, which means that extra MP is wasted.
Though not many people feel a need to HP wash on a mage, there are some tangible benefits to mages who do choose to HP wash. A washed mage can survive dispel more often than an unwashed mage, because she'll have more HP base than the normal mage. Currently, I have 2700 HP, which means that if I had begun washing at a lower level, I could mist sharks without Magic Guard and still survive. At Manon and Griffey, if I get stunned and dispelled, I could survive touch damage twice from the Kentauras and therefore survive long enough for the stun effect to disappear. I could take two hits from Pap after dispel before dying, and I can survive Pianus after dispel if I'm standing on a bomb.
In the end, it's up to each mage to decide what she want's to do, but be advised that it's too late to suddenly decide to begin HP washing at level 200.
4. Prediction
Washing is all about prediction: what are the final stats at level 200? The following are some common problems that HP washers will encounter.
MP and HP are gained upon level up with a slight randomization. In addition, when adding points to HP, a magician gains anywhere from 6-10 HP. That means that if a mage is unlucky, she could end up with an average of only 7 HP per point, which makes her HP gain to MP loss ratio slightly worse than the normal average of 8 HP per point, meaning overall she cannot wash as much. Though this is rarely the case, the randomization forces mages to keep calculating and recalculating at every level.
HP gear must be accounted for. Once HP is washed, a mage can’t go back. Backwashing, or washing HP back into MP yields horrible results. When washing out of HP and into MP in a backwash, a mage will lose 10 HP and gain only about 11 MP each point. This is an extremely low gain considering that when adding points into HP or MP, a mage gains an average of 8 HP and loses around 80 MP (at level 140).
After washing, the max MP serves as a cap to survivability. For example, if a mage has exactly 3500 HP and 14000 MP at level 200, she is done. Wearing any additional HP equips won't help her as much. If she only washed to 3200 HP and 17000 MP, she could wear 1050 HP in HP gear and survive 21250 damage. This means that the additional 1050 HP worn will increase her survivability by 5250. However, if she washed to 3500 HP and 14000 MP, wearing the same 1050 HP in HP gear will only allow her to survive 1050 more damage, because there wouldn’t be enough MP to sustain this extraneous HP.
When should a mage begin HP washing? The HP gained is an average 8 HP gain throughout the 200 levels, but the MP loss will increase as a mage levels more and more. Thus, it is better to begin washing at a low level. Unfortunately, most people usually don’t decide to invest in a mage until it reaches a high enough level that they decide that their mages will be their mains. Also, many people won't consider having a mage as their main character because they're under the assumption that mages can't do much at end-game.
The cost of AP resets is hefty, at 3100 NX per reset. It may be wise to just wait for an AP reset sale that happens usually during the summer or winter seasons, even though it may not yield as much. Nowadays, the difference between 5 to 6 months is around 60 to 120 levels, which is quite a huge difference in the amount of MP lost, especially if a mage is lukless.
To prepare for HP washing, a mage should attempt to gain as much INT as possible each level up. In order to accomplish this, a mage should attempt to obtain MW and wear as many INT equips as possible during each level up.
The reason for this is that the more INT a character has during level up, the more MP gained during that level up. The ratio for MP gain on level up is about 1 MP to 10 INT. For example, if a mage has 400 INT, she will gain roughly 40 MP in addition to the 20 MP she gains from the Magician skill "Improved MaxMP Increase". However, if she wears 100 INT in gear, her stats will then be 500 INT (400 + 100), which will allow her to gain roughly 50 MP in addition to the 20 MP she gains from the Magician skill " Improved MaxMP Increase". If she does this every level, she will end up with roughly 15% more MP in the end than a regular magician.
The more MP that a magician has, the more MP she may wash out. Thus, it is vital that all people considering HP washing buy or borrow INT gears and make connections with fourth job friends. This usually isn't available to people just starting out on the game.
Because of the fact that more MP is gained when a magician has more INT, a popular myth that has arisen is that being lukless will help increase the number of times a magician can wash. This theory may or may not be true. Though a lukless mage has more MP in the end, she will also lose more MP when she washes. If the amount lost is higher, it might result in both having the same amount of MP after optimization. Because of the insufficient data due to the lack of the number of magicians willing to HP wash, because, it cannot be determined whether or not being a lukless mage actually helps.
Due to the number of the problems with HP washing outlined above, it's vital that mages wash smart. HP washing is like getting a heart transplant; once it's done, it's irreversible. Also, HP washing on a mage is much more complex than HP Washing on other classes. Thus, in the sections below, I have laid out some general equations for computing the number of AP resets that a mage should use. I have also included proofs so that you may see how the equations work in relation to each other.
Calculation takes two steps. The first is to predict the HP and MP you will have at level 200, so that you have an idea of what you will have at level 200. Using this number is more accurate than using the HP and MP you currently have, because HP and MP gain upon level up are uneven and if you use the HP and MP you currently have, you might not end up with a 1:4 ratio at level 200. The second step is to calculate using your projected HP and MP at level 200 so that you end up with a 1:4 ratio.
Note that while the formulas outlined in the calculation steps below may help predict, they are not useful unless accurate, so it may be necessary to calculate and recalculate after every wash at every level.
5. Calculation Step 1: Estimation Step
In order to calculate properly, you must first predict your final stats: how many HP and MP will you have at level 200? The reason for this is that HP washing is all about planning for endgame, and since HP gain and MP gain are very different, equalizing your stats at a certain level will mean that after that level, your HP and MP will drift away from the 1:4 ratio.
1. In order to calculate for the amount of HP you will have at level 200, use the following formula:
(Current HP) +12(200-(Level))
The formula is based on the fact that you gain an average of 12 HP each level, for the remaining levels that you have yet to level up. Don't just input your current HP into current HP; include HP equips that you will possibly wear, such as a MoN (+300 HP) or a Master Adventurer Medal (+200 HP). You need to account for them, because as mentioned in the previous section, once you wash out the full number of points, your MP serves as a cap. If you don't include HP equips into your calculations, when you do hit 200 and you have washed all the way, you'll hardly gain anything by wearing HP equips. In other words, you need to give yourself some lenience.
After you have calculated this, record this number. This will be your (Max HP) stat in the 2nd calculation step.
2. In order to calculate for the amount of MP you will have at level 200, use the following formula:
(Current MP) + (3909 + 4(Int) -11(Level))(200 -(Level))/40
Derivation step:
The average amount of MP gained per level is calculated with the following formula:
23 +(2*(Improving Max MP Increase Level) + (Int)/10)
Credits to LazyBui for this formula. I'm assuming that you have maxed MP Increase, which is level 10, so the average amount of MP gained per level is actually:
43 +(Int)/10
Now, I'm making a second assumption that you'll dump all of your points into INT every level. That means that at level 199, you will gain the following amount of MP when you level to 200:
43 +((Int) +5(199 -(Level))) /10
Since the amount of MP gain per level is linear, we can model the amount of MP you will have at level 200, by averaging the MP you will gain this level with the MP you will gain at level 199, and then multiplying this average MP gain by the number of levels you have yet to gain. Thus:
[(43 +(Int) /10) + (43 +((Int) +5(199 -(Level))) /10)] /2 x (200 -(Level))
Now, I'm making a final assumption that you have level 20 Maple Warrior. That means that you will actually gain:
[(43 +(Int) /10) + (43 +((Int) +1.1(5)(199 -(Level))) /10)] /2 x (200 -(Level))
So, simplify this formula and you will end up with:
[(43 +(Int) /10) + (43 +((Int) +1.1(5)(199 -(Level))) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +1.1(5)(199 -(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +5.5(199 -(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +(1094.5 -5.5(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +109.45 -5.5(Level)) /10] /2 x (200 -(Level))
[43 +(Int) /10 +54.725 -5.5(Level)) /20] x (200 -(Level))
[43 +(Int) /10 +2189/40 -11(Level)) /40] x (200 -(Level))
[3909/40 +(Int) /10 -11(Level)) /40] x (200 -(Level))
[3909 +4(Int) -11(Level))] /40 x (200 -(Level))
[3909 +4(Int) -11(Level))](200 -(Level))/40
...which is the amount of MP you gain on the way to level 200. The amount of MP you will have at level 200 is the amount of MP you gain added to your current MP. So the formula for calculating final MP is:
(Current MP) + [3909 +4(Int) -11(Level))](200 -(Level))/40
After you have calculated this, record this number. This will be your (Max MP) stat in the 2nd calculation step.
3. Use the following formula to calculate for the average amount of MP you will lose during the course of your washing:
(Current MP Loss) +[(Max MP) -4(Max HP)] /[20(32 +(Current MP Loss))]
Derivation step:
To derive this formula, refer to formula 1 under the Calculation Step 2 section which calculates for quantity of AP resets you need using your HP, MP, and MP loss per point. Using formula 1, you can predict the number of AP resets you need using your Current HP and Current MP.
The reason that the most you can use is an estimate is that in order to find the actual, you need to know the value for the average MP loss, but you can't find that value without first knowing over how many levels you'll be washing. You won't know over how many levels you'll be washing unless you first find the quantity of AP resets you're using. Thus, you will reach a dilemma, since the equations are circular. That's why you use this prediction as your actual MP loss.
Your average MP loss is the average between your current MP loss and the MP loss at the final level you are washing. So:
[(Current MP Loss) +(Final MP Loss)] /2
To calculate for the amount for final MP Loss, consider that you lose 1 more MP for every 10 INT you have. Under the assumption that you're adding all of your points into INT, you will lose one more MP every two levels you wash. The number of levels you wash is the estimated quantity of AP resets you need divided by 5, for each of the 5 points you get per level up. So your average MP loss is:
[(Current MP Loss) +[(Current MP Loss) +5(Estimate) /10 /5]] /2
(Current MP Loss) +[(Estimate) /10] /2
(Current MP Loss) +(Estimate) /20
To calculate for the estimated quantity of AP resets that you need, use the first formula under the Calculation Step 2 section, but use Current MP Loss instead of Average MP Loss. The formula is the following:
((Max MP) -4(Max HP)) /(32 +(Current MP Loss))
The proof for that formula is in Calculations Step 2. Substituting it the above formula, you get:
(Current MP Loss) +[(Max MP) -4(Max HP)] /[20(32 +(Current MP Loss))]
After you have calculated this, record this number. This will be your (Average MP Loss) stat in the 2nd calculation step.
6. Calculation Step 2: Washing Step
There are a few sets of equations that will display the necessary data.
Notice that these formulas only work for large quantities, which may or may not constantly change due to chance. Also note that you must use the predicted HP and MP at level 200 from the Calculation Step 1 section as your Max HP and Max MP, and that you must account for all HP equips you will use. Additionally, you should estimate the average MP loss over the course of your washing, which should be around 2 points more than the MP you currently lose per AP reset. If I ever find out how to calculate for the amount of MP you lose, I will add it into my formulas, but for now, just buy an AP reset and try it out.
Without further ado:
1. In order to find the number of AP resets necessary to maximize HP and MP, use the following formula:
(Max MP) -4(Max HP)
32 +(Average MP Loss)
Derivation step:
Start with the Magic Ratio 1 HP to 4 MP.
Since: (Final HP) = (Max HP) +(Total HP Gain)
And: (Final MP) = (Max MP) -(Total MP Loss)
If: 4(Final HP) = (Final MP)
Then: 4[(Max HP) +(Average HP Gain)(Number of AP Resets Used)] = (Max MP) -(Average MP Loss)(Number of AP Resets Used)
4(Max HP) +4(Average HP Gain)(Number of AP Resets Used) = (Max MP) -(Average MP Loss)(Number of AP Resets Used)
4(Average HP Gain)(Number of AP Resets Used) +(Average MP Loss)(Number of AP Resets Used) = (Max MP) -4(Max HP)
[4(Average HP Gain) +(Average MP Loss)](Number of AP Resets Used) = (Max MP) -4(Max HP)
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Number of AP Resets Used) = [(Max MP) -4(Max HP)] / [32 +(Average MP Loss)]
2. In order to find the HP at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
8(Max MP) +(Max HP)(Average MP Loss)
32 +(Average MP Loss)
Derivation step:
Start with the previous formula, which calculates for the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
Since: (Final HP) = (Total HP Gain) +(Max HP)
If: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Final HP) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP)
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP)
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP) +(Max HP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP) +4(Max HP)(Average HP Gain) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final HP) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final HP) = [8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
3. In order to find the MP at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
4[(8(Max MP) +(Max HP)(Average MP Loss)]
32 +(Average MP Loss)
Derivation step:
Start with the formula presented in item 1, which calculates the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Since: (Final MP) = -(Total MP Loss) +(Max MP)
If: (Total MP Loss) = (Average MP Loss)(Number of AP Resets Used)
Then: (Final MP) = -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = (Average MP Loss)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +(Max MP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 1:
Since: (Final MP) = 4(Final HP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Final MP) = 4[(Average HP Gain)(Number of AP Resets Used) +(Max HP)]
(Final MP) = 4[(Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]] +(Max HP)]
(Final MP) = [4(Average HP Gain)(Max MP) -16(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +4(Max HP)
(Final MP) = [4(Average HP Gain)(Max MP) -16(Average HP Gain)(Max HP) +16(Max HP)(Average HP Gain) +4(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average HP Gain)(Max MP) +4(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 2:
Since: (Final MP) = 4(Final HP)
Then: (Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
4. In order to find the amount of damage you can survive at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
5[8(Max MP) +(Max HP)(Average MP Loss)]
32 +(Average MP Loss)
Derivation step:
Start with the formula presented in item 1, which calculates the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Since: (Amount of Survivable Damage) = (Final HP) +(Final MP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And if (Final MP) = -(Total MP Loss) +(Max MP)
Then: (Amount of Survivable Damage) = (Total HP Gain) +(Max HP) -(Total MP Loss) +(Max MP)
(Amount of Survivable Damage) = (Total HP Gain) +(Max HP) -(Total MP Loss) +(Max MP)
(Amount of Survivable Damage) = (Average HP Gain)(Number of AP Resets Used)
+(Max HP) -(Average MP Loss)(Number of AP Resets Used) +(Max MP)
(Amount of Survivable Damage) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP) +(Max HP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +(Max MP) [4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP) +4(Max HP)(Average HP Gain) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss) +4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +5(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [5(Average HP Gain)(Max MP) +5(Average MP Loss)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 1:
Since: (Amount of Survivable Damage) = 5(Final HP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Amount of Survivable Damage) = 5[(Average HP Gain)(Number of AP Resets Used) +(Max HP)]
(Final MP) = 5[(Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]] +(Max HP)]
(Final MP) = [5(Average HP Gain)(Max MP) -20(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +4(Max HP)
(Final MP) = [5(Average HP Gain)(Max MP) -20(Average HP Gain)(Max HP) +20(Max HP)(Average HP Gain) +5(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [5(Average HP Gain)(Max MP) +5(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 5[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 2:
Since: (Amount of Survivable Damage) = 5(Final HP)
Then: (Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 3:
Since: (Amount of Survivable Damage) = 5(Final MP)/4
If: (Final MP) = (Max MP) -(Total MP Loss)
And: (Total MP Loss) = (Average MP Loss)(Number of AP Resets Used)
Then: (Amount of Survivable Damage) = 5[(Max MP) -(Average MP Loss)(Number of AP Resets Used)]/4
(Amount of Survivable Damage) = 5[(Max MP) -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP)[4(Average HP Gain) +(Average MP Loss)] +4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss) +4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[4(Max MP)(Average HP Gain) +4(Average MP Loss)(Max HP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP)(Average HP Gain) +(Average MP Loss)(Max HP)]/[4(Average HP Gain) +(Average MP Loss)]]
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)]/[4(Average HP Gain) +(Average MP Loss)]]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)]/[32 +(Average MP Loss)]]
Proof 4:
Since: (Amount of Survivable Damage) = 5(Final MP)/4
Then: (Amount of Survivable Damage) = 5[4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]]
5. In order to find the total amount of HP gained after synchronizing HP and MP to the Magic Ratio, use the following formula:
8[(Max MP) -4(Max HP)]
32 +(Average MP Loss)
Derivation Step:
Since: (Total HP Gain) = (Final HP) -(Maxed HP)
If: (Final HP) = (Average HP Gain)(Number of AP Resets Used) +(Maxed HP)
Then: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used) +(Maxed HP) -(Maxed HP)
(Total HP Gain) = (Average HP Gain)[(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total HP Gain) = 8[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Proof:
Since: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Total HP Gain) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total HP Gain) = 8[(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
6. In order to find the total amount of MP lost after synchronizing HP and MP to the Magic Ratio, use the following formula:
(Average MP Loss)[4(Max HP) -(Max MP)]
32 +(Average MP Loss)
Derivation Step:
Since: (Total MP Gain) = (Final MP) -(Maxed MP)
If: (Final MP) = -(Average MP Gain)(Number of AP Resets Used) +(Maxed MP)
Then: (Total MP Gain) = -(Average MP Gain)(Number of AP Resets Used) +(Maxed MP) -(Maxed MP)
(Total MP Gain) = -(Average MP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[32 +(Average MP Loss)]
Proof:
Since: (Total MP Gain) = -(Average MP Gain)(Number of AP Resets Used)
Then: (Total MP Gain) = -(Average MP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[32 +(Average MP Loss)]
8. If you have any comments regarding this section on my work with derivations or proofs, or have anything to add to this section, please feel free to PM me or post a comment on this thread or on my profile. I welcome all math nerds to audit my work.
7. Automatic Calculation
This section is for people who have a programmable calculator. I only coded it for the TI-83 and TI-84 calculators, because it's the only calculator I'm familiar with. If you have a different calculator or if you want to use Excel, you'll have to figure out how to input this on your own.
Program Code|Comments
:ClrHome|ClrHome is Item 8 under the I/O tab in the PRGM menu.
:Disp "MAX HP|Disp is Item 3 under the I/O tab in the PRGM menu.
:Prompt A|Prompt is Item 3 under the I/O tab in the PRGM menu.
:Disp "MAX MP|
:Prompt B|
:Disp "LEVEL|
:Prompt L|
:Disp "INT|
:Prompt I|
:Disp "AVG MP LOSS|
:Prompt R|
:A+12(200-L->H|The -> is found as STO> above the "On" button. This is the formula for a prediction on the number of HP you have at level 200, stored in H.
:M+(3909+4I-11L)/40(200-L->M|This is the formula for a prediction on the number of MP you have at level 200, stored in M.
:R+(M-4H)/(20(32+R->R|This is the formula for the average MP loss over the number of levels you need to wash, based on an estimation of the number of AP resets you will be using. It will be used to calculate the number you will actually be using.
:32+R->C|32+R is a constant that shows up in the calculations, so it is stored in C.
:(M-4H)/C->Q|This calculates for the quantity of AP resets you will be using.
:(8M+HR)/C->O|This calculates for the final HP at level 200 after optimization.
:ClrHome|
:Disp Q, O, 4O, 5O, 8Q, -RQ|Displays in order: the quantity of AP resets needed, HP at 200, MP at 200, amount of survivable damage at 200, total HP gain, and total MP loss.
Notes:
1) Do not put spaces in any of the formulas. I only put spaces to make each line easier to read.
2) ClrHome clears the Home Screen.
3) Prompt prompts for the input of a variable.
4) Disp does one of two things. If it is followed by an apostrophe ("), it will display all of the characters following the apostrophe as text on the Home Screen. If it is followed by only characters, it will calculate as though each character is a variable and display the result on the Home Screen.
5) Notice that it is not necessary to complete a set of apostrophe (") or parenthesis at the end of word or word phrase, or at the end of a formula, respectively. These characters are implied, so it does nothing to add them in.
6) The -> is the store function. It inputs the results from the formula into that variable.
8. Beyond the Magic Ratio
It is perfectly normal to exceed the 1:4 ratio. During your wash, you will inevitably have more HP than one-fourth of your MP. The reason is you will pass it is that you are calculating for the stats you have at level 200. In the later stages of your mage career, you'll be gaining much more MP than HP (around 12 MP to 1 HP ratio), and this uneven gain will balance out your MP.
Thus, you don't need to worry about MP serving as an upper cap to survivability, because it'll balance out in the end (assuming you reach the end).
If you don't want to exceed the 1:4 ratio with your HP, what you could do is that you can wash to 1:4, then keep it at 1:4 throughout the rest of your mage career. What you would do in this case is just use your Current HP and MP in the Washing Step of Calculations. You would still, however, use the estimation for average MP loss, just for a bit more accuracy. After washing that number of AP resets, your HP and MP will be optimized, but every few levels, whenever there's an imbalance, you will just use one or two resets to bring it back to 1:4.
This method results in fewer HP and MP in the end, but it will benefit you more all through the middle. Also, this method is easier to implement if you want to calculate for leniency, or the amount of space you want to leave for HP equips, because you can just wash to a certain ratio, then let your HP and MP grow naturally again.
9. Screenshots
The following are screenshots of what I can survive without any HP equips (excluding MoNs and Medals) after washing:
http://img210.imageshack.us/img210/7162/maple0015k.jpg
http://img695.imageshack.us/img695/218/maple0002g.jpg
More images to come. I'll try to include a SS of the following:
1. Pap Bomb
2. Pianus Bomb
3. Touch damage from a Pianus Bomb
4. Touch damage from a shark
5. Anego
10. Links to Related Threads
Thread|Author|Comment
CoIorPaper's HP Washing Guide (http://www.sleepywood.net/forum/showthread.php?t=1611086)|KBunny (http://www.sleepywood.net/forum/member.php?u=200536)|The newest guide on HP washing. It's on par with iRomeo's guide in terms of usefulness, but it's still more of an "Introduction to HP Washing" typed guide.
HP/MP Washing Method (http://www.sleepywood.net/forum/showthread.php?t=1583498)|Pheonix_BMW (http://www.sleepywood.net/forum/member.php?u=58256)|I don't find Double Washing very helpful for mages, though it does work. Contrary to what Tamillan says, Double Washing is actually more expensive.
AP Reset for magician (http://www.sleepywood.net/forum/showthread.php?t=1579606)|misc86 (http://www.sleepywood.net/forum/member.php?u=132689)|I posted most of my data here.
Brawler/Gunslinger HP and MP formula thread (http://www.sleepywood.net/forum/showthread.php?t=1509117)|WTFOMGBBQ (http://www.sleepywood.net/forum/member.php?u=67314)|I found this guide interesting, even though mages never wash to that minimum point.
๑۩۞۩๑·.·.Fully revised HP washing guide + Crusader Powerguard leveling·.·.๑۩۞۩๑ (http://www.sleepywood.net/forum/showthread.php?t=1502061)|iRomeo (http://www.sleepywood.net/forum/member.php?u=149078)|I like this guide a lot because it's very comprehensive. Unfortunately, the author of this guide is banned. =[
HP Washing Guide (http://www.sleepywood.net/forum/showthread.php?t=1359085)|RoyalCatManDo (http://www.sleepywood.net/forum/member.php?u=55269)|Not a very useful guide, though it's the oldest one I could find. Also, it's possible to wash circularly, but it doesn't yield good results.
1. Introduction to Magic Guard
Magic Guard is the most fundamental survival skill in mages. In order to understand how a mage survives, one must first understand how Magic Guard works.
http://img188.imageshack.us/img188/2317/magicguard.jpg
The first sentence of the skill reads, “Temporarily replaces damage with MP instead of HP.” What this means is that damage is channeled from HP to MP, which means that MP is part of a magician’s HP.
The following is the skill table of Magic Guard:
Skill Level|MP Usage|% replaced by MP|Duration (seconds)
1|6|11|111
2|6|14|132
3|6|17|153
4|6|20|174
5|6|23|195
6|8|30|246
7|8|33|267
8|8|36|288
9|8|39|309
10|8|42|330
11|10|49|381
12|10|52|402
13|10|55|423
14|10|58|444
15|10|61|465
16|12|68|516
17|12|71|537
18|12|74|558
19|12|77|579
20|12|80|600
Notice that the most damage is channeled to MP at level 20. Thus, it is imperative that all magicians have Magic Guard maxed in order to ensure survival of the highest amount of damage possible. Many people are reluctant to do this because MP potions cost more than HP potions in the lower levels. If this is of concern, I still recommend washing because while MP costs more at lower level to replenish than HP does, in the higher levels MP potions will be cheaper than HP potions due to Mana Bulls and %-typed potions.
Here is how much HP and MP the average magician will have at various levels:
2nd Job
At level 30
image here to come
At level 40
image here to come
At level 50
image here to come
At level 60
image here to come
At level 70
image here to come
3rd Job
At level 80
image here to come
At level 90
image here to come
At level 100
http://img94.imageshack.us/img94/813/lv100.jpg
At level 110
http://img257.imageshack.us/img257/2208/lv110.jpg
At level 120
http://img340.imageshack.us/img340/7539/lv120.jpg
4th Job
At level 130
http://img257.imageshack.us/img257/2711/lv130.jpg
At level 140
http://img257.imageshack.us/img257/6151/lv140.jpg
At level 150
http://img338.imageshack.us/img338/7317/lv1501.jpg
At level 160
image to come
At level 170
image to come
At level 180
image to come
At level 190
image to come
At level 200
image to come
Notice that in these images, the magicians have quite a bit more MP than HP. In fact, the magicians have around six times the amount of MP as HP. This leads me to my next point.
The second sentence of the skill reads, “If MP reaches 0, the HP takes a full hit.” This concept is extremely important, since it is because of this that HP and MP must remain at a vital ratio in order to survive the maximum damage possible.
2. The Magic Ratio
At maxed level, which I will assume all mages have, Magic Guard channels 80% of the damage taken to MP. What this actually means is that the HP only takes 20% of the hit, which means that a magician can survive a damage equivalent to one damage point fewer than five times its HP, and its MP will absorb four times that damage taken to HP. Essentially, it means that the HP and MP should be in a constant, magic ratio of…
1 HP to 4 MP
… in order to capitalize on survival. Suppose a mage has 2000 HP and 8000 MP, which is just enough to survive a damage of 9999. This amount of damage will bring both his HP and his MP down to 1, which will allow him to survive the hit. Let us explore what happens when HP is not at this ratio.
Suppose a mage who has 1800 HP and 12000 MP is hit 9999 damage. According to the First Rule to Magic Guard, 20% of the damage is inflicted on the HP. This means that the mage will take 1999 damage to his HP, which is over the amount of HP she has, causing him to die. Suppose this same mage is hit 8999 damage. This will bring his HP down to 1 and his MP down to 4800; therefore, 4800 points of MP on this magician are wasted because they cannot be utilized by the HP.
This is the problem that most unwashed mages have, due to the nature of how HP and MP are gained upon level up within the game.
Suppose a mage who has 2200 HP and 6000 MP is hit 9999 damage. According to the first rule of Magic Guard, it would appear that this mage might be able to survive a damage of 10999, or five times his HP. However, this isn’t true. According to the Second Rule of Magic Guard, if MP reaches 0, the HP takes a full hit. Since 6000 MP will be drained completely from this 9999 hit, the rest of the 3999 damage not accounted for by the MP will hit the HP, which will cause this magician to die.
This generally does not happen unless a mage is completely loaded with many HP equips, doesn’t have MP Max maxed, is using an alternate AP skill build such as a STR mage, overwashed, or a combination of any of the above.
3. The Truth About Mana
To ensure the maximum amount of a survival on a mage takes an immense amount of planning and calculation, because washing a Mage is extremely different from washing other classes. In other classes, washing is a very simple and straightforward concept: its only rule is to wash until the MP hits the minimum point. The reason for this is that to other classes, MP is trivial; the only amount of MP necessary is the amount enough to cast all skills. Many physical classes at level 200 don't even use Sorcerer Elixers.
However, on a mage, MP is more important. Not only does it serve a major purpose in survivability through Magic Guard, it is a basis for attacking power. Skills like AMP double MP usage, easily causing each skill to take 50-100 MP per cast. In addition, ultimates such as Meteor can take up to 8000 MP to cast, which is only alleviated by having a higher MP base. It takes 11667 Max MP to have a Mana Bull completely recover one cast of Meteor at maxed level, which drains 7000 MP per cast.
Because of this importance of MP, some people are under the misconception that it's benefical to a mage to have as much MP as possible. Some people believe that it's necessary for all magicians to to hit the MP cap of 30000 with HB, or have 18750 MP without HB. This is complete BS. Meteor at maxed level costs 7000 MP per cast. That lame 8x MP washed out per point is hardly going to affect MP cost at all. Usually, the total MP lost will not exceed 3000, but even if it does, the following is a table shows that such a loss still won't put much of a dent in the amount healed by % potions.
Base MP|Ginseng (40%)|Mana Bull (60%)|Ginger Ale (70%)
15000|6000|9000|10500
15250|6100|9150|10675
15500|6200|9300|10850
15750|6300|9450|11025
16000|6400|9600|11200
16250|6500|9750|11375
16500|6600|9900|11550
16750|6700|10050|11725
17000|6800|10200|11900
17250|6900|10350|12075
17500|7000|10500|12250
17750|7100|10650|12425
18000|7200|10800|12600
18250|7300|10950|12775
18500|7400|11100|12950
18750|7500|11250|13125
As seen in the table, in an extreme example, even if 3750 MP is lost, which is more useful? A mage with 3000 HP and 15000 MP who can take a 15000 hit or a mage with 2625 HP and 18750 MP who can only take a 13125 hit? Neither of these two mages will be gaining any extra damage or usage for their Meteor, and no other spell in a Mage's skillset uses even a noticeable amount of MP due to MP Recovery and MP Eater, which means that extra MP is wasted.
Though not many people feel a need to HP wash on a mage, there are some tangible benefits to mages who do choose to HP wash. A washed mage can survive dispel more often than an unwashed mage, because she'll have more HP base than the normal mage. Currently, I have 2700 HP, which means that if I had begun washing at a lower level, I could mist sharks without Magic Guard and still survive. At Manon and Griffey, if I get stunned and dispelled, I could survive touch damage twice from the Kentauras and therefore survive long enough for the stun effect to disappear. I could take two hits from Pap after dispel before dying, and I can survive Pianus after dispel if I'm standing on a bomb.
In the end, it's up to each mage to decide what she want's to do, but be advised that it's too late to suddenly decide to begin HP washing at level 200.
4. Prediction
Washing is all about prediction: what are the final stats at level 200? The following are some common problems that HP washers will encounter.
MP and HP are gained upon level up with a slight randomization. In addition, when adding points to HP, a magician gains anywhere from 6-10 HP. That means that if a mage is unlucky, she could end up with an average of only 7 HP per point, which makes her HP gain to MP loss ratio slightly worse than the normal average of 8 HP per point, meaning overall she cannot wash as much. Though this is rarely the case, the randomization forces mages to keep calculating and recalculating at every level.
HP gear must be accounted for. Once HP is washed, a mage can’t go back. Backwashing, or washing HP back into MP yields horrible results. When washing out of HP and into MP in a backwash, a mage will lose 10 HP and gain only about 11 MP each point. This is an extremely low gain considering that when adding points into HP or MP, a mage gains an average of 8 HP and loses around 80 MP (at level 140).
After washing, the max MP serves as a cap to survivability. For example, if a mage has exactly 3500 HP and 14000 MP at level 200, she is done. Wearing any additional HP equips won't help her as much. If she only washed to 3200 HP and 17000 MP, she could wear 1050 HP in HP gear and survive 21250 damage. This means that the additional 1050 HP worn will increase her survivability by 5250. However, if she washed to 3500 HP and 14000 MP, wearing the same 1050 HP in HP gear will only allow her to survive 1050 more damage, because there wouldn’t be enough MP to sustain this extraneous HP.
When should a mage begin HP washing? The HP gained is an average 8 HP gain throughout the 200 levels, but the MP loss will increase as a mage levels more and more. Thus, it is better to begin washing at a low level. Unfortunately, most people usually don’t decide to invest in a mage until it reaches a high enough level that they decide that their mages will be their mains. Also, many people won't consider having a mage as their main character because they're under the assumption that mages can't do much at end-game.
The cost of AP resets is hefty, at 3100 NX per reset. It may be wise to just wait for an AP reset sale that happens usually during the summer or winter seasons, even though it may not yield as much. Nowadays, the difference between 5 to 6 months is around 60 to 120 levels, which is quite a huge difference in the amount of MP lost, especially if a mage is lukless.
To prepare for HP washing, a mage should attempt to gain as much INT as possible each level up. In order to accomplish this, a mage should attempt to obtain MW and wear as many INT equips as possible during each level up.
The reason for this is that the more INT a character has during level up, the more MP gained during that level up. The ratio for MP gain on level up is about 1 MP to 10 INT. For example, if a mage has 400 INT, she will gain roughly 40 MP in addition to the 20 MP she gains from the Magician skill "Improved MaxMP Increase". However, if she wears 100 INT in gear, her stats will then be 500 INT (400 + 100), which will allow her to gain roughly 50 MP in addition to the 20 MP she gains from the Magician skill " Improved MaxMP Increase". If she does this every level, she will end up with roughly 15% more MP in the end than a regular magician.
The more MP that a magician has, the more MP she may wash out. Thus, it is vital that all people considering HP washing buy or borrow INT gears and make connections with fourth job friends. This usually isn't available to people just starting out on the game.
Because of the fact that more MP is gained when a magician has more INT, a popular myth that has arisen is that being lukless will help increase the number of times a magician can wash. This theory may or may not be true. Though a lukless mage has more MP in the end, she will also lose more MP when she washes. If the amount lost is higher, it might result in both having the same amount of MP after optimization. Because of the insufficient data due to the lack of the number of magicians willing to HP wash, because, it cannot be determined whether or not being a lukless mage actually helps.
Due to the number of the problems with HP washing outlined above, it's vital that mages wash smart. HP washing is like getting a heart transplant; once it's done, it's irreversible. Also, HP washing on a mage is much more complex than HP Washing on other classes. Thus, in the sections below, I have laid out some general equations for computing the number of AP resets that a mage should use. I have also included proofs so that you may see how the equations work in relation to each other.
Calculation takes two steps. The first is to predict the HP and MP you will have at level 200, so that you have an idea of what you will have at level 200. Using this number is more accurate than using the HP and MP you currently have, because HP and MP gain upon level up are uneven and if you use the HP and MP you currently have, you might not end up with a 1:4 ratio at level 200. The second step is to calculate using your projected HP and MP at level 200 so that you end up with a 1:4 ratio.
Note that while the formulas outlined in the calculation steps below may help predict, they are not useful unless accurate, so it may be necessary to calculate and recalculate after every wash at every level.
5. Calculation Step 1: Estimation Step
In order to calculate properly, you must first predict your final stats: how many HP and MP will you have at level 200? The reason for this is that HP washing is all about planning for endgame, and since HP gain and MP gain are very different, equalizing your stats at a certain level will mean that after that level, your HP and MP will drift away from the 1:4 ratio.
1. In order to calculate for the amount of HP you will have at level 200, use the following formula:
(Current HP) +12(200-(Level))
The formula is based on the fact that you gain an average of 12 HP each level, for the remaining levels that you have yet to level up. Don't just input your current HP into current HP; include HP equips that you will possibly wear, such as a MoN (+300 HP) or a Master Adventurer Medal (+200 HP). You need to account for them, because as mentioned in the previous section, once you wash out the full number of points, your MP serves as a cap. If you don't include HP equips into your calculations, when you do hit 200 and you have washed all the way, you'll hardly gain anything by wearing HP equips. In other words, you need to give yourself some lenience.
After you have calculated this, record this number. This will be your (Max HP) stat in the 2nd calculation step.
2. In order to calculate for the amount of MP you will have at level 200, use the following formula:
(Current MP) + (3909 + 4(Int) -11(Level))(200 -(Level))/40
Derivation step:
The average amount of MP gained per level is calculated with the following formula:
23 +(2*(Improving Max MP Increase Level) + (Int)/10)
Credits to LazyBui for this formula. I'm assuming that you have maxed MP Increase, which is level 10, so the average amount of MP gained per level is actually:
43 +(Int)/10
Now, I'm making a second assumption that you'll dump all of your points into INT every level. That means that at level 199, you will gain the following amount of MP when you level to 200:
43 +((Int) +5(199 -(Level))) /10
Since the amount of MP gain per level is linear, we can model the amount of MP you will have at level 200, by averaging the MP you will gain this level with the MP you will gain at level 199, and then multiplying this average MP gain by the number of levels you have yet to gain. Thus:
[(43 +(Int) /10) + (43 +((Int) +5(199 -(Level))) /10)] /2 x (200 -(Level))
Now, I'm making a final assumption that you have level 20 Maple Warrior. That means that you will actually gain:
[(43 +(Int) /10) + (43 +((Int) +1.1(5)(199 -(Level))) /10)] /2 x (200 -(Level))
So, simplify this formula and you will end up with:
[(43 +(Int) /10) + (43 +((Int) +1.1(5)(199 -(Level))) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +1.1(5)(199 -(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +5.5(199 -(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +(1094.5 -5.5(Level)) /10)] /2 x (200 -(Level))
[43 +(Int) /10 + 43 +(Int) /10 +109.45 -5.5(Level)) /10] /2 x (200 -(Level))
[43 +(Int) /10 +54.725 -5.5(Level)) /20] x (200 -(Level))
[43 +(Int) /10 +2189/40 -11(Level)) /40] x (200 -(Level))
[3909/40 +(Int) /10 -11(Level)) /40] x (200 -(Level))
[3909 +4(Int) -11(Level))] /40 x (200 -(Level))
[3909 +4(Int) -11(Level))](200 -(Level))/40
...which is the amount of MP you gain on the way to level 200. The amount of MP you will have at level 200 is the amount of MP you gain added to your current MP. So the formula for calculating final MP is:
(Current MP) + [3909 +4(Int) -11(Level))](200 -(Level))/40
After you have calculated this, record this number. This will be your (Max MP) stat in the 2nd calculation step.
3. Use the following formula to calculate for the average amount of MP you will lose during the course of your washing:
(Current MP Loss) +[(Max MP) -4(Max HP)] /[20(32 +(Current MP Loss))]
Derivation step:
To derive this formula, refer to formula 1 under the Calculation Step 2 section which calculates for quantity of AP resets you need using your HP, MP, and MP loss per point. Using formula 1, you can predict the number of AP resets you need using your Current HP and Current MP.
The reason that the most you can use is an estimate is that in order to find the actual, you need to know the value for the average MP loss, but you can't find that value without first knowing over how many levels you'll be washing. You won't know over how many levels you'll be washing unless you first find the quantity of AP resets you're using. Thus, you will reach a dilemma, since the equations are circular. That's why you use this prediction as your actual MP loss.
Your average MP loss is the average between your current MP loss and the MP loss at the final level you are washing. So:
[(Current MP Loss) +(Final MP Loss)] /2
To calculate for the amount for final MP Loss, consider that you lose 1 more MP for every 10 INT you have. Under the assumption that you're adding all of your points into INT, you will lose one more MP every two levels you wash. The number of levels you wash is the estimated quantity of AP resets you need divided by 5, for each of the 5 points you get per level up. So your average MP loss is:
[(Current MP Loss) +[(Current MP Loss) +5(Estimate) /10 /5]] /2
(Current MP Loss) +[(Estimate) /10] /2
(Current MP Loss) +(Estimate) /20
To calculate for the estimated quantity of AP resets that you need, use the first formula under the Calculation Step 2 section, but use Current MP Loss instead of Average MP Loss. The formula is the following:
((Max MP) -4(Max HP)) /(32 +(Current MP Loss))
The proof for that formula is in Calculations Step 2. Substituting it the above formula, you get:
(Current MP Loss) +[(Max MP) -4(Max HP)] /[20(32 +(Current MP Loss))]
After you have calculated this, record this number. This will be your (Average MP Loss) stat in the 2nd calculation step.
6. Calculation Step 2: Washing Step
There are a few sets of equations that will display the necessary data.
Notice that these formulas only work for large quantities, which may or may not constantly change due to chance. Also note that you must use the predicted HP and MP at level 200 from the Calculation Step 1 section as your Max HP and Max MP, and that you must account for all HP equips you will use. Additionally, you should estimate the average MP loss over the course of your washing, which should be around 2 points more than the MP you currently lose per AP reset. If I ever find out how to calculate for the amount of MP you lose, I will add it into my formulas, but for now, just buy an AP reset and try it out.
Without further ado:
1. In order to find the number of AP resets necessary to maximize HP and MP, use the following formula:
(Max MP) -4(Max HP)
32 +(Average MP Loss)
Derivation step:
Start with the Magic Ratio 1 HP to 4 MP.
Since: (Final HP) = (Max HP) +(Total HP Gain)
And: (Final MP) = (Max MP) -(Total MP Loss)
If: 4(Final HP) = (Final MP)
Then: 4[(Max HP) +(Average HP Gain)(Number of AP Resets Used)] = (Max MP) -(Average MP Loss)(Number of AP Resets Used)
4(Max HP) +4(Average HP Gain)(Number of AP Resets Used) = (Max MP) -(Average MP Loss)(Number of AP Resets Used)
4(Average HP Gain)(Number of AP Resets Used) +(Average MP Loss)(Number of AP Resets Used) = (Max MP) -4(Max HP)
[4(Average HP Gain) +(Average MP Loss)](Number of AP Resets Used) = (Max MP) -4(Max HP)
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Number of AP Resets Used) = [(Max MP) -4(Max HP)] / [32 +(Average MP Loss)]
2. In order to find the HP at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
8(Max MP) +(Max HP)(Average MP Loss)
32 +(Average MP Loss)
Derivation step:
Start with the previous formula, which calculates for the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
Since: (Final HP) = (Total HP Gain) +(Max HP)
If: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Final HP) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP)
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP)
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP) +(Max HP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Final HP) = [(Average HP Gain)(Max MP) -4(Average HP Gain)(Max HP) +4(Max HP)(Average HP Gain) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final HP) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final HP) = [8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
3. In order to find the MP at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
4[(8(Max MP) +(Max HP)(Average MP Loss)]
32 +(Average MP Loss)
Derivation step:
Start with the formula presented in item 1, which calculates the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Since: (Final MP) = -(Total MP Loss) +(Max MP)
If: (Total MP Loss) = (Average MP Loss)(Number of AP Resets Used)
Then: (Final MP) = -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = (Average MP Loss)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +(Max MP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 1:
Since: (Final MP) = 4(Final HP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Final MP) = 4[(Average HP Gain)(Number of AP Resets Used) +(Max HP)]
(Final MP) = 4[(Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]] +(Max HP)]
(Final MP) = [4(Average HP Gain)(Max MP) -16(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +4(Max HP)
(Final MP) = [4(Average HP Gain)(Max MP) -16(Average HP Gain)(Max HP) +16(Max HP)(Average HP Gain) +4(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [4(Average HP Gain)(Max MP) +4(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 2:
Since: (Final MP) = 4(Final HP)
Then: (Final MP) = 4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 4[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
4. In order to find the amount of damage you can survive at level 200 after synchronizing HP and MP to the Magic Ratio, use the following formula:
5[8(Max MP) +(Max HP)(Average MP Loss)]
32 +(Average MP Loss)
Derivation step:
Start with the formula presented in item 1, which calculates the recommended number of AP resets:
(Number of AP Resets Used) = [(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Since: (Amount of Survivable Damage) = (Final HP) +(Final MP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And if (Final MP) = -(Total MP Loss) +(Max MP)
Then: (Amount of Survivable Damage) = (Total HP Gain) +(Max HP) -(Total MP Loss) +(Max MP)
(Amount of Survivable Damage) = (Total HP Gain) +(Max HP) -(Total MP Loss) +(Max MP)
(Amount of Survivable Damage) = (Average HP Gain)(Number of AP Resets Used)
+(Max HP) -(Average MP Loss)(Number of AP Resets Used) +(Max MP)
(Amount of Survivable Damage) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max MP)
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +(Max HP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP) +(Max HP)[4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +(Max MP) [4(Average HP Gain) +(Average MP Loss)]] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) -4(Average HP Gain) (Max HP) +4(Max HP)(Average HP Gain) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP) +4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)] +[4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss) +4(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [(Average HP Gain)(Max MP) +5(Average MP Loss)(Max HP) +4(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = [5(Average HP Gain)(Max MP) +5(Average MP Loss)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 1:
Since: (Amount of Survivable Damage) = 5(Final HP)
If: (Final HP) = (Total HP Gain) +(Max HP)
And: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Amount of Survivable Damage) = 5[(Average HP Gain)(Number of AP Resets Used) +(Max HP)]
(Final MP) = 5[(Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]] +(Max HP)]
(Final MP) = [5(Average HP Gain)(Max MP) -20(Average HP Gain)(Max HP)] /[4(Average HP Gain) +(Average MP Loss)] +4(Max HP)
(Final MP) = [5(Average HP Gain)(Max MP) -20(Average HP Gain)(Max HP) +20(Max HP)(Average HP Gain) +5(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = [5(Average HP Gain)(Max MP) +5(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 5[(Average MP Loss)(Max HP) +(Max MP)(Average HP Gain)] /[4(Average HP Gain) +(Average MP Loss)]
(Final MP) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Final MP) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 2:
Since: (Amount of Survivable Damage) = 5(Final HP)
Then: (Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]
Proof 3:
Since: (Amount of Survivable Damage) = 5(Final MP)/4
If: (Final MP) = (Max MP) -(Total MP Loss)
And: (Total MP Loss) = (Average MP Loss)(Number of AP Resets Used)
Then: (Amount of Survivable Damage) = 5[(Max MP) -(Average MP Loss)(Number of AP Resets Used)]/4
(Amount of Survivable Damage) = 5[(Max MP) -(Average MP Loss)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP) +[4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP)[4(Average HP Gain) +(Average MP Loss)] +4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[4(Max MP)(Average HP Gain) +(Max MP)(Average MP Loss) +4(Average MP Loss)(Max HP) -(Average MP Loss)(Max MP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[4(Max MP)(Average HP Gain) +4(Average MP Loss)(Max HP)]/[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Max MP)(Average HP Gain) +(Average MP Loss)(Max HP)]/[4(Average HP Gain) +(Average MP Loss)]]
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)]/[4(Average HP Gain) +(Average MP Loss)]]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)]/[32 +(Average MP Loss)]]
Proof 4:
Since: (Amount of Survivable Damage) = 5(Final MP)/4
Then: (Amount of Survivable Damage) = 5[4[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]]/4
(Amount of Survivable Damage) = 5[(Average HP Gain)(Max MP) +(Max HP)(Average MP Loss)] /[4(Average HP Gain) +(Average MP Loss)]]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Amount of Survivable Damage) = 5[8(Max MP) +(Max HP)(Average MP Loss)] /[32 +(Average MP Loss)]]
5. In order to find the total amount of HP gained after synchronizing HP and MP to the Magic Ratio, use the following formula:
8[(Max MP) -4(Max HP)]
32 +(Average MP Loss)
Derivation Step:
Since: (Total HP Gain) = (Final HP) -(Maxed HP)
If: (Final HP) = (Average HP Gain)(Number of AP Resets Used) +(Maxed HP)
Then: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used) +(Maxed HP) -(Maxed HP)
(Total HP Gain) = (Average HP Gain)[(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total HP Gain) = 8[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
Proof:
Since: (Total HP Gain) = (Average HP Gain)(Number of AP Resets Used)
Then: (Total HP Gain) = (Average HP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total HP Gain) = 8[(Max MP) -4(Max HP)] /[32 +(Average MP Loss)]
6. In order to find the total amount of MP lost after synchronizing HP and MP to the Magic Ratio, use the following formula:
(Average MP Loss)[4(Max HP) -(Max MP)]
32 +(Average MP Loss)
Derivation Step:
Since: (Total MP Gain) = (Final MP) -(Maxed MP)
If: (Final MP) = -(Average MP Gain)(Number of AP Resets Used) +(Maxed MP)
Then: (Total MP Gain) = -(Average MP Gain)(Number of AP Resets Used) +(Maxed MP) -(Maxed MP)
(Total MP Gain) = -(Average MP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[32 +(Average MP Loss)]
Proof:
Since: (Total MP Gain) = -(Average MP Gain)(Number of AP Resets Used)
Then: (Total MP Gain) = -(Average MP Gain)[(Max MP) -4(Max HP)] /[4(Average HP Gain) +(Average MP Loss)]
(Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[4(Average HP Gain) +(Average MP Loss)]
~~~~~
Substitution Step:
Average HP Gain is 8 HP. On level up, upon putting points in, a mage will always gain 6HP to 10HP.
Thus: (Total MP Gain) = (Average MP Gain)[4(Max HP) -(Max MP)] /[32 +(Average MP Loss)]
8. If you have any comments regarding this section on my work with derivations or proofs, or have anything to add to this section, please feel free to PM me or post a comment on this thread or on my profile. I welcome all math nerds to audit my work.
7. Automatic Calculation
This section is for people who have a programmable calculator. I only coded it for the TI-83 and TI-84 calculators, because it's the only calculator I'm familiar with. If you have a different calculator or if you want to use Excel, you'll have to figure out how to input this on your own.
Program Code|Comments
:ClrHome|ClrHome is Item 8 under the I/O tab in the PRGM menu.
:Disp "MAX HP|Disp is Item 3 under the I/O tab in the PRGM menu.
:Prompt A|Prompt is Item 3 under the I/O tab in the PRGM menu.
:Disp "MAX MP|
:Prompt B|
:Disp "LEVEL|
:Prompt L|
:Disp "INT|
:Prompt I|
:Disp "AVG MP LOSS|
:Prompt R|
:A+12(200-L->H|The -> is found as STO> above the "On" button. This is the formula for a prediction on the number of HP you have at level 200, stored in H.
:M+(3909+4I-11L)/40(200-L->M|This is the formula for a prediction on the number of MP you have at level 200, stored in M.
:R+(M-4H)/(20(32+R->R|This is the formula for the average MP loss over the number of levels you need to wash, based on an estimation of the number of AP resets you will be using. It will be used to calculate the number you will actually be using.
:32+R->C|32+R is a constant that shows up in the calculations, so it is stored in C.
:(M-4H)/C->Q|This calculates for the quantity of AP resets you will be using.
:(8M+HR)/C->O|This calculates for the final HP at level 200 after optimization.
:ClrHome|
:Disp Q, O, 4O, 5O, 8Q, -RQ|Displays in order: the quantity of AP resets needed, HP at 200, MP at 200, amount of survivable damage at 200, total HP gain, and total MP loss.
Notes:
1) Do not put spaces in any of the formulas. I only put spaces to make each line easier to read.
2) ClrHome clears the Home Screen.
3) Prompt prompts for the input of a variable.
4) Disp does one of two things. If it is followed by an apostrophe ("), it will display all of the characters following the apostrophe as text on the Home Screen. If it is followed by only characters, it will calculate as though each character is a variable and display the result on the Home Screen.
5) Notice that it is not necessary to complete a set of apostrophe (") or parenthesis at the end of word or word phrase, or at the end of a formula, respectively. These characters are implied, so it does nothing to add them in.
6) The -> is the store function. It inputs the results from the formula into that variable.
8. Beyond the Magic Ratio
It is perfectly normal to exceed the 1:4 ratio. During your wash, you will inevitably have more HP than one-fourth of your MP. The reason is you will pass it is that you are calculating for the stats you have at level 200. In the later stages of your mage career, you'll be gaining much more MP than HP (around 12 MP to 1 HP ratio), and this uneven gain will balance out your MP.
Thus, you don't need to worry about MP serving as an upper cap to survivability, because it'll balance out in the end (assuming you reach the end).
If you don't want to exceed the 1:4 ratio with your HP, what you could do is that you can wash to 1:4, then keep it at 1:4 throughout the rest of your mage career. What you would do in this case is just use your Current HP and MP in the Washing Step of Calculations. You would still, however, use the estimation for average MP loss, just for a bit more accuracy. After washing that number of AP resets, your HP and MP will be optimized, but every few levels, whenever there's an imbalance, you will just use one or two resets to bring it back to 1:4.
This method results in fewer HP and MP in the end, but it will benefit you more all through the middle. Also, this method is easier to implement if you want to calculate for leniency, or the amount of space you want to leave for HP equips, because you can just wash to a certain ratio, then let your HP and MP grow naturally again.
9. Screenshots
The following are screenshots of what I can survive without any HP equips (excluding MoNs and Medals) after washing:
http://img210.imageshack.us/img210/7162/maple0015k.jpg
http://img695.imageshack.us/img695/218/maple0002g.jpg
More images to come. I'll try to include a SS of the following:
1. Pap Bomb
2. Pianus Bomb
3. Touch damage from a Pianus Bomb
4. Touch damage from a shark
5. Anego
10. Links to Related Threads
Thread|Author|Comment
CoIorPaper's HP Washing Guide (http://www.sleepywood.net/forum/showthread.php?t=1611086)|KBunny (http://www.sleepywood.net/forum/member.php?u=200536)|The newest guide on HP washing. It's on par with iRomeo's guide in terms of usefulness, but it's still more of an "Introduction to HP Washing" typed guide.
HP/MP Washing Method (http://www.sleepywood.net/forum/showthread.php?t=1583498)|Pheonix_BMW (http://www.sleepywood.net/forum/member.php?u=58256)|I don't find Double Washing very helpful for mages, though it does work. Contrary to what Tamillan says, Double Washing is actually more expensive.
AP Reset for magician (http://www.sleepywood.net/forum/showthread.php?t=1579606)|misc86 (http://www.sleepywood.net/forum/member.php?u=132689)|I posted most of my data here.
Brawler/Gunslinger HP and MP formula thread (http://www.sleepywood.net/forum/showthread.php?t=1509117)|WTFOMGBBQ (http://www.sleepywood.net/forum/member.php?u=67314)|I found this guide interesting, even though mages never wash to that minimum point.
๑۩۞۩๑·.·.Fully revised HP washing guide + Crusader Powerguard leveling·.·.๑۩۞۩๑ (http://www.sleepywood.net/forum/showthread.php?t=1502061)|iRomeo (http://www.sleepywood.net/forum/member.php?u=149078)|I like this guide a lot because it's very comprehensive. Unfortunately, the author of this guide is banned. =[
HP Washing Guide (http://www.sleepywood.net/forum/showthread.php?t=1359085)|RoyalCatManDo (http://www.sleepywood.net/forum/member.php?u=55269)|Not a very useful guide, though it's the oldest one I could find. Also, it's possible to wash circularly, but it doesn't yield good results.