This is an interesting finding. There are two takeaways from the paper.
1. The length of streaks L for an independent Bernoulli process with success probability p (with q = 1-p) over n trials can easily be calculated.
L = log_{1/p} (n*q)
2. This estimate becomes more accurate as p decreases. Because the distribution of L is an extreme value distribution which gets more concentrated as p decreases.
This means for low values of p, L becomes more predictable and accurate.
I don’t know how this result will change my life, but at least now I know that I can predict streaks if I know p.
1. The length of streaks L for an independent Bernoulli process with success probability p (with q = 1-p) over n trials can easily be calculated.
L = log_{1/p} (n*q)
2. This estimate becomes more accurate as p decreases. Because the distribution of L is an extreme value distribution which gets more concentrated as p decreases.
This means for low values of p, L becomes more predictable and accurate.
I don’t know how this result will change my life, but at least now I know that I can predict streaks if I know p.