How to Use the Card Hand Swap Probability Calculator
This calculator helps card game players figure out the odds of drawing a specific card after a mulligan or hand swap. Enter your deck size, how many cards you currently hold, how many target cards remain in the deck, and how many cards you plan to swap.
The calculation uses the hypergeometric distribution — the standard probability model for drawing without replacement. It finds the chance that at least one of your swapped draws lands on a target card. More copies of the target card in your deck and a larger swap count both increase your odds.
Compare different deck configurations to find the optimal number of copies to include. For example, you can instantly see how much your odds improve by going from two to four copies of a key card, helping you make better deck building decisions.
Frequently Asked Questions
This calculator assumes no target cards are currently in your hand. If you already hold some, subtract them from the target count and enter only what remains in the deck.
Yes. Simply enter the number of cards you actually plan to swap, not your full hand size. The calculator adapts to any swap count you choose.