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The random walk moves one step 'up', 'right', 'down'
or 'left' with the probability of 0.25. (The walk can be stopped/started by
the 'Stop' and 'Start'-buttons.)

The walk is bounded
and every time it reaches a limit it restarts. Random walks in one, two or three dimensions
play an important role in many processes.

A walk in one dimension can represent a population
or a queue where the size of the population, or the queue, increases or decreases in random steps.
The population or the queue itself can be as real as a fortune or number of Trouble Reports, etc. The random walk
might be bounded – a fortune or a queue cannot be less than 0.

A popular example of a random walk is the famous *Gambler's Ruin* (see the literature.)
Of course, the random steps do not need to be equal-sized or with the same probability and can be more or less complicated.

The three dimensional walk is often used as a model for particles in a fluid and the statistical treatment can be
rather complicated.

(Note: repeated runs of the two dimensional walk
can sometimes show a path that looks far from random.)

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51. The Quincunx – a classical tool

Illustrates the binomial distribution as well as a random walk

*p*

*n*

*N*

*dt*