Separate the information types
Public information is available under the rules. Private information belongs to particular players. Random or unrevealed information may be unknown to everyone. These categories create different kinds of uncertainty.
State the model before calculating
The draw explorer assumes a known number of target and other tokens, equally likely draws and no replacement. A game with weighted objects, selective drawing or a changing bag needs a different model.
Use probability as a description
A calculated chance describes possible outcomes under stated assumptions. It cannot promise the next result or turn an unfavourable outcome into proof that the decision was unreasonable.
Update when the state changes
If known tokens leave a bag, the remaining composition changes. Recalculate using the current known state rather than carrying an earlier percentage forward unchanged.
Keep private information private
When teaching or discussing a game, follow its communication rules. Do not pressure someone to reveal information that the game explicitly keeps hidden.