Coin flip guide
Coin Flip Streaks: Specified Runs vs. Anywhere
‘Three heads in a row’ is incomplete unless you say whether you mean the next three flips or a run anywhere within a longer session.
A specified block
The next r fair flips are all heads with probability 2⁻ʳ. If either all heads or all tails qualifies, the probability is 2¹⁻ʳ for r ≥ 1. Three heads is 12.5%; three matching sides is 25%.
A streak anywhere
In three flips, at least two consecutive heads occurs in HHH, HHT, and THH: 3/8 = 37.5%. Counting HH at positions 1–2 and 2–3 separately would double-count HHH.
Either matching side
At least two matching consecutive sides in three flips occurs in every sequence except HTH and THT. Six of eight qualify, giving 75%. This differs from the 37.5% chance of consecutive heads.
The next flip does not compensate
After five heads, the next independent fair flip still has a 50% chance of heads. A streak describes the past; it does not create a debt tails must repay. The calculator keeps streak length separate from total heads target.
| Sequence | Contains HH? | Contains HH or TT? |
|---|---|---|
| HHH | Yes | Yes |
| HHT | Yes | Yes |
| HTH | No | No |
| HTT | No | Yes |
| THH | Yes | Yes |
| THT | No | No |
| TTH | No | Yes |
| TTT | No | Yes |
Sources and further reading
Worked examples use the independent fair-coin model unless a section explicitly discusses physical tossing.