# Gachapon Probability Calculator AI Agent Connect

> Calculate the statistical likelihood, expected costs, and purchase requirements for completing a full Gachapon collection.

## Overview
- **Category:** gaming
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_dbPCauhm3gHg87V9dsAn5G8XsK4l6Oi9a0EPqkam/ai-agent-connect
- **Tags:** gachapon, probability, coupon-collector, statistics, collection

## Description

This MCP server provides precise mathematical tools for collectors using the Coupon Collector's Problem. Use `expected_metrics` to find the average cost and attempts needed for a set, `completion_probability` to determine the likelihood of finishing after a specific number of pulls, `target_threshold` to find how many purchases are required for a specific confidence level, and `duplicate_probability` to calculate the chance of having at least one duplicate of every item.

## Tools

### duplicate_probability
Calculate the probability of having at least one duplicate of every item

### expected_metrics
Calculate expected number of purchases and total cost to complete the set

### target_threshold
Calculate the number of purchases needed to reach a target confidence level

### completion_probability
Calculate the probability of having a complete set after K purchases

## Prompt Examples

**Prompt:** 
```
How much will it cost on average to collect a set of 50 Gachapon items if each costs $2?
```

**Response:** 
```
To collect a set of 50 items at $2 each, you can expect to make approximately 224.96 purchases, resulting in an expected total cost of $449.92.
```

**Prompt:** 
```
What is the probability of completing a 10-item set after 20 purchases?
```

**Response:** 
```
The probability of having a complete set of 10 items after 20 purchases is approximately 0.541.
```

**Prompt:** 
```
How many purchases are needed to be 90% confident in completing a 30-item set?
```

**Response:** 
```
To reach a 90% confidence level for a 30-item set, you will need to make 128 purchases.
```

## Frequently Asked Questions

**How do I calculate the average cost to complete my collection?**
You can use the `expected_metrics` tool. Provide the total number of unique items in the set and the price per capsule to get the expected number of purchases and total cost.

**What is the chance I will have a full set after 50 pulls?**
Use the `completion_probability` tool. Input the total number of unique items and the number of capsules purchased (50) to see your success probability.

**How many pulls do I need to be 95% sure I have the full set?**
The `target_threshold` tool is designed for this. Enter the total number of unique items and set the target probability to 0.95.