Calculation method
Each die becomes a success or failure, then the binomial distribution counts the possible success totals. Compare extra dice and easier thresholds deliberately.
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
Separate die chance from pool chance
The pool size, success chance per die, and target successes define a binomial model when dice are independent. Enter the per-die probability as a design assumption only when every die uses the same condition.
Use the result in a design decision
Compare the chance of at least one success with the chance of two or more successes. This helps decide whether adding a die makes a task feel reliably achievable or merely less punishing.