How this calculator works
Specify your own rare-event odds and trial frequency. The calculator spreads waking time evenly over calendar time, counts trial opportunities and multiplies by the event probability. For the chance of at least one occurrence it uses independent completed trials. This is a toy probability model for coincidence reasoning: it cannot measure a personal miracle rate or establish that real experiences are independent.
Formula
Trials = calendar seconds × (waking hours / 24) / seconds per trial. Expected count = trials / odds. P(at least one) = 1 - (1 - 1/odds)^floor(trials).
Worked example
With 12 waking hours per day, 2,000,000 calendar seconds provide 1,000,000 one-second trial opportunities. At one-in-a-million odds the expected count is 1, while the probability of at least one is about 63.2%.
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Frequently asked questions
Does an expected count of one guarantee an event?
No. Expectation is a long-run average. The probability of one or more can be substantially below 100%.
Why specify waking hours?
It scales how many trial opportunities occur during calendar time. This model uses an average daily fraction rather than a sleep schedule.
Are real coincidences independent trials?
Often they are not. Shared causes, selective attention and an unclear definition of an event can make the model unsuitable.