Battle of attrition
If you explore tiles while you are fighting against an enemy, your health and mana will regenerate. However, the monster will also regenerate its health, so it's not a good idea to explore mid-battle.
Or is it?
Battle of attrition is the term used by Desktop Dungeons creators of define a fight when you are exploring mid-fight to gain health and mana. Another widespread term on the forum is regen-fighting.
As you will often want to fighter monster at an higher level than you are, they would often heal quicker than you. So knowing if you can do it is not always obvious. here are some tips to know when you can do it.
Note that you can read Annotated Playthrough: Regenfighting for more explanation.
When to regen-fight
Whenever a tile is explored, the player and all monsters will heal a number of hit points equal to their level. So a 5th level monster heals 5 hit points per tile. Some special abilities, such as fast regen can modify this, but such abilities are rare. Since most difficult monsters will be higher level than you, this means they also heal more health than you. If you want to win a long-term battle of attrition, you'll need to deal more damage then them or have some other kind of advantage. Often times, a glyph such as BURNDAYRAZ or APHEELSIK is exactly the advantage you need to do this.
In general, your regen-fight is efficient when
- you have high attack power,
- you have high physical/magic resistance (depending on the enemy's attack type),
- you have Damage Reduction or Life steal ability to decrease incoming damage,
- you have some method of poisoning (and monster is not undead),
- you have corrosive or Burning Strike ability,
- the monster has low attack power,
- the monster has zero to low (physical) resistance.
And those not a good target of regen-fighting are monsters with
- Fast regen - only Monk class or characters with high poison ability can have a chance.
- Poisonous - unless you have HALPMEH or Poison Immune.
- Mana burn - unless you have Mana Burn Immune.
- Curse Bearer - only if you have some resists or damage reduction, with insufficient popcorns.
- Weakening or Corrosive - just no.
If you are in a long fight, your maximum health and mana is not a big deal here. The important thing is the efficiency of regeneration and attack. Let's see some common examples and learn how to determine if you can win the fight (with minimum resources). The easiest method to estimate the efficiency is simply calculating the average damage done for each when a certain amount of tile is explored.
You may have lower attack and lower health regeneration than your target, but the mana regeneration fills the gap. Many glyphs can be used with these mana.
BURNDAYRAZ is the standard glyph as it always spawns. Its damage alone seems below average, but its burning lowers targets' regeneration rate so it's not bad. HALPMEH is actually very poor. But being the only glyph which directly heals you, high attack and resistances make this glyph much better than usual. BYSSEPS has average damage per mana rate, However, you will need other glyphs because it can be only used once per hit, and health is mostly consumed faster than mana. So it's not an ideal glyph to use. PISORF requires a lot of walls to use in chain, so most of the time you will use a fixed secondary target monster. Then the efficiency is bad. APHEELSIK is literally made for regen-fighting, but since it is too great you will over-poison the target without help of other glyphs. BLUDTUPOWA is a unique glyph which allows you to mana-regen-fight. This is below average for standard characters, but you can evade debuffs, Physical resist or a super strong attack.
Since BURNDAYRAZ is the only glyph spawning in every run, this will be your main glyph used for regen-fighting. This glyph is good because leaving a burning stack will lower its health regeneration rate by 1.
Let's say you are Lv5 with 30 attack, the enemy is Lv6 with 40 attack. By exploring 6 tiles, - You heal 5×6 = 30 health. That's 3/4 of an attack, so 30 × 3/4 = 22.5 damage is done by normal attack. - You cast one fireball. That's 20 damage, actually 21 if the burning pop damage is considered. - The enemy heals (6-1)×6 = 30 health. - All thing considered, 22.5 + 21 - 30 = 13.5 damage is done per six tiles. It's positive so I win the battle, though its efficiency is around average.
Also, to show how resistances are superb on regen-fighting, let's consider the same situation with 25% resists. Then the enemy's attack is effectively 30. - You heal 30 health. That's one full attack, so 30 damage is done by normal attack. - You cast one fireball, that's 21 damage. - Enemy heal 30 health. - 30 + 21 - 30 = 21 damage is done per six tiles. Now the efficiency became 1.5× better! 25% resists may seem weak, but it's really a big deal. If you stack another 25% resists on top of it, it becomes 36 per six tiles, being 2.7× better! If you have full 65% resists (actually it's quite impossible for lv5 character but anyway) it becomes 58.5 per six tiles, being 4.3× better.
HALPMEH is actually a poor glyph without an improved melee ability. This glyph can also be a good choice when the enemy has low attack, or have Magic resist. Let's think about the same situation.
By healing 5 tiles, - You heal 25 health and 5 mana. HALPMEH is used once, so you heal 45 health in total. - 45 health is 9/8 of an attack, so 30 × 9/8 = 33.75 damage. - The enemy heals 6×5 = 30 health. - So you are dealing 3.75 damage per five tiles. Sadly, this fight will use up all of your blackspaces left.
If you improved your melee ability by having 25% resists, - 45 health is 3/2 of an attack, so 30 × 3/2 = 45 damage. - Enemy health 30 health. - You are dealing 15 damage per five tiles. Yeah... BURNDAYARAZ slightly wins. If you stacked 50% resists, the damage done is 37.5 damage per five tile. Now HALPMEH is winning against BURNDAYRAZ. Needless to say, full 65% resists make HALPMEH a great regen-fighting tool.
For 6 tiles revealed, BURNDAYRAZ does 4×(level)+7 damage. For standard character who boosted no base attack, 3 BYSSEPS does 3×(30%×5×(level)) = 4.5×(level) damage. So BYSSEPS is slightly weaker than BURNDAYRAZ, but its damage isn't that bad. If you are Orc, BYSSEPS overshadows BURNDAYRAZ in terms of damage.
However, you can only use BYSSEPS once per attack. Your health bar can often tank 2-3 hits from the enemy, but it means only 2-3 shots of BYSSPES are usable, while your mana bar allows maybe 5 shots. The same rule applies for regen-fighting. If you should erode some resistances, that's great go ahead with BYSSEPS. If not, you will have to find other glyph to use spare mana, and when you find BURNDAYRAZ just use it instead.
When you are pushing a monster into a wall, the mana efficiency of PISORF is exactly same with BYSSEPS. So it's quite average, and if you are under Binlor this gives you piety. But when you don't have enough wall, you should find a stationary target to push it against. Then PISORF does only 40% of your base attack instead of 60%, making it very dissapointing glyph to use.
This poison glyph is arguably the singlemost best glyph when you are doing a regen-fight. By simple calcaulation, you can completely stop the regen of a monster whose level is twice of you. Actually this glyphs is too strong so that you will apply overflowing amount of poison to target. Generally BURNDAYRAZ is used with spare mana, but other glyphs all stand their chance because APHEELSIK is just too strong. To make things simple, let's just assume you have BURNDAYRAZ and burning isn't considered at all.
Let's say you are Lv8 with 50 attack. the enemy is Lv10 with 90 attack. - Since the target's level is equal or less than twice of your level, its regeneration is completely halted. - The monster will fully recover the poison by 80/10 = 8 tiles. - Exploring 8 tiles will heal you 64 health points. That's 64/90 of an attack, 50×64/90 = ~36 damage is done. - Exploring 8 tiles will heal you 8 mana points, but you need 5 mana to cast APHEELSIK. Spare 3 mana is half a fireball, which deals 16 damage. - So 36 + 16 = 52 damage is done per 8 tiles. This is quite a good deal.
BLUDTUPOWA makes you possible to kill some quirky enemies such as Wraith, Acid Blob or Naga. Above three monsters all have reduced health so you don't even need to regen-fight normally. Often this glyph is used with BURNDAYRAZ, and actually it's the best since burning stack will give a huge boost to the damage done. You can usually win the battle with it. However, regen-fight with BLUDTUPOWA eats up too much blackspaces so it's not encouraged to use it too often.
Let's say you are Lv5, and the enemy is Lv8. You are using BURNDAYRAZ. - Also assume you start regen-fight with 4 burning stacks already on it. (You already used up 12 tiles by casting BLUDTUPOWA 4 times) - For 3 tiles explored and 3 tiles consumed, you cast 1 fireball. First one deals 24 damage, and it grows to maximum 30. - Since the enemy has lowered regeneration, it heals 7×3 = 21 health points. - So first 6 tiles will do 3 damage, and second 6 will 4 damage, ..., to maximum 9 damage. - If the enemy had 30 health left when 4 fireballs are cast, you need 30 blackspaces to completely kill it (by burn stack pop) and total 48 tiles(!) are used.
If you purchased or Battlemage Ring, each fireball deals 5 more damage with the same situation. - With same situation above, the enemy would only have 10 health left when 4 fireballs are cast. - First 6 tiles will do 8 damage, and popping the burn stack will kill the monster. - So you need total 18 tiles to completely kill it. That's super better.
Let's say you are Lv4, and the enemy is lv9. - By exploring 5 tiles you can cast one APEELSIK to completely stop its regen. - Use up 5 more blackspaces to convert health into mana, and that's 5/6 fireball, which deals at ~14 to ~17 damage. 17 damage per 10 blackspaces isn't bad, and it's at least positive. Normally a lv4 character stands no chance against lv9. Boosting your spellcasting power further improves the efficiency.
Some classes have special ability to regen-fight.
The Monk class is the king of regen-fighting, having high Physical resist and double health regeneration. In most cases the Monk class uses Orc race. The Monk can win any proper monster when enough blackspaces are given.
Orc Monk does not have a poor base attack, and regens very fast to use BYSSEPS enough. And since the health is fully healed too fast, Orc Monk has a problem keeping the burn stack. Mixed use of BURNDAYRAZ and BYSSEPS is a good choice, but BYSSEPS alone can be an effective glyph.
Monk can use BLUDTUPOWA effecively since he recovers double health from exploring, which can be converted into mana. Though it's a viable choice against some monsters, you should conserve blackspaces as they are critical resources for the Monk class.
The Gorgon is another good regen-fighter. The Gorgon needs additional bonus damage to be strong. Since her poisoning ability is great, APHEELSIK or Venom Dagger has only a little use. Also BURNDAYRAZ's regeneration lowering is not very charming, though it's still good with BYSSEPS.
The Chemist has two special forms, health form and mana form.
Health form is equal to having 25% better HALPMEH, just like the Paladin. But since he has no natural damage and HALPMEH isn't an attractive option for regen-fighting, it's generally not good. You need a descent boost of attack power and resistances to be more effective than just using the mana.
The Rat Monarch is a special class. The damage done gradually grows, and the Rat Monarch can win just anybody when enough blackspaces are given. HALPMEH helps stacking corrosion stacks, but isn't very good for landing a killing blow. PISORF doesn't do good damage unless you stacked a huge amount of corrosion, and it's not common. BURNDAYRAZ is often the best glyph in final blow, and APHEELSIK is somewhat overshadows by BURNDAYRAZ.
One interesting glyph is CYDSTEPP, which allows the Rat Monarch to stack corrosion stacks to a big monster such as bosses. This glyph doesn't help to regen-fight for other classes.
Regen Fighting Math
Let's define :
- Dh = damage caused by hero (in hitpoints, or hp)
- Dm = damage caused by the monster (hp)
- Lh = point restored by hero per tile (in hitpoints/tile, or hp/t) (usually level of the hero)
- Lm = point restored by the monster per tile explored (hp/t) (usually level of the monster, or level-1 if the monster is burning)
- Df = damage caused by fireball (hp)
- Cf = number of tiles to cast a new fireball (usually, cost in mana) (t)
- T = number of tiles required to kill the monster (t)
- Hh = total health of the hero
- M = total mana of the hero
- Hm = health of the monster in the beginning of combat (normally full health but you could do some damage to him before level up
- H = remaining health of the monster before you begin regen-fighting him (hp)
- Ph=DhLh = Hero power (for monks you need to multiply Lh by 2)
- Pm=DmLm = Monster power (for trolls with fast regen you need to multiply Lm by 2)
You have the total damage caused to the monster by the hero per tile (taking into account the regeneration) : Dt=(DhLh-DmLm)/Dm [hp/t] or Dt=(Dh/Dm)Lh-Lm
You can regen fight if DhLh>DmLm or Ph>Pm (1)
Each tile you regenerate 1 mp/t (except Chemist in mana mode) = Df/Cf. Usualy it's 4×Lf/6 (5 if wizard or Mystic Balance, and 8 if Berserker) Moreover, your attack gets +1 because of burning effect (we count one hit, one fireball, regen fight)
If you keep burning effect on a monster every time when you begin regen fighting, his effective regeneration gets lowered by 1
Dt = (DhLh - Dm(Rm - Df ⁄ Cf)) ⁄ Dm (in hp/t)
So, you can regen fight if Dh*Rh > Dm(Rm - Df/Cf) If you decided not to cast fireballs, you can regen fight if Dh*Rh > Dm*Rm
Now, lets have a closer look at the formula: We have for both the monster and the hero a ratio emerging : Damages*Regeneration (in hp*hp/t), which we could call the hit-regeneration ratio. The higher, the more potent is the character in regen fighting (he strikes stronger than his opponent and/or regenerates quicker). However, when we take into account the fireball, the damages caused by the fireball per turn (ratio Df/Cf) reduces the regeneration per tile (Rm) of the monster, hence that new value "Dm(Rm-Df/Cf)" for the hit-regeneration ratio of the monster.
Finally, the number of tile required to kill the monster in regen fighting would be : T = H/Dt or T = H*Dm/(Rh*Dh-Dm(Rm-Df/Cf)) (in t)
For efficient regen fighting, for H, we should consider the remaining health of the monster once the hero has used its full stock of health and mana for the original strikes (before starting the regeneration). This the higher max health and mana, the less tile you will use for the regeneration part of the fight.
You can derive H from Hh, M and Hm. Assuming you are using fireballs:
Physical damage performed before beginning regen-fighting: Dphysical = Dh × ⌊Hh / Dm⌋ (example: ⌊1,7⌋=1)
Fireball damage performed before beginning regen-fighting: Dmagic = (Df + 1) × ⌊M / Cf⌋
H = Hm - Dphysical - Dmagic
Also, note that every damages should be adapted with the opponent's resistance, player's glyph and so on.