Calculation method
Without replacement uses an exact bag draw; with replacement uses independent draws. The physical rule matters when tuning bag-building systems.
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
Read the draw as a finite bag
Enter the total tokens before the draw, the target tokens among them, and the number drawn without replacement. The result is the chance of at least the requested target count, so it changes after every draw; it is not the same as repeatedly rolling independent dice.
Use the result in a design decision
For a bag with 12 success tokens in 30 total, compare a one-token draw against a three-token draw before choosing an effect strength. Test the lowest and highest likely bag states so players do not encounter an unexpected swing after tokens are removed.