Combat

Integer division discards fractional parts. Other intermediate results also discard fractions at the specified calculation steps, not only at the end; apply explicitly stated rounding separately. Separately rounded bonuses assume the running total is nonnegative. If a penalty makes it negative, calculate the complete updated total before discarding its fractional part. These examples cover normal, valid character stats and damage—not invalid states or values outside the normal range.

These formulas model the game’s calculations. Exact agreement with the running game has not been verified at every rounding boundary, so hand calculations and spreadsheets may differ.

Consider displayed level 70, rebirth level 10, Dexterity 120, Xelima and Long Sword talents, effective Long Sword mastery 100, a long-sword critical attack with an available critical charge, and no equipment, hero-set, manufacturing or monster-specialty hit bonus.

The skill term is $10+\lfloor 100·90/100\rfloor =100$. The critical adds 130; Dexterity adds $\lfloor (120-50)·1.2+0.5\rfloor =84$; Xelima adds 15. The Long Sword multiplier applies to that complete sum: $trunc((100+130+84+15)·1.05)=345$.

L means displayed level; R means rebirth level. Adjusted level is $A=min(140,L+R)$.

For effective weapon/hand mastery S, $H_s=10+\lfloor 90S/100\rfloor$. Add flat equipment and eligible hero-set bonuses. An eligible critical adds $trunc(C_h(100+H_s)/200)$ plus the manufacturing adjustment; $C_h$ is the listed coefficient. Otherwise apply any listed noncritical dash bonus.

Eligible Dexterity adds $\lfloor 1.2(\mathrm{D}\mathrm{E}\mathrm{X}-50)+0.5\rfloor$. Against monsters, add the appropriate flat specialty bonus and include its percentage in the final multiplier. Add Xelima's flat bonus, then apply the combined applicable Long Sword, Fencing and Archery factor to the complete sum. Truncate and enforce the minimum.

Base Defense Ratio is $2\mathrm{D}\mathrm{E}\mathrm{X}$ plus equipment defense. Apply each subsequent talent penalty separately, truncating after each multiplication.

The threshold is $min(99,max(m,trunc(62H/D)))$, where H is the attacker's effective hit ratio, D the target's effective defense ratio and m the applicable minimum above. Defense is bounded away from zero in the player-defense path.

For integer threshold p, the exact roll probability is $(42949672p+1)/4294967296$. The integer engine includes both endpoints and uses an inclusive comparison after integer division, so the probability differs slightly from p percent. No integer multiplication wraps for these thresholds.

For nonnegative stage input D, armor PA a and shield PA s on an eligible successful block:

Omit the shield term without a block. These stage formulas exclude Hammer/Tank adjustments.

Let W be scalar base weapon damage, STR effective Strength, S effective weapon mastery and L displayed level.

Apply the matching talent multiplier to the table's starting damage. An eligible critical uses $C_d(2.05+L/400)(175+S/4)/200$, where $C_d$ is the listed critical coefficient. These divisions are floating-point, including S divided by 4. A noncritical dash uses its listed multiplier instead.

Combine base-stage factors and truncate the integer damage assignment. Add applicable hero-armor damage, apply eligible Minor Berserk/Berserk, then add flat equipment damage including the weapon's upgrade level.

Against a player, apply Vitality's reduction before the hit roll. Conditional weapon/reputation effects also precede the roll. After a hit, add the skill's consecutive-hit bonus and applicable extra consecutive-attack damage.

Next apply the combined map/event and talent damage multiplier. Crush adds its extra fraction to this multiplier; it does not independently multiply every other percentage modifier. Against players, selected-armor upgrade reduction precedes armor/shield absorption. Against monsters, flat specialty damage and its percentage adjustment precede physical absorption.

For spell-circle calculations, use level A and mage level $M=\lfloor A/10\rfloor$. Circles 1 through 10 have penalty coefficients 5, 5, 8, 8, 10, 14, 28, 32, 36 and 40 respectively.

Start with effective Magic-skill mastery and add $\lfloor 1.15(\mathrm{M}\mathrm{A}\mathrm{G}-50)+0.5\rfloor$ when eligible.

For circle C below M, add $5(M-C)$. For C above M, set $a=A-10M$, $b=(C-M)P_C$, and $c=10(C-M)$; subtract $b-trunc(ab/c)$. Truncate the fractional correction rather than rounding to nearest. Equal circle and mage level has no adjustment.

After the equipment, minimum and hero-set/Xelima steps above, apply the combined applicable Fencing and Ice multiplier, then truncate to an integer.

For flat equipment magic resistance B no greater than 260, leave B unchanged. Otherwise replace it by $trunc(200+0.7(B-200)+{\log }_{1.27}(B-200))$. The logarithm's arguments and result are single precision; the sum is assigned to integer resistance.

Then add $S_r+max(0,\mathrm{M}\mathrm{A}\mathrm{G}-50)$, where $S_r$ is effective Magic Resistance skill. Apply any Xelima penalty and truncate before enforcing the final minimum.

The normal resistance-roll threshold is $min(99,max(m,trunc(50H/R_m)))$, with effective magic hit ratio H, effective target magic resistance $R_m$ and the applicable minimum m above. Convert the resulting threshold using the exact integer chance conversion in Physical chance to hit.

Let B be the combined magic-absorption stat. Before attacker penetration and special target exceptions, compute effective MA in single precision:

Apply attacker-specific penetration next, then round to the nearest integer, with positive halves upward.

For normal nonnegative spell-damage input D, initial Magic scaling is $D\leftarrow trunc(D+D·0.003\mathrm{M}\mathrm{A}\mathrm{G}+0.5)$. This is an integer damage assignment.

Applicable hero/weapon effects and reputation damage precede flat magic-damage equipment bonuses. Monster targets then receive the attacker's specialty additions; percentage magic damage and applicable map/event/talent multipliers follow. Integer assignments truncate unless an explicit rounding addition is present.

A crush next rounds $D·C_m$ using an added 0.5, where $C_m$ is the effective magic-crush multiplier. The subsequent player Vitality subtraction is nonlinear.

The armor-location selector draws uniformly from integers 0 through 10,000, including both endpoints:

The extra endpoint belongs to the helmet branch.

For effective Shield mastery S, the chance parameter is $0.10+0.009S$: 0.10 at mastery 0 and 1.00 at mastery 100.

For floating chance argument q between 0 and 1, the exact probability is $(\lfloor 4294967295q\rfloor +1)/4294967296$. This uses the actual calculated floating argument. The comparison is inclusive; callers can suppress a zero-chance draw, as the crush paths do.

From incoming endurance damage E, a successful block changes armor wear to $\lceil 0.4E\rceil$; shield wear is $\lceil 0.8E\rceil$.

The amount is not uniform between half Vitality and full Vitality. With $v=\mathrm{V}\mathrm{I}\mathrm{T}+1$ and canonical random sample $0\le U<1$, the unmodified amount is $\lfloor v/2\rfloor +(v/2)(1-U^{0.2})$, with the second division floating-point. U is a finite-precision uniform sample.

Apply red-slate additions, HP-max penalties, stored recovery, combined equipment-and-talent HP recovery, then Xelima, in that order. Discard the fractional part of the final healing amount before capping it.

For effective MAG and canonical sample $0\le U<1$, the unmodified amount is $\mathrm{M}\mathrm{A}\mathrm{G}/3+(\mathrm{M}\mathrm{A}\mathrm{G}/1.5)(1-U^{0.35})$, with floating-point divisions. Discard the fractional part after applying the recovery bonuses, before capping.

The base amount is 13 plus the sum of 3 independent uniform integer rolls from 1 through $\lfloor \mathrm{V}\mathrm{I}\mathrm{T}/15\rfloor$, inclusive. A faces count of 0 returns 0 instead of rolling an invalid range. Equipment SP recovery adds a truncated percentage of this integer amount.

Thus, with VIT from 10 through 14 and no equipment recovery bonus, the uncapped amounts by displayed level are 23 SP through level 20, 20 SP at levels 21–40, and 13 SP above level 40.

$D$ is the integer damage entering the absorption stage. Let $a_p$ and $a_m$ be the monster's current physical and magical absorption fractions, using percentages divided by 100. The equations summarize staged game arithmetic; rounding near boundaries can differ from hand calculations.

For a normal non-elemental physical hit with positive physical absorption:

$h$ is current HP divided by normal maximum HP, measured before the hit. This explanation covers the normal, non-overhealed range $0<h\le 1$. A Hammer weapon without the talent gets neither reduction. Truncate the remaining damage, not the absorbed amount; the minimum of 1 applies within this physical absorption step.

For normal spell absorption, apply Fire penetration before converting absorption to an integer percentage:

Then truncate the remaining damage:

These are separate conversions of absorption and remaining damage. This spell step has no local damage minimum. Neither calculation uses the player absorption cap of 80% or the player magical-absorption curve.

For a normal Beholder with 30% physical absorption, 45% magical absorption and 400 maximum HP, hold the absorption-stage input at 101 damage:

These examples compare a fixed stage input, not otherwise identical whole attacks with different talents. Later processing can change the damage actually lost.