Background: In cases(mainly in End to End UI tests), where a number of test paths(selection of alternative test steps) can be huge due to combinations however expected results are same and few. In those scenarios, I strongly feel the need to introduce an element of randomness to pick a test path as we are finding more and more issues manually while following a particular random path whereas the standard automated E2E test mostly passes following the primary flow.
Context: In the end-to-end scenario consisting steps let's say [A-Z] where any of the steps may have alternative sub steps[a- g] can be run either on web/mobile app so if we vary any of the sub-steps in user journey, we are finding issues on some specific sub-steps selection but not in general.Also we cannot afford to run each unique combination of selection due to huge combinations either manually or by automation.
Problem statement: What is the standard/accepted common wisdom to design the randomness in alternative sub steps selection in end to end UI tests?
Edit: Adding more meaningful example
Example: An long user journey, consisting of multiple steps where each step independently can be done on either web or mobile app. And cases were found where doing some step in mobile doesn't reflect back in web app or vice versa.