Game Mechanics
Cumulative Probability in Blooket
Most players misunderstand what multiple pulls actually do to your odds. Cumulative probability is the math that fixes that.
Published: May 25, 2026
Updated: May 25, 2026
Cumulative probability is the core math behind every calculator on this site. This guide explains it in plain language so you can reason about your own budgets.
The formula that matters
Cumulative probability answers one question: "If I open n packs, what is the chance I get at least one of my target?" The formula is P = 1 - (1 - p)^n, where p is the single-pull rate and n is the number of opens.
This is not additive. A 1% rate over 100 pulls is not 100%. It is about 63.4%. Over 200 pulls it is about 86.6%. The curve rises quickly at first, then slows down forever without ever reaching 100%.
Why most players get this wrong
- Adding rates together (1% × 100 = 100%) — this is wrong and leads to guaranteed-expectation thinking.
- Assuming that if you miss 50 times, the next pull is more likely — each pull is independent. The rate does not change.
- Treating expected value as a guarantee — an expected 100 opens for one hit means on average, not in your specific session.
How to use cumulative probability for budgeting
The Chase Calculatoruses this exact formula to show you the token budget needed for 50%, 90%, and 99% probability. That gives you three planning anchors: the optimistic budget, the realistic budget, and the "almost certain" budget.
If the 99% budget feels unreachable, that is useful information. It means your target is rare enough that you should consider a different goal or a different pack.