Okay so crate has 1 rare with 60% chance/possibility of dropping it has epic with 30% chance it has legendary with 9.5% chance of dropping it has mythic with 0.4% chance and it has then godly with 0.1% each of them costs 500 coins and if you boost luck you get about 0.3% chance for godly so how much coins do you need to get one garanteed godly in both luck boost and without luck boost scenario

Let's calculate the expected number of coins required to get one guaranteed godly item under two scenarios: without the luck boost and with the luck boost.

### 1. **Without Luck Boost**

- **Probability of getting a godly item:** \( p = 0.1\% = 0.001 \)
- **Expected number of crates needed:** \( \frac{1}{p} = \frac{1}{0.001} = 1000 \) crates
- **Cost per crate:** 500 coins
- **Total cost without luck boost:**
  \[
  \text{Total cost} = 1000 \times 500 = 500,000 \text{ coins}
  \]

### 2. **With Luck Boost**

- **Probability of getting a godly item with luck boost:** \( p' = 0.3\% = 0.003 \)
- **Expected number of crates needed:** \( \frac{1}{p'} = \frac{1}{0.003} = 333.\overline{3} \) crates (approximately 334 crates)
- **Cost per crate:** 500 coins
- **Total cost with luck boost:**
  \[
  \text{Total cost} = 334 \times 500 = 167,000 \text{ coins}
  \]

### Summary
- **Without luck boost:** **500,000 coins**
- **With luck boost:** **167,000 coins**

These are the expected amounts of coins you would need to get one guaranteed godly item in each scenario.

Would you like more details or have any questions?

Here are five related questions:
1. How does the expected number of crates change if the chance of getting a godly item doubles?
2. What is the probability of not getting any godly items after spending 500,000 coins?
3. If you could increase the luck boost to 0.5%, how would that affect the total coins needed?
4. How would the calculations change if the cost per crate increased to 1000 coins?
5. What is the expected number of crates needed to get one godly if you only open crates with the luck boost?

**Tip:** Boosting your chances significantly reduces the expected cost, making it a valuable strategy when probabilities are low.

Learn how to calculate the coins needed to guarantee a godly item in a crate probability problem. This involves understanding probability theory and expected value calculations. Explore scenarios with and without luck boost for optimal strategies. Suitable for advanced high school students.

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