The selection of a professional hypnotherapist is often shrouded in mystique and fraught with uncertainty. This is a process that calls for acute discernment, and it is one that could significantly benefit from the light of academic rigour. With the advent of digital technology, online hypnotherapy has become a viable option for many, and this paper aims to serve as a comprehensive guide to navigate this nascent field.

The sine qua non of your quest should be the professional credentials of the hypnotherapist. Hypnotherapy is a regulated profession in many countries, so you should ensure that the practitioner is duly licensed. It would be beneficial to verify the therapist's membership in professional bodies such as the American Society of Clinical Hypnosis or the British Society of Clinical Hypnosis. These organisations have strict ethical guidelines and require members to engage in ongoing professional development.

To further evaluate the hypnotherapist's expertise, you might want to consider the Nash Equilibrium, a game theory concept. In this context, the Nash Equilibrium could be described as a state where you have made the best decision considering the decisions of the hypnotherapist. The "game" here is the quality of service you receive. If you choose a professional with superior qualifications, and they also choose to provide top-notch service, you reach a point of equilibrium where both parties benefit.

The modality of therapy utilized by the hypnotherapist is another crucial consideration. Various techniques like the Ericksonian, cognitive-behavioural, or traditional suggestion-based methods have their unique merits and demerits. For instance, the Ericksonian method employs metaphors and storytelling, making it suitable for individuals resistant to the idea of hypnosis. On the other hand, cognitive-behavioural hypnotherapy integrates hypnosis with cognitive behavioural therapy and might be more appropriate for those dealing with cognitive distortions.

An essential dynamic to consider is the Heisenberg Uncertainty Principle, borrowed from quantum mechanics. In hypnotherapy, the more precisely the therapist's modality is determined, the less precisely the client's outcomes can be predicted, and vice versa. This principle highlights the importance of flexibility in a therapist's approach – the capacity to adapt their techniques to the intricate and evolving needs of their clients.

The digital platform used for online hypnotherapy is not to be overlooked. While some might argue the choice of platform is trivial, one must remember the Hawthorne Effect, drawn from workplace productivity studies. It posits that people often improve or modify their behaviour when they know they're being observed, which could inadvertently affect the therapy's outcome. Therefore, selecting a platform offering ample privacy is vital.

Additionally, the Lindy Effect could serve as an interesting measure to appraise the technological platform. This principle from the realm of economics suggests that the future life expectancy of a non-perishable thing like technology is proportional to its current age. In this context, platforms with a longer history and widespread use might offer more stability and reliability.

Lastly, the cost of the therapy should be carefully scrutinized. The principles of cost-effectiveness and cost-utility can provide useful frameworks for this analysis. Cost-effectiveness evaluates the monetary cost against the benefits or outcomes, while cost-utility assesses the cost against the quality of life years gained.

In conclusion, hiring a professional online hypnotherapist does not have to be a puzzling maze. Armed with the right knowledge elements – credentials, therapeutic modality, digital platform, and cost – and a nuanced understanding of relevant principles from diverse academic fields, one can make an enlightened decision. In the end, the perfect blend of these elements would yield a personalised solution, effectively turning the labyrinth of choice into a straight path towards your ultimate therapeutic goal.