In regression testing, Test case prioritization (TCP) is a technique to arrange all the available test cases. TCP techniques can improve fault detection performance which is measured by the average percentage of fault detection (APFD). History-based TCP is one of the TCP techniques that consider the history of past data to prioritize test cases. The issue of equal priority allocation to test cases is a common problem for most TCP techniques. However, this problem has not been explored in history-based TCP techniques. To solve this problem in regression testing, most of the researchers resort to random sorting of test cases. This study aims to investigate equal priority in history-based TCP techniques. The first objective is to implement different history-based TCP techniques. The second objective is to explore the problem of equal priority in history-based TCP techniques. The third objective is to explore random sorting as a solution to the problem of equal priority in history-based TCP techniques. Datasets of historical records of test cases from conventional and modern sources were collected. History-based TCP techniques were applied to different datasets. The History-based TCP techniques were checked for the problem of equal priority. Then random sorting was used as a solution to the problem of equal priority. Finally, the results were elaborated in terms of APFD and execution time. The results indicate that history-based techniques also suffer from the problem of equal priority like other types of TCP techniques. Secondly, random sorting does not produce optimal results while trying to solve the problem of equal priority in history-based TCP. Furthermore, random sorting deteriorates the results of history-based TCP techniques when employed to solve the problem of equal priority. One should resort to random sorting if no other solution exists. The decision to choose the best solution requires a cost-benefit analysis keeping in view the context and solution under consideration.