Many players are curious about how damage is calculated during bear battles, so here’s a detailed breakdown of the mechanics and an example simulation to clarify things.

Bear Battle Overview:

• The bear consists of 5,000 specialized infantry units, each with 10 defense and 83.33 health.
• Unlike typical battles that continue until one side loses all troops, bear battles last a fixed duration of 10 turns.
• Since the bear is infantry-based, archers inflict 10% more damage due to their “ranged strike” ability.
• Damage dealt to the bear is accumulated over all 10 turns and includes contributions from infantry, cavalry, and archers.
• Troops do not die during these battles, so damage remains consistent unless hero skills with chance effects are involved.
• Upgrading the bear trap adds a 25% attack bonus to all your troop types.

Let’s dive into an example using commonly known troop stats:

Troop Base Stats (Tier 6):

• Infantry: Attack 243, Lethality 10, Health 730, Defense 10
• Cavalry: Attack 730, Lethality 10, Health 243, Defense 10
• Archer: Attack 974, Lethality 10, Health 183, Defense 10

Bear Stats:

• Infantry bear units each have Defense 10 and Health 83.33
• Total bear troops: 5,000
• Bear trap level 5 grants +25% attack to your troops (5% per level)

Calculating Attack per Troop:

The formula for attack per troop, ignoring hero skill modifiers, is:

attack_per_troop = base_attack × (1 + attack_bonus) × (lethality / 100)

Since lethality is 10 and attack_bonus is 0.25:

attack_per_troop = base_attack × 1.25 × 0.10 = base_attack × 0.125

Applying this:

• Infantry attack per troop = 243 × 0.125 = 30.375
• Cavalry attack per troop = 730 × 0.125 = 91.25
• Archer attack per troop = 974 × 0.125 = 121.75

Bear Defense per Troop:

Calculated as:

bear_defense = health × defense / 100 = 83.33 × 10 / 100 = 8.333

Damage Computation:

The formula involves the army size, attack, defense, and skill modifiers. The army parameter is the square root of the product of remaining attacker troops and bear troops:

army = sqrt(remaining_troops × bear_troops)

Assuming 6,000 troops per type attacking a bear of 5,000:

army = sqrt(6000 × 5000) ≈ 5477.23

Base damage per troop type is then:

base_damage = army × attack_per_troop / bear_defense / 100 × skillmod

Calculations without skillmod:

• Infantry: 5477.23 × 30.375 / 8.333 / 100 = ~199.65
• Cavalry: 5477.23 × 91.25 / 8.333 / 100 = ~599.76
• Archer: 5477.23 × 121.75 / 8.333 / 100 = ~800.22

Applying the 10% archer bonus:

archer_damage = 800.22 × 1.10 = 880.24

Summing up the damage from all troop types for the first round:

total_round_damage = 199.65 + 599.76 + 880.24 = 1,679.65

Final Damage over 10 Rounds:

Since the battle lasts 10 turns and damage per round is consistent:

total_damage = 1,679.65 × 10 = 16,796.5

The game rounds this up to the nearest whole number:

final_score = ceil(16,796.5) = 16,797

This matches the damage output produced by the battle simulator exactly.

In summary, understanding these calculations helps players optimize their troop compositions and upgrades to maximize damage against the bear in these fixed-turn battles.

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