How coin flip streak probability works
The chance that the next k fair flips are all a chosen side is (1/2)k. Three heads in the next three flips is 1 in 8. Five heads in the next five is 1 in 32.
Finding at least one streak somewhere inside a longer series is different because possible runs overlap. This calculator uses dynamic programming to count the probability that no qualifying run has appeared after each flip, then subtracts that value from 100%.
Chosen-side streak versus either-side streak
- Chosen in advance
- You specify heads or tails before flipping. HHH qualifies, while TTT does not if heads was chosen.
- Either identical side
- A run of all heads or all tails qualifies. This is more likely because there are two acceptable sides.
Why streaks do not change the next flip
After ten heads in a row, the next independent fair flip is still 50% heads and 50% tails. Believing tails is now due is the gambler's fallacy. The streak may be unusual as a whole, but it does not give the coin a memory.
Frequently asked questions
What are the odds of five heads in a row?
For a chosen side over the next five fair flips, the chance is 1 in 32, or 3.125%.
Are either heads or tails streaks more likely?
Yes. If either identical side qualifies, there are more acceptable sequences than when one side is chosen in advance.
Does a long streak prove the coin is unfair?
No. A streak can occur with a fair process. Repeated evidence across many controlled trials is needed before concluding the probability is biased.