Calculation method
This focuses on opening access to key cards. Full redraw once means the whole hand is returned before one independent redraw; it is not a game-specific mulligan engine.
Assumptions and limits
This is a tabletop design scenario using your inputs, not a prediction of player experience. Check your game???exact rules and edge cases before finalizing a design.
Related tools
Model the first decision players see
Deck size, target copies, and opening hand size produce the chance of seeing at least one target before any optional mulligan or draw rule. Add those rules only if the calculator explicitly models them.
Use the result in a design decision
Compare the chance for a key starter at different copy counts before adding redundancy. A low opening probability can be intentional, but it should match the game???stated pace and recovery tools.