๐ช Streak Probability Calculator
Assumes each trial is independent โ earlier results don't affect later ones.
Enter the probability of a single outcome (as a percentage โ 50 for a fair coin flip, about 16.7 for a specific die face) and the number of times in a row you want it to occur, to calculate the probability of that streak happening.
How to use
- Enter the probability of a single outcome, as a percentage (50 for a fair coin).
- Enter how many times in a row you want it to occur.
- The probability of that streak, and roughly "1 in how many" it represents, are calculated automatically.
How the calculation works
Trials whose outcomes do not influence each other are called independent. Coin flips and dice rolls are independent: whether the last flip came up heads does not change the odds for the next one. For independent trials, the probability that several outcomes all occur is the product of their individual probabilities. With a per-trial probability p and a streak length N, the chance of N identical results in a row is p ร p ร โฆ ร p, or p^N. For a fair coin p = 0.5, so five heads in a row is 0.5^5 = 0.03125, about 3.1%. A common misreading is that after four heads, tails is somehow "due". This is the gambler's fallacy: a coin has no memory, so the next flip is still 50/50 no matter what preceded it. The small value of p^N describes the odds of a streak seen in advance โ it says nothing about the next single flip once part of the streak has already happened.
Worked example
A fair coin (50% per flip), five in a row 1. Convert the per-trial probability: 50% โ 0.5 2. Multiply once per trial: 0.5 ร 0.5 ร 0.5 ร 0.5 ร 0.5 3. Result: 0.5^5 = 0.03125 That is 3.125%, or roughly 1 in 32. For a specific die face three times running, the per-trial probability is 1 รท 6 โ 16.67%, so (1/6)ยณ = 1/216 โ 0.46% โ about 1 in 216.
Things to be aware of
- This assumes each trial is independent. It does not apply where earlier results change later odds, such as drawing without replacement.
- It gives the probability of the same outcome repeating. The odds of a particular ordered sequence, such as alternating heads and tails, are calculated differently.
- Once part of a streak has already occurred, the probability of the next single trial is simply the per-trial probability again.
- Enter a per-trial probability above 0% and below 100%; at either extreme the idea of a streak stops being meaningful.
FAQ
What calculation does this do?
Assuming each trial is independent (earlier results don't affect later ones), the probability of N results in a row at per-trial probability p is simply p raised to the Nth power (p^N).
Can I use this for rolling the same die face three times in a row?
Yes โ enter about 16.67 (= 1/6 ร 100) as the per-trial probability and 3 as the streak length to get the probability of that specific face coming up three times in a row.
Is this for "heads then tails" patterns, or just "the same result every time"?
This tool calculates the probability of the same outcome occurring every time in a row (e.g. heads every time). It doesn't handle probabilities for a specific alternating or mixed sequence.