Streak Calculator

Popular streak (run) questions and answers.

All questions have p(Heads) and p(Tails) = 1/2 (50%)

1. Question: Probability run of of Heads of at least 5 in 20 trials? Answer: 0.2498703

(32751/131072)

2. Question: Probability run of Heads of at least 5 in 100 trials? Answer: 0.8101096

(64183494979494598846972364275/79228162514264337593543950336)

3. Question: Probability run of Heads of at least 5 in 200 trials? Answer: 0.9659034

4. Question: Probability run of Heads of at least 6 in 200 trials? Answer: 0.8009322

5. Question: Probability run of Heads of 6 in 100 trials? Answer: 0.54609362

(21632997006968743673674929893/39614081257132168796771975168)

6. Question: Probability run of Heads of at least 7 in 100 trials? Answer: 0.3175204

(6289139215543317778531752497/19807040628566084398385987584)

7. Question: Probability run of Heads of 20 in 1,000,000 trials? Answer: 0.3792540

8. Question: Probability run of Heads of 19 in 1,000,000 trials? Answer: 0.6146780

9. Question: Probability any run of 20 in 1,000,000 trials? Answer: 0.6146776

10. Question: Probability any run of at least 3 in 9 trials? Answer: 0.78515625

(201/256)

11. Question: Probability any run of at least 6 in 200 trials? Answer: 0.9653128

12. Question: Probability no run of at least 10 in 5000 trials? Answer: 0.0862866

(1 - 0.9137134)

Info

A Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure". In practice it refers to a single experiment which can have one of two possible outcomes.

This streak calculator assumes only wins and losses in the Probability of Success text box. It does not take into account any ties or pushes.

Disclaimer: This JavaScript calculator is accurate as tested. There are sure to be errors or browser failures for very small probabilities, very large number of trials and streak length since JS does a good job of rounding.

Calculator Instructions

INPUTS:

Streak Length (or more): Enter a streak number.

Trials: Series Length: Enter number of hands, rolls, spins, games etc.

(note: max trial length about 30,000,000 and DO NOT ADD commas (separators).

US style commas are added automatically)

Probability of Success: Enter a decimal value between 0 and 1.

For repeating decimals, like 1/6, enter min 8 repeats 0.166666666 is more accurate than .166 or .167 (no need to round)

RESULTS:

Calculate Button: Click Calculate to show Streak Probability

Yes. Streak Probability: The value returned is for at least 1 run of a streak length that you entered.

No. Streak Probability: The value returned is for NO run of a streak length (or greater) that you entered.

Example: Series Length: 20, Streak Length:5, Probability of Success: 0.50 (the default value) returns: 0.249870300292969 which is for at least 1 run of length 5 or more.

Also the values for the theoretical average number of trials is shown for streak length or more (a). These values are NOT for the number of trials that you entered.

Streak length (k) or more: the average number of trials (win/loss or success/failure is a trial) for a streak of the length you entered or greater

for example: 5 or more)

To add commas to larger values in RESULTS Averages: Just click the value in the text box.

This streak calculator assumes only wins and losses in the Probability of Success text box. It does not take into account any ties or pushes.

Streak length should be greater than 1 and trials between 2 and 20 million.

My Google Chrome goes to 30 million trials with no problem. (be careful)

example: adding to R Console

runs.r(5, 20, 0.5)

then press enter

Some run/trials probability data results using Fibonacci numbers. p(success) = 1/2.

For a specific run. example: Heads

runTrialsFib(2,2) means 'at least' a run of 2 in 2 trials. Trials are from 2 to 50.

More data for p(success)=1/2 found here: Streak Data Results

run/trials probability data results using Fibonacci numbers. p(success) = 1/2.

table is for runs from 1 to 10 and trials to 30.