Coin-flip streaks and what they do not prove
Five heads in a specified row is 1 in 32 on a fair coin. The run does not schedule the next toss or prove a system.
A run of heads is a normal product of a fair coin. It looks like a message because people are good at seeing messages. The run has a probability. It does not have a plan for the next toss, and it does not prove the coin is charmed or broken.
This is for adults 18 and older. The fractions are about fair coins. They are not a system, and they are not a suggestion to stake money on streaks. Laws differ by place.
A specified run is a small fraction
Five heads in a row, on five specific tosses, has probability 1/32. That is 1/2 multiplied five times. Ten heads in a specified row of ten has probability 1/1024. These numbers are exact for a fair coin. They describe that row, not "a streak somewhere in a long afternoon."
Somewhere is a bigger event. In 100 tosses there are many overlapping windows of five. You should expect some runs. Their appearance is not a discovery. Independent events keep the next toss at 1/2 after a run of either face. The coin is not keeping score.
What people think the run proves
One story says the coin is hot, so heads is now more likely. Another says the coin is due for tails, so heads is less likely. Both stories invent a memory. The gambler's fallacy is the second story, and the hot-hand version is its mirror. A fair coin supports neither.
A third story says a long run proves the coin is unfair. A long specified run is evidence worth a look if you can examine the coin, because 1/1024 is small. It is weak evidence if you waited until you saw a run and ignored the many coins and many nights that produced nothing odd. Selection makes ordinary rarity look like a scandal. Standard deviation is the wider language for "this total was allowed."
Games that are not coins
Roulette spins are close to the coin story if the wheel is fair, with one correction: the zeros mean red and black are not 1/2. A streak of red does not fill a debt. Card shoes are slightly different, because dealt cards stay out. A streak of banker wins in baccarat is still a poor reason to believe the next hand is scheduled. The dependence in a shoe is small beside the story people tell.
Sports streaks are a worse analogy. Teams are not fair coins. Win streaks mix skill, schedule and luck. Do not export a coin fraction onto a league and call it analysis.
Use the fraction, then stop
Calculate the specified run if you want to see how small it is. Then notice how many chances you had to see one. If you are about to raise a stake because a display shows five reds, you are using the fraction backward. The display is a history. The price of the next spin is the payout and the wheel, which a house edge describes better than a streak does.
A run is also a common moment to abandon a limit, because it feels informative. It is not. If streaks are how evenings get expensive, stop and use a local support service. The next toss was never going to explain the last five.
Frequently asked questions
Does five heads make tails more likely? No. On a fair coin the next toss is still 1/2, regardless of the previous row. The 1/32 figure applied to those five tosses before they happened.
How often should I see a streak? A specified row of five is 1 in 32. In a long sequence, overlapping rows make some streak unsurprising. "Somewhere" is not the same event as "these next five."
Can a streak prove a game is rigged? A single selected streak is weak proof. A mechanism you can test is stronger. Do not confuse a rare-looking history, chosen after you noticed it, with an investigation.