Editing Las Vegas algorithm (section)

=== Application scenarios ===
Las Vegas algorithms have different criteria for the evaluation based on the problem setting. These criteria are divided into three categories with different time limits since Las Vegas algorithms do not have set time complexity. Here are some possible application scenarios:

* Type 1: There are no time limits, which means the algorithm runs until it finds the solution.
* Type 2: There is a time limit t<sub>max</sub> for finding the outcome.
* Type 3: The utility of a solution is determined by the time required to find the solution.

(Type 1 and Type 2 are special cases of Type 3.)

For Type 1 where there is no time limit, the average run-time can represent the run-time behavior. This is not the same case for Type 2.

Here, ''P''(''RT'' ≤ ''t<sub>max</sub>''), which is the probability of finding a solution within time, describes its run-time behavior.

In case of Type 3, its run-time behavior can only be represented by the run-time distribution function ''rtd'': ''R'' → [0,1] defined as ''rtd''(''t'') = ''P''(''RT'' ≤ ''t'') or its approximation.

The run-time distribution (RTD) is the distinctive way to describe the run-time behavior of a Las Vegas algorithm.

With this data, we can easily get other criteria such as the mean run-time, standard deviation, median, percentiles, or success probabilities ''P''(''RT'' ≤ ''t'') for arbitrary time-limits ''t''.