Probability of 4 Tails in a Row: Formula, Calculator & Odds

Probability of 4 Tails in a Row: Formula, Calculator & Odds..The probability of 4 tails in a row with a fair coin is 1/16, or 6.25%. Four flips have 16 equally likely outcomes, and only TTTT is all tails, so the odds are 15 to 1 against. This assumes a fair coin and independent flips.

Say you’re flipping coins with a friend and you hit four tails in a row. It feels like something, doesn’t it? It is a bit unusual, about one time in sixteen, but it’s no miracle. One thing to flag early: people search this topic with two different questions in mind. Some want a run of four tails in a row. Others want exactly four tails anywhere in, say, 10 flips. Those have very different answers, and this page covers both. If you’d like to try it as you read, a free online coin flip will do the job.

What Is the Probability of 4 Tails in a Row?

The probability of 4 tails in a row is 1/16, or 6.25%, for a fair coin flipped four times. A fair coin has equal chances of heads and tails. Each flip is independent, so earlier flips never change later ones.

That’s the chance that your next four flips are all tails. It’s not the chance of finding a run of four tails somewhere in a longer series, and it’s not the chance of getting four tails in any order. Both of those come up further down, with their own numbers.

Probability of 4 Tails in a Row as a Percentage and Odds

The probability of 4 tails in a row as a percentage is 6.25%, which is 1/16 as a fraction and 0.0625 as a decimal. The odds are 15 to 1 against, because one outcome works and fifteen don’t. Probability and odds describe the same chance in two different ways.

Fraction	Decimal	Percentage	Odds
1/16	0.0625	6.25%	15 to 1 against

If you’d settle for four of the same face, TTTT or HHHH, the chance doubles to 2/16, which is 12.5%.

Why the Probability of 4 Tails in a Row Is 1/16: Sample Space of 4 Coin Flips

A sample space is the list of every possible outcome. Four flips of a fair coin give 2 × 2 × 2 × 2 = 16 outcomes, all equally likely, and exactly one of them is TTTT. That’s why the chance is 1 out of 16.

Grouped by how many tails each outcome has, the list looks like this:

Tails	Outcomes	How many
4	TTTT	1
3	TTTH, TTHT, THTT, HTTT	4
2	TTHH, THTH, THHT, HTTH, HTHT, HHTT	6
1	THHH, HTHH, HHTH, HHHT	4
0	HHHH	1

Add the last column and you get 16. TTTT is the loner in the top row.

Probability of 4 Tails in a Row Formula

For independent flips, the formula is P = (1/2)ⁿ, where n is the number of tails in a row. For four tails, (1/2)⁴ = 1/16. It’s the multiplication rule: multiply the chance of each flip to get the chance that all of them go your way.

Written out, that’s 1/2 × 1/2 × 1/2 × 1/2 = 1/16. Every extra tail halves the chance, so five tails is 1/32 and ten is about 0.1%. If you’d like a refresher on the rule, Khan Academy’s probability basics are free and easy to follow.

Probability of 4 Tails in a Row Using the Binomial Formula

The binomial formula gives the chance of exactly k tails in n flips: P(X = k) = C(n, k) × (1/2)ᵏ × (1/2)ⁿ⁻ᵏ. For 4 tails in 4 flips, it gives 1/16, matching the multiplication rule. It counts tails and nothing else.

The working is short: C(4, 4) = 1, so P(X = 4) = 1 × 1/16 × 1 = 1/16. The Wikipedia page on the binomial distribution covers the general case.

Here’s the limit to keep in mind. The binomial formula counts how many tails, not where they sit. So it can’t directly give you a run of four tails inside a longer sequence. In 5 flips, “exactly 4 tails” includes THTTT, which has no run of four. We’ll handle runs by counting sequences instead.

Probability of 4 Tails in a Row: Solved Example, Step by Step

Here are two quick examples, a fair coin and a biased one. Both follow the same steps: write the chance of one tail, multiply it by itself four times, and convert to a percentage. Only the starting number changes.

Fair coin. What is the probability of 4 tails in a row?

1. The chance of tails is 1/2, or 0.5.
2. Multiply four times: 0.5 × 0.5 × 0.5 × 0.5 = 0.0625, which is 1/16.
3. Convert to a percentage: 0.0625 × 100 = 6.25%.

Biased coin. If tails comes up 60% of the time, then 0.6⁴ = 0.1296, about 13%, roughly double the fair-coin answer.

So 6.25% belongs to a fair coin and no one else.

Consecutive Tails Probability Calculator: How to Work It Out Yourself

A consecutive tails probability calculator, which finds the probability of 4 tails in a row, just raises the chance of tails to the power of the streak. For four tails, type 0.5, raise it to the power of 4, and multiply by 100 to get 6.25%. Any online tool does the same arithmetic, however it’s labeled.

You’ll see this idea sold as a probability of getting 4 tails in a row calculator, or a probability of 4 tails in a row calculator online. It’s one multiplication either way. A coin flip probability calculator saves you a few button presses, but it’s worth doing it by hand once so the answer stops feeling like magic. Longer streaks work the same way: the probability of 3 tails in a row is 12.5%, and 5 tails in a row is 3.125%.

Probability of 4 Tails in a Row in 6, 8, 10 and 20 Flips

The chance of a run of at least four tails somewhere in a longer sequence grows with every flip: 12.5% in 6 flips, 18.75% in 8, about 24.5% in 10, and about 47.8% in 20. A longer sequence gives a streak more places to start.

Number of flips	Chance of a run of 4+ tails	Exact fraction
4	6.25%	1/16
6	12.5%	8/64
8	18.75%	48/256
10	about 24.5%	251/1,024
20	about 47.8%	501,239/1,048,576

How do we get those? We count the sequences with no TTTT and subtract. Those counts run 2, 4, 8, 15, 29, 56, 108, 208, 401, 773 for 1 through 10 flips, so for 10 flips it’s 1,024 − 773 = 251. On average, you’ll wait about 30 flips for your first TTTT, though any single wait can be far shorter or longer.

Probability of Exactly 4 Tails in 6, 8, 10 and 20 Coin Flips

Exactly 4 tails anywhere, in any order, is a different question with different numbers: about 23.44% in 6 flips, 27.34% in 8, 20.51% in 10, and only about 0.46% in 20. The tails don’t have to touch each other.

Number of flips	Chance of exactly 4 tails (any order)	Exact fraction
6	about 23.44%	15/64
8	about 27.34%	70/256
10	about 20.51%	210/1,024
20	about 0.46%	4,845/1,048,576

In plain words, C(n, 4) counts the ways to choose which 4 of the n flips are tails, and you divide by the 2ⁿ total sequences. Now compare this table with the one above. In 20 flips, the probability of 4 tails in a row (a run of four or more) is about 47.8%, but exactly four tails total is only about 0.46%. Why the huge gap? Because in 20 flips you’d expect about 10 tails, so having only four is the unusual outcome. A run, meanwhile, can sit inside a sequence with plenty of other tails.

How the Probability of 4 Tails in a Row Compares With 2, 3, 5 and 10 Tails

Every extra tail halves the chance: 25% for two, 12.5% for three, 6.25% for four, 3.125% for five, and about 0.0977% for ten. Four sits in the middle of the pack, unlikely on one try but nothing to brag about.

Tails in a row	Probability
2	25%
3	12.5%
4	6.25%
5	3.125%
10	0.0977%

Heads follow the same numbers on a fair coin, so the probability of 4 heads in a row is also 6.25%, and the 10 tails in a row probability is about 0.0977%.

Does Getting 3 Tails Make the Fourth More Likely?

No. After three tails, the chance of tails on the next flip is still 1/2. Flips are independent events, so earlier results never change later ones. The coin has no memory of what it just did.

After TTT, the two possible results are TTTT and TTTH, and each has a 1/16 chance as a full sequence. They’re exactly equally likely. The hunch that heads is “due” is the gambler’s fallacy, and the opposite hunch, that tails will keep rolling, is just as wrong. For the general idea, see independent events or our guide on does heads make tails more likely.

Common Mistakes With the Probability of 4 Tails in a Row

Most errors come from answering a slightly different question than the one asked. A quick checklist:

• A run versus a count. Exactly 4 tails anywhere in 5 flips is 5/32, or 15.625%, but a run of 4 tails in 5 flips is 3/32, or 9.375%.
• Next four flips versus somewhere in n flips. The probability of 4 tails in a row on the next four flips is 6.25%. Somewhere in 20 flips is about 47.8%.
• Exactly 4 versus at least 4. The tables above show a run of 4 or more, and exactly 4 tails total, which are not the same thing.
• Forgetting biased coins. The 6.25% answer changes if tails isn’t 1/2.
• Thinking heads is due. It isn’t.

Try It Yourself: Test the Probability of 4 Tails in a Row

Here’s a simple experiment. Flip a coin four times, write down whether you got TTTT, and repeat 160 times. With 160 sets, you’d expect about 10 all-tails rounds (160 ÷ 16 = 10). Your number will wander around the probability of 4 tails in a row, and that wandering is the lesson.

My result: [INSERT MY REAL RESULT FROM FLIPPING 160 SETS OF 4]

A coin flip simulator runs the sets quickly, and you can also try a heads or tails generator or a plain random coin toss and tally by hand. One honest caveat: the Diaconis, Holmes and Montgomery paper Dynamical Bias in the Coin Toss predicted that real coins land on their starting side about 51% of the time, and a large 2023 experiment found a similar effect. It’s a tiny effect, but it means a real coin isn’t perfectly 50/50. Wolfram MathWorld has more on coin tossing if you want to dig in.

Conclusion: The Probability of 4 Tails in a Row

The probability of 4 tails in a row is 1/16, or 6.25%, and it comes from one idea: multiply 1/2 by itself four times. That’s uncommon on a single try, but a run of four tails turns up somewhere in 20 flips nearly half the time, while exactly four tails in 20 flips is a rare outcome indeed. Keep the two meanings of the probability of 4 tails in a row separate and most of the confusion disappears. And whatever you see, three tails never make a fourth likelier, because the coin simply doesn’t remember. To watch a few runs yourself, try a flip a coin online session, and for more streak math, see our guide to coin flip streaks explained.

How I checked these numbers: I listed all 16 outcomes of four flips by hand and counted the winner, then confirmed it with the formula (1/2)⁴. For runs in longer sequences, I counted the sequences with no TTTT and subtracted them from the total, and cross-checked the 5-flip case by listing TTTTT, TTTTH and HTTTT. For “exactly 4 tails,” I used C(n, 4) divided by 2ⁿ.