Game math

Bag / Token Draw Probability Calculator

Model target tokens drawn from a bag, cup, or cube pool.

Tabletop design inputs

Scenario

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.