Case 1
- How many flips in a row?
- 5
0.031250
Open with these valuesCoin Flip Streak Calculator
0.031250chance
Result: 0.031250 chanceEvery flip you add halves the chance: P(n) = (1/2)ⁿ. Five heads in a row is 1 in 32, ten is 1 in 1024. This is the chance for one named side before you start flipping — a coin four heads deep still lands 50/50 on the next throw.
Worked examples
Case 2
- How many flips in a row?
- 10
0.000977
Open with these valuesCase 3
- How many flips in a row?
- 1
0.500000
Open with these valuesHow it's calculated
P(n) = (1/2)ⁿ
- StepEnter how many flips in a row should show the same named side.
- StepThe chance is halved once for every flip in the streak.
- ResultRead the probability; the table gives the same thing as 1-in-X odds.
What this number means
One named side, before the first flip
The figure is the chance that the next n flips all show a side you name in advance. Ask instead for any matching streak, heads or tails, and the chance doubles.
A fair coin has no memory
After four heads the next flip is still 50/50. The formula describes a streak before it starts, not the odds of the next single throw once one is under way.
A long streak in many flips is expected
This number is the chance of a streak starting right now. Finding a streak of at least n somewhere inside a much longer sequence is considerably more likely, because a longer run offers far more starting points.
Every extra flip halves the chance
Five in a row is 1 in 32, eight is 1 in 256 and ten is 1 in 1024. Twenty is 1 in 1048576, and that is where the input range stops.
Commonly misread
After five heads, tails is due.
That is the gambler's fallacy. Each flip of a fair coin is independent, so the next one is 50/50 whatever came before.
Ten heads in a row proves the coin is rigged.
Ten in a row is 1 in 1024 from any given starting point, and a long session of flipping offers a great many starting points. What astonishes on its own is expected somewhere in enough flips.
Five heads is as likely as five of the same side.
All heads is 1 in 32, while any matching streak is twice as likely, 1 in 16. This calculator gives the named-side figure.
Reference table
| Flips | Odds | Probability |
|---|---|---|
| 1 | 1 in 2 | 0.500000 |
| 5 | 1 in 32 | 0.031250 |
| 8 | 1 in 256 | 0.003906 |
| 10 | 1 in 1024 | 0.000977 |
| 20 | 1 in 1048576 | 0.000001 |
Questions
How do I calculate the probability of a coin flip streak?
Raise one half to the number of flips: P(n) = (1/2)ⁿ. Each flip of a fair coin is an independent 50/50 event, so you multiply the chances together. For five flips in a row that is (1/2)⁵ = 1/32 = 0.03125, or odds of 1 in 32.
What are the odds of getting 5 heads in a row?
The odds are 1 in 32, a probability of 0.03125 or about 3.1 percent. Because each flip is independent and has a 1-in-2 chance, five flips give 2⁵ = 32 equally likely sequences, and only one of them is five heads.
Does it matter whether the streak is heads or tails?
Not for a named side: all heads and all tails each come out at (1/2)ⁿ, and that is the number this calculator gives. If you instead ask for any matching streak, heads or tails, the chance is twice as large, because two of the 2ⁿ sequences qualify.
Why does each extra flip halve the chance?
Every flip you add multiplies the running probability by another 1/2, so the chance halves at each step: 1 in 2, then 1 in 4, 1 in 8, 1 in 16, and so on. Ten flips in a row is already 1 in 1024, and twenty is over 1 in a million.
After four heads, is tails more likely on the next flip?
No, and that belief has a name: the gambler's fallacy. A fair coin has no memory, so the next flip is still 50/50 whatever came before. The formula gives the chance of a streak before you start flipping, not the odds of the next single flip once a streak is under way.
Sources and last check
Information, not professional advice.