Card Shuffling Analysis

Mathematical analysis of collision probability and shuffle sufficiency in the riffle shuffle — a project for the Advanced Algorithms & Combinatorics course in my CS Master's at IE Business School.

Topics Covered

• Riffle shuffle model – Gilbert-Shannon-Reeds (GSR) formulation
• Collision probability – how likely two cards end up adjacent after k shuffles
• Shuffle sufficiency – the minimum number of riffle shuffles needed to achieve near-uniform randomness (the classic "7 shuffles" result)
• Theoretical derivations with empirical validation

Structure

├── analysis.ipynb   # Main notebook with proofs and experiments
├── report.pdf       # Written report submitted for the course
└── utils.py         # Shuffle simulation helpers

Running the Notebook

pip install numpy matplotlib jupyter
jupyter notebook analysis.ipynb