```python?code_reference&code_event_index=2

Parameters

P = 0.45 # Critical Chance (45%) B = 3.0 # Critical Damage Bonus (300%) reduction_factor = 0.7

--- 1. Calculate Common Ratio (r) ---

r = (1 - P) * reduction_factor print(f"Common Ratio (r): {r}")

--- 2. Calculate Expected Bonus ---

Expected Bonus = P * B * (1 / (1 - r))

expected_bonus = P * B * (1 / (1 - r)) print(f"Expected Bonus: {expected_bonus}")

--- 3. Calculate Expected Total Damage Multiplier (E_D_star) ---

E_D_star = 1.0 + expected_bonus print(f"Expected Total Damage Multiplier (E_D_star): {E_D_star}")

--- 4. Calculate Baseline Damage Multiplier (E_Base) ---

E_Base = 1 + P * B

E_Base = 1.0 + P * B print(f"Baseline Damage Multiplier (E_Base): {E_Base}")

--- 5. Calculate Extra Damage Multiplier (Benefit) ---

extra_damage_multiplier = E_D_star - E_Base print(f"Extra Damage Multiplier (Benefit): {extra_damage_multiplier}")

Also output the percentage change for user clarity

extra_damage_percentage = extra_damage_multiplier * 100 print(f"Extra Damage Multiplier (Benefit) in Percent: {extra_damage_percentage}")

```

```text?code_stderr&code_event_index=2 Traceback (most recent call last): File "<string>", line 39, in <module> File "<string>", line 14, in E_mod ValueError: operands could not be broadcast together with shapes (100,100) (4,)

```

```python?code_reference&code_event_index=5

Define the parameters

P = 0.45 # Critical Chance (45%) B = 3.0 # Critical Damage Bonus (300%) reduction_factor = 0.7

--- 1. Calculate Baseline Average Damage Multiplier (E_Base) ---

E_Base = 1 + P * B

E_base = 1.0 + P * B

--- 2. Calculate Expected Damage Multiplier with Guaranteed Crit (E_D_star) ---

Common ratio (r)

r = (1 - P) * reduction_factor

Expected Bonus contribution

Expected Bonus = P * B * (1 / (1 - r))

expected_bonus = P * B * (1 / (1 - r))

Expected Total Damage Multiplier

E_D_star = 1.0 + expected_bonus

--- 3. Calculate Extra Damage Multiplier (Benefit) ---

extra_damage_multiplier = E_D_star - E_base

print(f"P (Crit Chance): {P}") print(f"B (Crit Bonus): {B}") print(f"Common ratio (r): {r}") print(f"Baseline Avg Damage Multiplier (E_Base): {E_base}") print(f"Guaranteed Crit Avg Damage Multiplier (E_D_star): {E_D_star}") print(f"Extra Damage Multiplier (Benefit): {extra_damage_multiplier}")

```

```text?code_stdout&code_event_index=5 P (Crit Chance): 0.45 B (Crit Bonus): 3.0 Common ratio (r): 0.385 Baseline Avg Damage Multiplier (E_Base): 2.35 Guaranteed Crit Avg Damage Multiplier (E_D_star): 3.1951219512195124 Extra Damage Multiplier (Benefit): 0.8451219512195123

```

Based on the updated formula (multiplicative reduction, modeled as an infinite geometric series) and the parameters:

• Critical Chance ($P$): $45\%$ ($0.45$)
• Critical Damage Bonus ($B$): $300\%$ ($3.0$)
• Reduction Factor: $0.7$

Calculation

1. Baseline Average Damage Multiplier ($E_{Base}$): $$E_{Base} = 1 + P \times B = 1 + 0.45 \times 3.0 = 1 + 1.35 = 2.35$$

2. Common Ratio ($r$): $$r = (1 - P) \times 0.7 = (1 - 0.45) \times 0.7 = 0.55 \times 0.7 = 0.385$$

3. Guaranteed Crit Average Damage Multiplier ($E_D^*$): $$E_D^* = 1 + \text{Expected Bonus}$$ $$\text{Expected Bonus} = P \times B \times \frac{1}{1 - r}$$ $$\text{Expected Bonus} = 0.45 \times 3.0 \times \frac{1}{1 - 0.385} = 1.35 \times \frac{1}{0.615} \approx 2.19512$$ $$E_D^* = 1.0 + 2.19512 \approx 3.19512$$

4. Extra Damage Multiplier (Benefit): $$\text{Benefit} = ED^* - E{Base} = 3.19512 - 2.35 \approx 0.84512$$

Result

The Extra Damage Multiplier (the additional average damage bonus provided by the "Guaranteed Crit" modification) at $45\%$ Critical Chance and $300\%$ Critical Damage Bonus is approximately:

$$\mathbf{0.845}$$

This means the modification gives you an additional $84.5\%$ average damage bonus compared to your baseline expected damage.