# Card Draw Probability Calculator MCP for AI Agents MCP

> Card Draw Probability Calculator helps TCG players figure out the math behind drawing specific cards. It uses hypergeometric distribution to calculate exactly how likely you are to hit your targets in a deck, giving you an edge at the table.

## Overview
- **Category:** gaming
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_7a5epFkLxzxKMoByBBzmvGpY8pdJ2BmVrsQQWOP1/mcp
- **Tags:** tcg, ccg, probability, mtg, yugioh, hypergeometric, mulligan

## Description

This MCP gives deep statistical analysis to competitive card game players. Instead of guessing or relying on gut feelings about draw rates, you get precise mathematical probabilities for every scenario. You can use it to calculate the likelihood of drawing key cards over several turns, which is critical when building a decklist or strategizing a mulligan.

## Tools

### track_deck_progression
Updates your available card pool state after effects like scrying or thinning have altered the deck composition.

### get_distribution_table
Generates a full, detailed table showing the probability for every possible number of target cards you might draw.

### calculate_draw_probability
Outputs the specific percentage chance of drawing at least one or more designated target cards in your next set of draws.

### evaluate_mulligan_decision
Compares your current hand's quality against expected post-mulligan quality to recommend if you should keep your starting hand.

## Prompt Examples

**Prompt:** 
```
What are my chances of drawing at least 2 lands in my next 7 cards if I have 24 lands in a 60-card deck?
```

**Response:** 
```
**Draw Probability Report**

The probability of drawing at least 2 lands is approximately **85.3%**.

This calculation assumes:
*   Total Deck Size: 60 cards
*   Target Cards (Lands): 24
*   Cards Drawn: 7

You're highly likely to hit your land count, suggesting a solid foundation for the current turn.
```

**Prompt:** 
```
Should I mulligan my current hand? My hand quality score is 0.5, the penalty is 1, initial size was 7, deck is 60 with 10 targets, and success threshold is 0.6.
```

**Response:** 
```
**MULLIGAN RECOMMENDED**

Your expected card quality after taking a mulligan (approx. 0.72) is significantly higher than your current hand score of 0.5.

*   **Action:** Mulligan
*   **Reasoning:** The potential gain outweighs the penalty cost, increasing overall game stability.
```

**Prompt:** 
```
Show me the full probability distribution for drawing targets from a 40-card deck with 4 copies of a card in my next 5 draws.
```

**Response:** 
```
**Full Distribution Table (Targets)**

| Targets Drawn | Probability |
| :---: | :---: |
| 0 | 56.5% |
| 1 | 35.7% |
| 2 | 7.2% |
| 3 | 0.6% |
| 4 | 0.01% |

This table shows the likelihood of every outcome, helping you plan for both low-target and high-target scenarios.
```

## Capabilities

### Calculate card draw chances
Determine the probability of pulling specific target cards from your remaining deck pool.

### Generate full distribution tables
See a complete breakdown of all possible drawing outcomes, from zero targets to maximum targets.

### Evaluate hand retention decisions
Get an objective recommendation on whether you should keep your current opening hand or take the mulligan based on expected quality.

### Update deck state after effects
Track changes to your card pool when effects like scrying or thinning remove cards from the draw pile.

## Use Cases

### Did I include enough rare cards in my deck?
A deck builder wants to know if running 4 copies of a powerful land is worth the slot. They ask their agent to run `calculate_draw_probability` using their target card count and desired draws, getting an immediate, quantifiable answer on the viability of the ratio.

### Should I pass up this mulligan?
A player gets a suboptimal opening hand. Instead of tossing it immediately, they prompt their agent to run `evaluate_mulligan_decision` with specific penalty parameters, receiving an objective recommendation that saves them from a costly mistake.

### How does thinning affect my draw chance?
During a match, the opponent uses a card effect that thins your deck. The player immediately calls `track_deck_progression` to update their resource pool and recalculates their odds for the next turn, preventing an underestimation of risk.

### I need to know my worst-case draw scenario.
A strategist wants a full picture of potential outcomes. They use `get_distribution_table` to see not just the average chance, but the exact percentage breakdown for drawing 0 targets versus drawing 3 or more.

## Benefits

- Know the real odds before you play. Instead of hoping, use `calculate_draw_probability` to get a precise percentage chance of hitting your key cards.
- Improve your opening hands immediately. Let the `evaluate_mulligan_decision` tool tell you if that gut feeling about mulligans is statistically sound.
- Understand every single outcome. The `get_distribution_table` gives you a full breakdown, letting you see how unlikely it is to draw nothing or too much.
- Adapt mid-game. After effects like scrying change your pool; use `track_deck_progression` to keep your deck's math accurate throughout the match.
- Stop guessing at board state. By modeling draw rates, you can build strategies that are mathematically guaranteed to perform better than luck alone.

## How It Works

The bottom line is that it replaces complex manual combinatorial math with one simple command.

1. You input the parameters: how many total cards are in the deck, how many target cards you need, and how many draws you plan.
2. The MCP runs the hypergeometric distribution calculation against those numbers to find the mathematical odds of success.
3. Your agent returns a precise percentage or probability range, telling you exactly what chance you have.

## Frequently Asked Questions

**How does the calculator handle mulligans?**
The `evaluate_mulligan_decision` tool compares your current hand's quality score against the statistical expectation of a new hand, accounting for the reduction in hand size caused by the `mulliganPenalty`.

**Can I track changes to my deck after scrying?**
Yes, use the `track_deck_progression` tool to update your `currentDeckSize` and `currentTargetCount` after seeing cards via scry or removing cards through deck thinning.

**What mathematical model is used for these calculations?**
The server uses the hypergeometric distribution, which is the standard model for sampling without replacement from a finite population, making it perfect for card games.