Three ways to write the same chance
A 1-in-20 chance is 1/20 = 0.05 = 5%. Odds in favor compare successes to failures, so that same probability is 1:19 in favor or 19:1 against. Always check whether the denominator counts all outcomes or just failures.
An average is not a deadline
With fixed independent rate p, the expected number of attempts to first success is 1/p. At 5%, that is 20 tries. The chance of succeeding within 20 tries is only 1 − 0.9520 ≈ 64.15%. Some runs end earlier and some much later.
Plan a probability, not a promise
For target chance c, the minimum attempt count is ceil(log(1 − c)/log(1 − p)). At 5%, 59 attempts give at least a 95% chance. Without a guarantee, a nonzero failure probability remains after any finite number of attempts.
Inputs matter more than decimal places
A precise formula cannot repair an incorrect rate. Use a published rate for your exact target and check whether attempts are independent. Rounded inputs create rounded answers. The examples on this site are hypothetical, not measured odds for a real product. Set a spending limit before using chance-based purchases.
Put the idea to work
Pull odds · Raffle odds · Custom pity · Tries for a target chance