Calculation method
Expected value and extra dice use the stated rule. The target chance is an explicitly labeled simulation to handle unlimited chains safely.
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
Distinguish expected value from chain chance
The entered trigger and extra-die rule determine additional rolls. The displayed expected value treats repeated explosions mathematically, while any bounded target simulation must be read as a labelled approximation rather than an infinite-chain guarantee.
Use the result in a design decision
Test a low target and a high target separately. Explosions can make rare dramatic outcomes available without making ordinary success reliable, which is often the design choice that matters.