Target chance is different from expected value
Expected attempts describe a long-run average. A target chance asks for enough attempts to reach a confidence level. At low rates, those numbers can be very different.
For example, a 1% chance has an expected value of 100 attempts for one success, but reaching about a 90% chance takes around 230 attempts. The higher the confidence target, the more expensive it gets.
Common targets and what they mean
A 50% target is roughly a coin flip. An 80% target is more comfortable but still leaves a real miss chance. A 90% or 95% target can look reassuring, but the cost may become hard to justify.
Always read the miss chance too. A 90% hit chance is also a 10% miss chance. If the cost is high, that remaining risk matters.
The reverse formula
The attempts-needed formula is n = ln(1 - target probability) / ln(1 - success rate). The result is rounded up because you cannot buy a fraction of a pull, box, pack, or ticket.
PrizeOdds Calculator includes this reverse calculation in the at least one success calculator and expected cost calculator.
How to use this for planning
Pick a target chance before spending, then calculate the required attempts and cost. If the cost feels too high, lower the target, wait, trade, buy directly, or skip.
Do not move the target higher while you are already missing. That is how a planned purchase turns into chasing.
Responsible use reminder
Probability can help you understand risk, but it cannot guarantee a result. Set a budget before buying pulls, boxes, packs, or prize tickets, and stop when that limit is reached.
FAQ
Is 50% a good target?
It depends on your budget. A 50% chance still misses half the time, so it should not be treated as safe.
Why do 90% and 95% need so many attempts?
Because the formula is reducing the chance of missing every attempt. Removing the last bit of miss risk takes many extra attempts.
Can I use this for blind boxes?
Yes, if you convert the desired variants into a single-box success rate first.
Does this work with prize pools without replacement?
No. Shrinking prize pools need the without-replacement calculator instead.