Flip a Coin Simulator: One Flip or a Thousand, With a Tally: how it works
This flip a coin simulator flips one coin or up to 1,000 at once. Every flip is a fair 50-50 pick made in your browser. A running tally counts heads and tails, a streak counter tracks the longest run of one side, and a bar shows the split settling toward 50% as the flips pile up. Presets cover 5, 10 and 100 flips.
One flip or a thousand
The page opens on a batch of ten. Press Flip for ten more, or set how many to anything from 1 to 1,000. Behind the coin faces each flip is a draw of 0 or 1, where 1 is heads and 0 is tails, so the sum of a batch is its number of heads. No flip looks at the one before it. The tally keeps adding across batches until you reset it, recent batches stay in the history, and the share link carries your settings.
Flip a coin 5 times: the worked answer
Five flips can fall in 2 × 2 × 2 × 2 × 2 = 32 ways, all equally likely. Sort them by heads and the counts run 1, 5, 10, 10, 5, 1. So 2 heads and 3 heads each have a 31.25% chance, 1 and 4 each have 15.625%, and none or all five each have 3.125%. At least one head is 31 in 32, or 96.875%. HHHHH is exactly as likely as HTHHT, at 1 in 32. All 32 are listed under the tool.
What the settling bar shows
The share of heads closes in on 50% as you flip more, yet the count rarely sits on half. In 100 flips, exactly 50 heads turns up about 8% of the time, while 96.5% of batches finish between 40 and 60. In 1,000 flips, about 95% land between 470 and 530: a share within three points of 50%, with a gap that can still be 30 coins. The typical gap is half the square root of the number of flips.
Tips
- Classroom classic: half the class invents 100 flips on paper, the other half runs the simulator. Invented lists avoid long runs. Real ones hold a run of six or more about 81% of the time.
- Settling something between two people? Say aloud who is heads before you press, and agree that one flip decides. Best of three only counts if you agreed to it first.
- Ten flips split 5 and 5 less often than people guess: 252 of the 1,024 outcomes, or 24.6%.
- After five heads in a row the next flip is still 50-50. The coin has no memory, and the tally will show you that tails is never owed.
- For a probability lesson, have each student run the 5 preset twenty times, record the heads count, and pool the class results against the 1, 5, 10, 10, 5, 1 pattern.
Questions and answers
Is this coin flip simulator fair?
Yes. Each flip gives heads and tails the same chance and ignores every flip before it, so a run of seven is luck and not a fault. The flips are made in your browser and sent nowhere. That is fine for games, chores and lessons. Do not use it for anything with money at stake.
What are the odds when you flip a coin 5 times?
There are 32 equally likely sequences. The chance of exactly 0, 1, 2, 3, 4 or 5 heads is 1, 5, 10, 10, 5 and 1 out of 32, which is 3.125%, 15.625%, 31.25%, 31.25%, 15.625% and 3.125%. Getting all five the same, heads or tails, is 2 in 32, or 6.25%.
Why do I not get exactly 50% heads?
Because 50% is where the share heads in the long run, not a promise for any batch. The spread of the heads count grows with the square root of the flips: about 5 either way in 100 flips and about 16 in 1,000. The percentage tightens while the raw gap widens, and both are what a fair coin does.
How long a streak should I expect?
Longer than feels natural. In 10 flips there is a 46% chance of a run of four or more of one side. In 100 flips a run of five or more is close to certain at 97%, and a run of seven or more happens in a little over half of all batches, about 54%.
Is a real coin exactly 50-50?
Very nearly. The mathematician Persi Diaconis predicted that a caught coin lands the same way up as it started about 51% of the time, and a 2023 University of Amsterdam study of 350,757 tosses measured 50.8%. A simulated flip has no starting side, so that small bias does not exist here.