🔥 Coin Toss Streak Calculator
Find out how likely a winning (or losing) streak really is. Enter the streak length and number of flips to see the probability of that streak occurring.
What This Calculator Does
This calculator estimates how likely it is to see a run of consecutive identical coin flip results (all heads or all tails) somewhere within a longer sequence of flips.
How the Math Works
For a fair coin, the probability that any specific run of k flips are all the same is (1/2)^k, since each flip is independent. The calculator uses an approximation treating each possible starting position in the sequence as roughly independent to estimate the overall probability of seeing the streak at least once:
- P(streak at one spot) = (0.5)^k
- P(at least one streak) ≈ 1 − (1 − (0.5)^k)^(n − k + 1)
- Expected flips to first see the streak ≈ 2^(k+1) − 2
This is a close approximation rather than an exact formula (the exact calculation requires a recursive/Markov-chain method), but it is accurate enough for general intuition-building, such as understanding why a 5-flip winning streak is far more common over 100 flips than most people expect. For general educational use only.