📖 Overview
Use this calculator to evaluate deck consistency and opening hand reliability for board game card systems.
⚙️ How It Works
Uses a hypergeometric model to estimate the probability of drawing at least a target number of desired cards without replacement.
The Formula
P(X ≥ k) = Σ [ C(K,i) × C(N−K, n−i) ] / C(N,n), for i = k..min(K,n)
| N | Total deck size |
| K | Desired cards in deck |
| n | Cards drawn |
| k | Minimum desired hits needed |
💡This is the standard card-draw probability model used for TCGs and deck builders when cards are drawn without replacement.
Quick Reference
| Deck setup | Draw target | Probability |
|---|---|---|
| 8 targets in 60-card deck | At least 1 in 7 draws | ~65.34% |
| 8 targets in 60-card deck | At least 2 in 10 draws | ~24.19% |
| 12 targets in 40-card deck | At least 1 in 5 draws | ~85.10% |
| 6 targets in 50-card deck | At least 1 in 6 draws | ~55.73% |
Practical Tips
💡 Lower deck size or higher target-card count strongly increases hit odds.
💡 Use this to compare consistency before finalizing deck lists.
Frequently Asked Questions
❓ Why not use simple percentage?
Simple percentage ignores no-replacement effects and is less accurate for card draws.
❓ Can required hits exceed cards drawn?
No, required hits must be less than or equal to cards drawn.