What this calculator finds
A "streak" (or run) is a block of consecutive flips that all land the same way — for example five heads in a row. This tool answers a precise question: given n flips of a coin that lands heads with probability p, what is the chance of seeing at least one run of r or more consecutive heads somewhere in those flips? By symmetry, the same numbers apply to a run of tails when the coin is fair; for a biased coin, set p to the probability of the outcome whose streak you care about.
Why it is not simply (1/2)ʳ
A common mistake is to compute (1/2)ʳ and stop. That is the probability of a specific block of r heads at one fixed starting position — for r = 5, that is 1/32 ≈ 3.125%. But in a sequence of n flips a run of length r can begin at many different positions, and those windows overlap, so you cannot just multiply or add them. The correct probability of getting such a run anywhere in n flips is larger. For 10 fair flips and r = 5 the true answer is 11/32 of a naive guess away from intuition: exactly 0.109375 (10.9375%), which is 112 of the 1024 possible sequences.
The exact method
This calculator uses a run-length recurrence (a small dynamic program), which gives the exact probability rather than an approximation. It tracks the length of the current trailing head-run after each flip. Each flip, a head extends the run and a tail resets it to zero; as soon as the run reaches r, that sequence is counted as a success. Summing the probability mass that reaches the "r" state gives P(streak). The chance that no such streak occurs is simply the complement, 1 − P(streak).
Expected longest streak
The calculator also reports the expected length of the longest head-run, computed as E[L] = Σr≥1 P(longest run ≥ r). For 10 fair flips the expected longest head-run is about 2.80; for 100 fair flips it rises to roughly 6. A useful rule of thumb for a fair coin is that the longest run of heads in n flips is close to log₂(n): log₂(100) ≈ 6.64, which is why long sequences almost always contain a surprisingly long streak.
Reference points for a fair coin (p = 0.5)
- 5+ heads in 10 flips: 0.109375 (about 1 in 9).
- 3+ heads in 10 flips: 0.5078125 (just over even odds).
- 5+ heads in 100 flips: about 0.8101 — a 5-streak is the norm, not the exception, over 100 flips.
- 7+ heads in 100 flips: about 0.3175.
- At least 1 head in 10 flips (r = 1): 1 − 0.5¹⁰ = 0.999023.
Frequently Asked Questions
What is the chance of 5 heads in a row within 10 flips of a fair coin?
Does it work for tails, or for a biased coin?
Why can a long streak appear "against the odds"?
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 |