Random walk simulator
Set steps, repetitions, upward-move probability and an absolute |S| barrier.
First and mean walk paths
Barrier lines show +B and −B. The main result counts reaching either one.
Selected steps
| Step | First walk | Mean walk |
|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||
How to use this page
- Set steps, number of walks and p.
- Choose a barrier and seed.
- Compare empirical mean and deviation with theory.
What this page does not do: The simulation is limited to 500,000 total steps. The empirical barrier rate depends on repetitions and seed.
Further reading
A simple random walk adds +1 with probability p or −1 with probability 1−p at every step. For p = 0.5 the final mean is 0, while spread grows with the square root of the number of steps.
Repeated walks let you compare empirical mean and standard deviation with theory and estimate how often a barrier is reached.
Frequently asked questions
Does a random walk predict prices or draws?
No. It is a simple educational model of accumulated independent steps.
What does reaching the barrier mean?
The path reached +B or −B at least once within the selected horizon.
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.