Understanding the Blink-free Photo Calculator
This tool estimates the odds of capturing a group photo where nobody's eyes are closed, and tells you how many shots to take to reach a chosen confidence level. It treats each person's blink as an independent random event — a fair assumption for casual photos where a flash, fatigue, or lighting hasn't synchronized everyone's blinking.
The formula
If a single person blinks in a given photo with probability p, the chance that person's eyes are open is (1 − p). For a group of n people, assuming their blinks are independent of one another, the probability that everyone's eyes are open at once is the product of each person's chance:
- P(blink-free photo) = (1 − p)n — the chance a single shot has zero blinks.
- P(at least one blink) = 1 − (1 − p)n — the complement, and the "failure" chance for one shot.
Because each shot is an independent trial, taking multiple photos follows a geometric distribution. To reach a target confidence level C (say, 95%) of getting at least one blink-free shot, solve for the smallest whole number of photos k satisfying:
k ≥ ln(1 − C) / ln(1 − (1 − p)n)
The calculator also reports the average (expected) number of shots until the first blink-free photo, which is 1 / (1 − p)n, and converts the required shot count into real time using your camera's burst rate (photos per second).
Why group size matters so much
Because the per-person probabilities multiply, adding people to a photo shrinks the success chance exponentially. At a 10% individual blink rate, a solo portrait succeeds about 90% of the time, but a group of 10 succeeds only about 35% of the time (0.910) — which is why large group photos so often need several attempts.
Choosing a blink probability
There's no universal value for p — it depends on lighting, whether a flash fires, how tired the subjects are, and their age (young children tend to blink less predictably than adults). A commonly used starting point is around 10% per person per photo; raise it for bright flash or tired subjects, and lower it for calm, well-lit conditions without a flash.
Frequently Asked Questions
How is the probability of a blink-free photo calculated?
How many photos should I take to get one blink-free shot?
Why does adding people to the photo hurt the odds so much?
What blink probability should I use?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |