Overlapping strips of blank sequence cards with copper and silver tokens. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
A run can belong to more than one window
For a run of three heads within four flips, the possible length-three windows are positions 1–3 and 2–4. Each window is all heads with probability 1/8 for a fair coin. Adding them gives 1/4, but the sequence HHHH belongs to both windows. That overlap has probability 1/16 and must not be counted twice.
Verify the small case by enumeration
The qualifying four-flip sequences are HHHT, THHH and HHHH. Each has probability 1/16, so the event probability is 3/16 = 18.75%. The simple sum of window probabilities gives 25%, which is the expected number of qualifying windows in this case, not the probability that at least one exists. Those are different quantities.
Track the current run instead of summing windows
The Coin Toss Streak Calculator tracks the probability of being in each unfinished run-length state. A head extends a head run; a tail resets it. When a path first reaches the chosen length, its probability is moved into the “at least one run” total. This avoids counting an already successful path again when another overlapping window appears.
Specify the side and the horizon
A head-only run and a run of either identical side are different events. In four fair flips, at least three consecutive identical outcomes on either side has probability 6/16 = 37.5%, because the three tail-run sequences are disjoint from the three head-run sequences. The number of flips is a fixed horizon, not an expected stopping time. Read waiting time versus fixed-horizon probability for that distinction. If order does not matter and you only need the total heads count, use the binomial coin-count tool. Independent flips and constant heads probability are assumptions of both calculations.
Check the model behind your result
Use the Coin Toss Streak Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26