Simulators
Random Streaks: How Long Runs Really Get
Random sequences contain longer streaks than most people expect. The simulator below flips a virtual coin, finds the longest run of heads and compares your results with the exact distribution.
Loading the simulator
Longest run in 200 flips
Expected longest run
7.0 heads in a rowFor example, in 200 fair flips the average longest run of heads is 7.0. This is the exact value, not a simulation result.
Median longest run
7The middle value: at least half of all sequences of 200 flips have a longest run of heads of 7 or more.
More flips, longer runs
The more flips in a sequence, the longer its longest run tends to be. Each extra flip is one more place where a long run can start.
Heads or tails
These numbers count runs of heads only. The longest run of either side, heads or tails, is at least as long and often longer.
What the simulator shows
- SequenceEvery flip in order, heads and tails, so you can see the runs with your own eyes.
- Longest runThe longest unbroken block of heads in that sequence.
- Distribution vs exactHow often each longest run appeared in your repeats, next to the exact probability for the same number of flips.
Human-made vs random
Made up by hand
- Switches between heads and tails often
- Avoids runs that look too long
- Looks even and tidy
Real random flips
- Switches only as often as chance makes it
- Usually contains at least one long run
- Looks clumpy, with blocks of the same side
What a long streak tells you
| Claim | Answer |
|---|---|
| The coin must be unfair | Not by itself – long runs are normal |
| Tails is now due | No – each flip is independent |
| The streak will continue | No – the next flip has the same chance |
| Long runs are rare | Not in long sequences |
Checking whether a coin is fair needs many flips and a statistical test, not one run that looks surprising.
Words on this page
- Run (streak)
- Several flips in a row that land on the same side.
- Longest run
- The longest unbroken block of heads in one sequence of flips.
- Expected value
- The average result over a very large number of sequences.
- Median
- The middle value: at least half of the results are at or above it, and at least half at or below it.
- Independent
- One flip does not affect any other flip.
Questions
How long are streaks in random coin flips?
It depends on the number of flips. For example, in 200 fair flips the expected longest run of heads is 7.0 and the median is 7. More flips mean longer runs.
Do streaks mean a game is not random?
No. Long runs are a normal part of random sequences. A long sequence with no long runs at all would be more unusual than one with a long streak.
Is a long streak a sign of cheating?
One streak is not evidence. Checking whether a coin or a draw is fair needs many results and a statistical test, not a single run that looks surprising.
Is tails more likely after a long run of heads?
No. Each flip is independent, so heads and tails keep the same chance after any run. Believing that the other side is due is called the gambler's fallacy.